Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.13450
Giulia Bertaglia
Mathematical models and numerical methods are a powerful resource for better understanding phenomena and processes throughout the fluid dynamics field, allowing significant reductions in the costs, which would otherwise be required to perform laboratory experiments, and even allowing to obtain useful data that could not be gathered through measurements.The correct characterization of the interactions that occur between the fluid and the wall that surrounds it is a fundamental aspect in all contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational method and the interpretation of the results and their application to cases of practical interest.In this work, innovative mathematical models able to predict the behavior of the fluid-structure interaction (FSI) mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented FSI systems in which the constitutive equation of the material is directly embedded into the system as partial differential equation [1]. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems [2]. To avoid the loss of accuracy in the stiff regimes of the proposed systems, asymptotic-preserving IMEX Runge-Kutta schemes are considered for the time discretization, which are able to maintain the consistency and the accuracy in the diffusive limit, without restrictions due to the scaling parameters [3]. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to in-vivo measurements for the latter.REFERENCES[1] Bertaglia, G., Caleffi, V. and Valiani, A. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system. Comput. Methods Appl. Mech. Eng., 360(C):112772 (2020).[2] Bertaglia, G., Ioriatti, M., Valiani, A., Dumbser, M. and Caleffi, V. Numerical methods for hydraulic transients in visco-elastic pipes. J. Fluids Struct., 81:230-254 (2018).[3] Pareschi, L. and Russo, G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput., 25:129-155 (2005).
{"title":"Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels","authors":"Giulia Bertaglia","doi":"10.4995/yic2021.2021.13450","DOIUrl":"https://doi.org/10.4995/yic2021.2021.13450","url":null,"abstract":"Mathematical models and numerical methods are a powerful resource for better understanding phenomena and processes throughout the fluid dynamics field, allowing significant reductions in the costs, which would otherwise be required to perform laboratory experiments, and even allowing to obtain useful data that could not be gathered through measurements.The correct characterization of the interactions that occur between the fluid and the wall that surrounds it is a fundamental aspect in all contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational method and the interpretation of the results and their application to cases of practical interest.In this work, innovative mathematical models able to predict the behavior of the fluid-structure interaction (FSI) mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented FSI systems in which the constitutive equation of the material is directly embedded into the system as partial differential equation [1]. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems [2]. To avoid the loss of accuracy in the stiff regimes of the proposed systems, asymptotic-preserving IMEX Runge-Kutta schemes are considered for the time discretization, which are able to maintain the consistency and the accuracy in the diffusive limit, without restrictions due to the scaling parameters [3]. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to in-vivo measurements for the latter.REFERENCES[1] Bertaglia, G., Caleffi, V. and Valiani, A. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system. Comput. Methods Appl. Mech. Eng., 360(C):112772 (2020).[2] Bertaglia, G., Ioriatti, M., Valiani, A., Dumbser, M. and Caleffi, V. Numerical methods for hydraulic transients in visco-elastic pipes. J. Fluids Struct., 81:230-254 (2018).[3] Pareschi, L. and Russo, G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput., 25:129-155 (2005).","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134343888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12583
Víctor Tomás Andrés Ruiz, José Martínez Casas, Javier Carballeira Morado, Francisco David Denia Guzmán, D. Thompson
The main goal of the present work lies in the identification of the railway track properties that influence acoustic radiation, as well as in the analysis of these properties for the reduction of sound levels. This is achieved through a dynamic model of the railway wheel and track that allows the study of rolling noise, produced as a result of wheel/rail interaction. The vibroacoustic calculation methodology consists of characterising the railway wheel and track, using finite element techniques and periodic structure theory [1,2], respectively. Subsequently, the response of the railway components, which is caused by the roughness present in the surface of the wheel and rail, is determined. Finally, after having the vibrational response of the railway elements, the sound power radiated by them is calculated using the acoustic model developed by D. J. Thompson et al. and implemented in TWINS software [3]. The influence of the track properties on the sound radiation is analysed through statistical techniques applied to the acoustic power results of different track configurations. To do this, the geometry of the rail profile is parameterised and simulations are carried out by modifying these parameters and the viscoelastic properties of the track components. From the results obtained, a number of guidelines are presented for the noise mitigation of the involved railway subcomponents. Between the worst and the best track design, there are differences of approximately 7.5 dB(A) in the radiation (considering the wheel, rail and sleeper noise), which means that an optimised track design can be found with an acoustic radiation 5.5 times lower than another design.
目前工作的主要目标在于确定影响声辐射的铁路轨道特性，以及分析这些特性以降低声级。这是通过铁路车轮和轨道的动态模型来实现的，该模型允许研究由于车轮/轨道相互作用而产生的滚动噪声。振动声学计算方法包括表征铁路车轮和轨道，分别使用有限元技术和周期结构理论[1,2]。随后，铁路部件的响应，这是由存在于车轮和轨道表面的粗糙度引起的，被确定。最后，在得到铁路构件的振动响应后，利用D. J. Thompson等人开发的声学模型计算其辐射的声功率，并在TWINS软件中实现[3]。通过统计方法对不同轨道配置的声功率结果进行分析，分析了轨道特性对声辐射的影响。为此，将轨道轮廓的几何形状参数化，并通过修改这些参数和轨道部件的粘弹性特性进行仿真。根据所获得的结果，提出了一些有关铁路子部件的噪声缓解准则。在最差和最佳轨道设计之间，辐射差异约为7.5 dB(A)(考虑到车轮，轨道和轨枕噪声)，这意味着优化轨道设计的声辐射可以比另一种设计低5.5倍。
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Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12418
Bastian Oesterle, Jan Trippmacher, A. Tkachuk, M. Bischoff
Hierarchic shear deformable Reissner-Mindlin shell formulations possess the advantage of being intrinsically free from transverse shear locking [1], [2]. Transverse shear locking is avoided a priori through reparametrization of the kinematic variables. This reparametrization yields beam, plate and shell formulations with distinct transverse shear degrees of freedom.The efficiency of explicit dynamic analyses of thin-walled structures is limited by the critical time step size, which depends on the highest frequency of the discretized system. If Reissner-Mindlin type shell elements are used for discretization of a thin structure, the highest transverse shear frequencies limit the critical time step in explicit dynamic analyses, while being relatively unimportant for the structural response of the system. The basic idea of selective mass scaling is to scale down the highest frequencies in order to increase the critical time step size, while keeping the low frequency modes unaffected, see for instance [3]. In most concepts, this comes at the cost of non-diagonal mass matrices.In this contribution, we present recent investigations on selective mass scaling with hierarchic formulations. Since hierarchic formulations possess distinct transverse shear degrees of freedom, they offer the intrinsic ability for selective mass scaling of the shear frequency modes, while keeping the bending dominated modes mostly unaffected and retaining the diagonal structure of a lumped mass matrix. We discuss the effects of transverse shear parametrization, locking and mass lumping on the accuracy of results and a feasible time step.REFERENCES[1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Computer Methods in Applied Mechanics and Engineering, Vol. 254. pp. 170-180, 2013.[2] B. Oesterle, E. Ramm and M. Bischoff, A shear deformable, rotation-free isogeometric shell formulation. Computer Methods in Applied Mechanics and Engineering, Vol. 307, pp. 235-255, 2016.[3] G. Cocchetti, M. Pagani and U. Perego, Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Computers and Structures, Vol. 27, pp. 39-52, 2013.
分层剪切可变形Reissner-Mindlin壳公式具有本质上不受横向剪切锁定的优点[1]，[2]。通过对运动变量的重新参数化，可以避免横向剪切锁定。这种重新参数化产生梁，板和壳具有明显的横向剪切自由度的公式。薄壁结构显式动力分析的效率受到临界时间步长的限制，而临界时间步长取决于离散系统的最高频率。如果采用Reissner-Mindlin型壳单元对薄结构进行离散化，则最高横向剪切频率限制了显式动力分析的临界时间步长，而对系统的结构响应相对不重要。选择性质量缩放的基本思想是降低最高频率以增加临界时间步长，同时保持低频模式不受影响，参见[3]。在大多数概念中，这是以非对角质量矩阵为代价的。在这一贡献，我们提出了最近的研究选择性质量缩放与层次公式。由于分层公式具有不同的横向剪切自由度，因此它们提供了剪切频率模态的选择性质量标度的内在能力，同时保持弯曲主导模态基本不受影响，并保留集中质量矩阵的对角结构。讨论了横向剪切参数化、锁定和质量集总对结果精度和可行时间步长的影响。[1]李建平，李建平，等几何壳有限元。应用力学与工程中的计算机方法，卷254。科学进展，2013.[2]B. Oesterle, E. Ramm和M. Bischoff，剪切变形，无旋转等几何壳公式。应用力学与工程学报，2016.[3]G. Cocchetti, M. Pagani和U. Perego，固体壳单元显式动力学分析的选择性质量标度和临界时间步长估计。计算机与结构，Vol. 27, pp. 39-52, 2013。
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Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12236
P. Blondeel, Pieterjan Robbe, S. François, G. Lombaert, S. Vandewalle
Engineering problems are often characterized by significant uncertainty in their material parameters. Multilevel sampling methods are a straightforward manner to account for this uncertainty. The most well known multilevel method is the Multilevel Monte Carlo method (MLMC). First developed by Giles, see [1], this method relies on a hierarchy of successive refined Finite Element meshes of the considered engineering problem, in order to achieve a computational speedup. Most of the samples are taken on coarse and computationally cheap meshes, while a decreasing number of samples are taken on finer and computationally expensive meshes. Classically, the mesh hierarchy is constructed by selecting a coarse mesh discretization of the problem, and recursively applying an h-refinement approach to it, see [2]. This will be referred to as h-MLMC. However, in the h-MLMC mesh hierarchy, the number of degrees of freedom increases almost geometrical with increasing level, leading to a large computational cost. An efficient manner to reduce this computational cost, is by means of the novel sampling method called p-refined Multilevel Quasi-Monte Carlo (p-MLQMC), see [3]. The p-MLQMC method uses a hierarchy of p-refined Finite Element meshes, combined with a deterministic Quasi-Monte Carlo sampling rule. This combination significantly reduced the computational cost with respect to h-MLMC. However, the p-MLQMC method presents the practitioner with a challenge. This challenge consists in adequately incorporating the uncertainty, represented as a random field, in the Finite Element model. In previous work, see [4], we have tackled this challenge by investigating how the evaluation points, used to calculate point evaluations of the random field by means of the Karhunen-Loève (KL) expansion, need to be selected in order to achieve the lowest computational cost. We found that using sets of nested evaluation points across the mesh hierarchy, i.e., the Local Nested Approach (LNA), yields a speedup up to a factor 5 with respect to sets consisting of non-nested evaluation points, i.e., the Non-Nested Approach (NNA). Furthermore, we have shown that p-MLQMC-LNA yields a speedup up to a factor 70 with respected to h-MLMC. Currently, our research focus lies on implementing the use of higher order Quasi-Monte Carlo rules, and hierarchical shape functions in p-MLQMC. Both paths show promising results for further computational savings in the p-MLQMC method. All the aforementioned implementations are benchmarked on a slope stability problem, with spatially varying uncertainty in the ground. The chosen quantity of interest (QoI) consists of the vertical displacement of the top of the slope.[1] Michael B. Giles. Multilevel Monte Carlo path simulation. Oper. Res., 56(3):607–617, 2008. [2] K. A. Cliffe, M. B. Giles, R. Scheichl, and A. L. Teckentrup. Multilevel Monte Carlo methods and applications to elliptic pdes with random coefficients. Comput. Vis. Sci., 14(1):3, Aug 2011. [3] Phili
工程问题通常以材料参数的显著不确定性为特征。多层抽样方法是解释这种不确定性的一种直接方式。最著名的多层方法是多层蒙特卡罗方法(MLMC)。该方法首先由Giles开发，参见[1]，该方法依赖于所考虑的工程问题的连续精细有限元网格的层次结构，以实现计算加速。大多数样本是在粗糙且计算成本低的网格上采集的，而越来越多的样本是在精细且计算成本高的网格上采集的。经典的网格层次结构是通过选择问题的粗网格离散化，并递归地应用h-细化方法来构建的，参见[2]。这将被称为h-MLMC。然而，在h-MLMC网格层次中，自由度的数量随着层次的增加几乎呈几何级数增加，导致计算成本很大。一种有效的方法来减少这种计算成本，是通过新的采样方法称为p-精炼多电平拟蒙特卡罗(p-MLQMC)，见[3]。p-MLQMC方法使用p-精炼有限元网格的层次结构，结合确定性准蒙特卡罗采样规则。这种组合大大降低了h-MLMC的计算成本。然而，p-MLQMC方法给实践者带来了挑战。这一挑战包括在有限元模型中充分纳入以随机场表示的不确定性。在之前的工作中，我们通过研究如何选择评估点来解决这个挑战，这些评估点用于通过karhunen - lo (KL)展开来计算随机场的点评估，以实现最低的计算成本。我们发现，在网格层次结构中使用嵌套评估点的集合，即局部嵌套方法(LNA)，相对于由非嵌套评估点组成的集合，即非嵌套方法(NNA)，产生高达5倍的加速。此外，我们已经证明，p-MLQMC-LNA的加速速度高达h-MLMC的70倍。目前，我们的研究重点是在p-MLQMC中使用高阶拟蒙特卡罗规则和分层形状函数来实现。这两种路径都显示了在p-MLQMC方法中进一步节省计算量的有希望的结果。上述所有实现都是基于斜坡稳定性问题进行基准测试的，该问题在地面上具有空间变化的不确定性。所选的兴趣量(qi)由斜坡顶部的垂直位移组成迈克尔·b·贾尔斯。多层蒙特卡罗路径模拟。③。生物医学工程学报，36(3):673 - 678,2008。[10] K. A.克里夫，M. B.贾尔斯，R.谢奇尔，A. L.特肯特鲁普。多电平蒙特卡罗方法及其在随机系数椭圆偏面中的应用。第一版。粘度科学。生态学报，14(1):3,2011年8月。[3] Philippe Blondeel, Pieterjan Robbe, csamdric Van hoorickx, Stijn franois, Geert Lombaert和Stefan Vandewalle。galerkin有限元法的p-精炼多级拟蒙特卡罗法及其在土木工程中的应用。算法，13(5)，2020。[4] Philippe Blondeel, Pieterjan Robbe, Stijn franois, Geert Lombaert和Stefan Vandewalle。论p-mlqmc方法中随机场评价点的选取。arXiv, 2020年。
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Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12383
M. Adam, H. Andres, K. Rehfeld
AbstractObservational records provide a strong basis for constraining sea ice models within a narrow range of climate conditions. Given current trends away from these conditions, models need to be tested over a wider range of climate states. The past provides many such examples based on paleoclimate data, including abrupt tipping points. However, the millennial-duration of typical paleoclimatesimulations necessitates balancing the inclusion and sophistication of model processes against computational cost. We investigate the impact on climate mean states and variability of introducing sea ice dynamics into the simplified general circulation model PlaSim-LSG [1-3].Considering the technical constraints of PlaSim-LSG, we choose to integrate a modied version of the MITgcm's dynamical sea ice component [4, 5] into the model setup. We adapt the component to the structure and parallelization scheme of PlaSim-LSG, validate the physical consistency and stability of the component, and evaluate the impact of sea ice dynamics onto the simulated climate from decadal to millennial time scales. Specifically, we compare climatologies, variability and scaling of the extended model to control simulations of the preexisting setups, and quantify how additional sea ice dynamics affect well-known climatic biases of the PlaSim model family.With our extended PlaSim-LSG model we aim at capturing the key small-scale sea ice processes that are important to past climate tipping points while maintaining model efficiency for millennial simulations. Sea ice is a key component of coupled atmosphere-ocean processes that led to large-amplitude, abrupt climate variability in the past [6-8]. Therefore, the extended model can be usedto investigate the role of sea ice for such oscillations. This facilitates the understanding of processes that lead to current mismatches between palaeoclimate data and simulations, and that impact thesimulated surface climate variability [9].References[1] K. Fraedrich et al. Meteorol. Z. 14.3 (2005), 299-304. doi: 10.1127/0941-2948/2005/0043.[2] F. Lunkeit et al. Tech. rep. 2011. url: https://www.mi.uni-hamburg.de/en/arbeitsgruppen/theoretische-meteorologie/modelle/sources/psreferencemanual-1.pdf.[3] H. J. Andres et al. Clim. Past 15.4 (2019), 1621-1646. doi: 10.5194/cp-15-1621-2019.[4] J. Zhang et al. J. Geophys. Res. 102.4 (1997), 412-415.[5] M. Losch et al. Ocean Model. 33.1-2 (2010), 129-144. doi: 10.1016/j.ocemod.2009.12.008.[6] T. M. Dokken et al. Paleoceanography 28.3 (2013), 491-502. doi: 10.1002/palo.20042.[7] G. Vettoretti et al. Geophys. Res. Lett. 43.10 (2016), 5336-5344. doi: 10.1002/2016GL068891.[8] C. Li et al. Quat. Sci. Rev. 203 (2019), 1-20. doi: 10.1016/j.quascirev.2018.10.031.[9] N. Weitzel et al. presented at Fall Meeting AGU. 2020. url: https://agu.confex.com/agu/fm20/webprogram/Paper739241.html.
摘要观测记录为在狭窄的气候条件范围内制约海冰模式提供了坚实的基础。鉴于目前偏离这些条件的趋势，需要在更大范围的气候状态下对模型进行检验。过去的古气候数据提供了许多这样的例子，包括突然的临界点。然而，典型的古气候模拟需要持续千年，这就需要在模型过程的包容性和复杂性与计算成本之间取得平衡。考虑到 PlaSim-LSG 的技术限制，我们选择将 MITgcm 的动态海冰组件[4, 5]的修正版集成到模型设置中。我们根据 PlaSim-LSG 的结构和并行化方案调整了该组件，验证了该组件的物理一致性和稳定性，并评估了海冰动力学对十年至千年时间尺度模拟气候的影响。具体来说，我们将扩展模型的气候学、变异性和规模与原有设置的控制模拟进行了比较，并量化了额外的海冰动力学如何影响 PlaSim 模型系列众所周知的气候偏差。海冰是大气-海洋耦合过程的关键组成部分，而大气-海洋耦合过程导致了过去大振幅的气候突变[6-8]。因此，扩展模式可用于研究海冰在这种振荡中的作用。参考文献[1] K. Fraedrich et al. Meteorol.14.3 (2005), 299-304. doi: 10.1127/0941-2948/2005/0043.[2] F. Lunkeit et al.2011. url: https://www.mi.uni-hamburg.de/en/arbeitsgruppen/theoretische-meteorologie/modelle/sources/psreferencemanual-1.pdf.[3] H. J. Andres et al. Clim.Doi: 10.5194/cp-15-1621-2019.[4] J. Zhang et al. J. Geophys.102.4 (1997), 412-415.[5] M. Losch et al. Ocean Model.33.1-2 (2010), 129-144. Doi: 10.1016/j.ocemod.2009.12.008.[6] T. M. Dokken et al. Paleoceanography 28.3 (2013), 491-502. Doi: 10.1002/palo.20042.[7] G. Vettoretti et al. Geophys.Res.Lett.43.10 (2016), 5336-5344. doi: 10.1002/2016GL068891.[8] C. Li et al.Quat.Sci. Rev. 203 (2019), 1-20. doi: 10.1016/j.quascirev.2018.10.031.[9] N. Weitzel et al. presented at Fall Meeting AGU.2020. url: https://agu.confex.com/agu/fm20/webprogram/Paper739241.html.
{"title":"The role of dynamic sea ice in a simplified general circulation model used for palaeoclimate studies","authors":"M. Adam, H. Andres, K. Rehfeld","doi":"10.4995/yic2021.2021.12383","DOIUrl":"https://doi.org/10.4995/yic2021.2021.12383","url":null,"abstract":"AbstractObservational records provide a strong basis for constraining sea ice models within a narrow range of climate conditions. Given current trends away from these conditions, models need to be tested over a wider range of climate states. The past provides many such examples based on paleoclimate data, including abrupt tipping points. However, the millennial-duration of typical paleoclimatesimulations necessitates balancing the inclusion and sophistication of model processes against computational cost. We investigate the impact on climate mean states and variability of introducing sea ice dynamics into the simplified general circulation model PlaSim-LSG [1-3].Considering the technical constraints of PlaSim-LSG, we choose to integrate a modied version of the MITgcm's dynamical sea ice component [4, 5] into the model setup. We adapt the component to the structure and parallelization scheme of PlaSim-LSG, validate the physical consistency and stability of the component, and evaluate the impact of sea ice dynamics onto the simulated climate from decadal to millennial time scales. Specifically, we compare climatologies, variability and scaling of the extended model to control simulations of the preexisting setups, and quantify how additional sea ice dynamics affect well-known climatic biases of the PlaSim model family.With our extended PlaSim-LSG model we aim at capturing the key small-scale sea ice processes that are important to past climate tipping points while maintaining model efficiency for millennial simulations. Sea ice is a key component of coupled atmosphere-ocean processes that led to large-amplitude, abrupt climate variability in the past [6-8]. Therefore, the extended model can be usedto investigate the role of sea ice for such oscillations. This facilitates the understanding of processes that lead to current mismatches between palaeoclimate data and simulations, and that impact thesimulated surface climate variability [9].References[1] K. Fraedrich et al. Meteorol. Z. 14.3 (2005), 299-304. doi: 10.1127/0941-2948/2005/0043.[2] F. Lunkeit et al. Tech. rep. 2011. url: https://www.mi.uni-hamburg.de/en/arbeitsgruppen/theoretische-meteorologie/modelle/sources/psreferencemanual-1.pdf.[3] H. J. Andres et al. Clim. Past 15.4 (2019), 1621-1646. doi: 10.5194/cp-15-1621-2019.[4] J. Zhang et al. J. Geophys. Res. 102.4 (1997), 412-415.[5] M. Losch et al. Ocean Model. 33.1-2 (2010), 129-144. doi: 10.1016/j.ocemod.2009.12.008.[6] T. M. Dokken et al. Paleoceanography 28.3 (2013), 491-502. doi: 10.1002/palo.20042.[7] G. Vettoretti et al. Geophys. Res. Lett. 43.10 (2016), 5336-5344. doi: 10.1002/2016GL068891.[8] C. Li et al. Quat. Sci. Rev. 203 (2019), 1-20. doi: 10.1016/j.quascirev.2018.10.031.[9] N. Weitzel et al. presented at Fall Meeting AGU. 2020. url: https://agu.confex.com/agu/fm20/webprogram/Paper739241.html.","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129469811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12217
R. Schussnig, D. Pacheco, M. Kaltenbacher, T. Fries
In various practically relevant incompressible flow problems, such as polymer flow or biomedicalengineering applications, the dependence of fluid viscosity on the local shear rate plays an impor-tant role. Standard techniques using inf-sup stable finite elements lead to saddle-point systemsposing a challenge even for state-of-the-art solvers and preconditioners.For efficiency, projection schemes or time-splitting methods decouple the governing equations forvelocity and pressure, resulting in more, but easier to solve linear systems. Doing so, boundaryconditions and correction terms at intermediate steps have to be carefully considered in order toprohibit spoiling accuracy. In the case of Newtonian incompressible fluids, pressure and velocitycorrection schemes of high-order accuracy have been devised (see, e.g. [1, 2]). However, the exten-sion to generalised Newtonian fluids is a non-trivial task and considered an open question. Deteixet al. [3] successfully adapted the popular rotational correction scheme to consider for shear-ratedependent viscosity, but this resulted in substantial numerical overhead caused by necessarily pro-jecting viscous stress components.In this contribution we address this shortcoming and present a split-step scheme, extending pre-vious work by Liu [4]. The new method is based on an explicit-implicit treatment of pressure,convection and viscous terms combined with a Pressure-Poisson equation equipped with fully con-sistent Neumann and Dirichlet boundary conditions. Through proper reformulation, the use ofstandard continuous finite element spaces is enabled due to low regularity requirements. Addition-ally, equal-order velocity-pressure pairs are applicable as in the original scheme.The stability, accuracy and efficiency of the higher-order splitting scheme is showcased in challeng-ing numerical examples of practical interest.[1] Karniadakis, G. E., Israeli, M. and Orszag, S. A. High-order splitting methods for the incom-pressible Navier-Stokes equations. J. Comput. Phys., (1991).[2] Timmermans, L.J.P., Minev, P.D. and Van de Vosse, F. N. An approximate projection schemefor incompressible flow using spectral elements. Internat. J. Numer. Methods Fluids, Vol.22(7), pp. 673–688, (1996).[3] Deteix, J. and Yakoubi, D. Shear rate projection schemes for non-Newtonian fluids, Comput.Methods Appl. Mech. Engrg., Vol. 354, pp. 620–636, (2019).[4] Liu, J. Open and traction boundary conditions for the incompressible NavierStokesequations.J. Comput. Phys., Vol. 228(19), pp. 7250..7267, (2009).
在各种实际相关的不可压缩流动问题中，如聚合物流动或生物医学工程应用，流体粘度对局部剪切速率的依赖起着重要作用。使用不稳定有限元的标准技术导致鞍点系统即使对最先进的求解器和预调节器也是一个挑战。为了提高效率，投影方案或时间分裂方法将速度和压力的控制方程解耦，从而得到更多但更容易求解的线性系统。这样做时，必须仔细考虑中间步骤的边界条件和校正条件，以防止破坏精度。在牛顿不可压缩流体的情况下，已经设计了高阶精度的压力和速度校正方案(参见，例如[1,2])。然而，扩展到广义牛顿流体是一项不平凡的任务，被认为是一个开放的问题。Deteixet al.[3]成功地采用了流行的旋转校正方案来考虑剪切速率相关的粘度，但这导致了大量的数值开销，这是由于必然会投影粘性应力分量造成的。在本文中，我们解决了这一缺点，并提出了一个分步方案，扩展了Liu[4]之前的工作。该方法基于对压力、对流和粘性项的显式-隐式处理，并结合具有完全一致Neumann和Dirichlet边界条件的压力-泊松方程。通过适当的重新制定，使用标准的连续有限元空间是可能的，因为低规则性要求。此外，与原方案一样，速度-压力对也适用。高阶分裂方案的稳定性、准确性和效率在具有挑战性的实际意义的数值例子中得到了展示。[1]Karniadakis, g.e.， israel, M.和Orszag, s.a.不可压缩Navier-Stokes方程的高阶分裂方法。j .第一版。理论物理。,(1991)。[2]Timmermans, L.J.P, Minev, P.D.和Van de Vosse, f.n.使用谱元素的不可压缩流的近似投影方案。国际的。j .号码。方法流体，Vol.22(7)， pp. 673-688， (1996).[3]Deteix, J.和Yakoubi, D.非牛顿流体的剪切速率投影方案，计算机学报。方法:。动力机械。Engrg。， Vol. 354, pp. 620-636， (2019).[4]刘杰。不可压缩navierstokes方程组的开边界和牵引边界条件。第一版。理论物理。，第228卷(19)，第7250页。7267年,(2009)。
{"title":"Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow","authors":"R. Schussnig, D. Pacheco, M. Kaltenbacher, T. Fries","doi":"10.4995/yic2021.2021.12217","DOIUrl":"https://doi.org/10.4995/yic2021.2021.12217","url":null,"abstract":"In various practically relevant incompressible flow problems, such as polymer flow or biomedicalengineering applications, the dependence of fluid viscosity on the local shear rate plays an impor-tant role. Standard techniques using inf-sup stable finite elements lead to saddle-point systemsposing a challenge even for state-of-the-art solvers and preconditioners.For efficiency, projection schemes or time-splitting methods decouple the governing equations forvelocity and pressure, resulting in more, but easier to solve linear systems. Doing so, boundaryconditions and correction terms at intermediate steps have to be carefully considered in order toprohibit spoiling accuracy. In the case of Newtonian incompressible fluids, pressure and velocitycorrection schemes of high-order accuracy have been devised (see, e.g. [1, 2]). However, the exten-sion to generalised Newtonian fluids is a non-trivial task and considered an open question. Deteixet al. [3] successfully adapted the popular rotational correction scheme to consider for shear-ratedependent viscosity, but this resulted in substantial numerical overhead caused by necessarily pro-jecting viscous stress components.In this contribution we address this shortcoming and present a split-step scheme, extending pre-vious work by Liu [4]. The new method is based on an explicit-implicit treatment of pressure,convection and viscous terms combined with a Pressure-Poisson equation equipped with fully con-sistent Neumann and Dirichlet boundary conditions. Through proper reformulation, the use ofstandard continuous finite element spaces is enabled due to low regularity requirements. Addition-ally, equal-order velocity-pressure pairs are applicable as in the original scheme.The stability, accuracy and efficiency of the higher-order splitting scheme is showcased in challeng-ing numerical examples of practical interest.[1] Karniadakis, G. E., Israeli, M. and Orszag, S. A. High-order splitting methods for the incom-pressible Navier-Stokes equations. J. Comput. Phys., (1991).[2] Timmermans, L.J.P., Minev, P.D. and Van de Vosse, F. N. An approximate projection schemefor incompressible flow using spectral elements. Internat. J. Numer. Methods Fluids, Vol.22(7), pp. 673–688, (1996).[3] Deteix, J. and Yakoubi, D. Shear rate projection schemes for non-Newtonian fluids, Comput.Methods Appl. Mech. Engrg., Vol. 354, pp. 620–636, (2019).[4] Liu, J. Open and traction boundary conditions for the incompressible NavierStokesequations.J. Comput. Phys., Vol. 228(19), pp. 7250..7267, (2009).","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130153260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12211
D. Lauwers, M. Meinke, W. Schröder
The study of gas-liquid multiphase flows has been an active research topic for many decades. They occur in processes belonging to industries including chemical, pharmaceutical, food, energy, and machinery industries. As processes in these fields become more refined, there is an increasing demand for the detailed analysis and accurate prediction of such flows. There are many categories of multiphase gas-liquid flows. We consider a dispersed phase in a carrier phase, such as small gas bubbles in liquids or liquid droplets in a gas. The technical application is a pulsed electrochemical machining (PECM) process, in which gas bubbles are generated in a liquid electrolyte during the electrochemical removal of material. The simulation method is based on an Eulerian-Eulerian model for the dispersed gas-liquid bubbly flow. The conservation equations are volumetrically averaged, resulting in one set of conservation equations per phase. The liquid phase is using a Lattice-Boltzmann method, while the gas phase is modelled by a Finite-Volume method. Interface terms between the phases result in a two-way coupled system. Both methods are formulated on a shared Cartesian grid similar to the concept in [1], which facilitates the exchange of information between the two solvers and an efficient implementation on HPC hardware. This coupled multiphase approach combines the advantages of the Lattice Boltzmann method as an efficient prediction tool for low Mach number flows with those of a finite-volume method for the Navier-Stokes equation used for the phase with larger density changes. To accurately model the turbulent motion of the liquid phase on all relevant scales, a cumulant-based collision step for the Lattice-Boltzmann scheme [2] is combined with a Smagorinsky sub-grid-scale turbulence model. In the finite-volume solver, the effects of the sub-grid-scale turbulence are incorporated according to the MILES approach. For the validation of the new method, large-eddy simulations (LES) of turbulent bubbly flows are performed. The accuracy of the predictions is evaluated comparing the results to reference data from experiments and other simulations for generic test cases, for which good agreement is found. The applicability of the method will be demonstrated for a bubbly turbulent channel flow, which mimics the phenomena in the PECM process.
{"title":"A coupled lattice Boltzmann/finite volume method for turbulent gas-liquid bubbly flows","authors":"D. Lauwers, M. Meinke, W. Schröder","doi":"10.4995/yic2021.2021.12211","DOIUrl":"https://doi.org/10.4995/yic2021.2021.12211","url":null,"abstract":"The study of gas-liquid multiphase flows has been an active research topic for many decades. They occur in processes belonging to industries including chemical, pharmaceutical, food, energy, and machinery industries. As processes in these fields become more refined, there is an increasing demand for the detailed analysis and accurate prediction of such flows. There are many categories of multiphase gas-liquid flows. We consider a dispersed phase in a carrier phase, such as small gas bubbles in liquids or liquid droplets in a gas. The technical application is a pulsed electrochemical machining (PECM) process, in which gas bubbles are generated in a liquid electrolyte during the electrochemical removal of material. The simulation method is based on an Eulerian-Eulerian model for the dispersed gas-liquid bubbly flow. The conservation equations are volumetrically averaged, resulting in one set of conservation equations per phase. The liquid phase is using a Lattice-Boltzmann method, while the gas phase is modelled by a Finite-Volume method. Interface terms between the phases result in a two-way coupled system. Both methods are formulated on a shared Cartesian grid similar to the concept in [1], which facilitates the exchange of information between the two solvers and an efficient implementation on HPC hardware. This coupled multiphase approach combines the advantages of the Lattice Boltzmann method as an efficient prediction tool for low Mach number flows with those of a finite-volume method for the Navier-Stokes equation used for the phase with larger density changes. To accurately model the turbulent motion of the liquid phase on all relevant scales, a cumulant-based collision step for the Lattice-Boltzmann scheme [2] is combined with a Smagorinsky sub-grid-scale turbulence model. In the finite-volume solver, the effects of the sub-grid-scale turbulence are incorporated according to the MILES approach. For the validation of the new method, large-eddy simulations (LES) of turbulent bubbly flows are performed. The accuracy of the predictions is evaluated comparing the results to reference data from experiments and other simulations for generic test cases, for which good agreement is found. The applicability of the method will be demonstrated for a bubbly turbulent channel flow, which mimics the phenomena in the PECM process.","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127939283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12598
Susanne Held, W. Dornisch, Nima Azizi
The aim of this work is to derive a formulation for linear two-dimensional elasticity using just one degree of freedom. With the Airy stress function, a measure without further physical meaning is chosen to this single degree of freedom. The corresponding Airy equation requires higher order basis functions for the discretization of the formulation [1]. Isogeometric structural analysis (IGA) is based on shape functions of the system in Computer-Aided design (CAD) software [2]. These shape functions can fulfill the requirement of high continuity and therefore the formulation is obtained through IGA methods. Non-Uniform Rational B-splines (NURBS) are used to discretize the domain and to solve the occurring differential equations within the Galerkin method [3]. The received one-degree of freedom formulation allows to compute stresses as direct solution of the underlying system of equations. Numerical examples demonstrate the accuracy for a quadratic plate under standard, but also under complex loading. For constant or linear loading functions only one element is sufficient to receive the exact solution – a general advantage of using higher order basis functions. The correct convergence behaviour of the proposed formulation is proved by the -error norm for a complex load situation. Here, only a few refinement steps yield a good approximation with a very small error of the stresses.
{"title":"An Isogeometric Element Formulation for Linear Two-Dimensional Elasticity Based on the Airy Equation","authors":"Susanne Held, W. Dornisch, Nima Azizi","doi":"10.4995/yic2021.2021.12598","DOIUrl":"https://doi.org/10.4995/yic2021.2021.12598","url":null,"abstract":"The aim of this work is to derive a formulation for linear two-dimensional elasticity using just one degree of freedom. With the Airy stress function, a measure without further physical meaning is chosen to this single degree of freedom. The corresponding Airy equation requires higher order basis functions for the discretization of the formulation [1]. Isogeometric structural analysis (IGA) is based on shape functions of the system in Computer-Aided design (CAD) software [2]. These shape functions can fulfill the requirement of high continuity and therefore the formulation is obtained through IGA methods. Non-Uniform Rational B-splines (NURBS) are used to discretize the domain and to solve the occurring differential equations within the Galerkin method [3]. The received one-degree of freedom formulation allows to compute stresses as direct solution of the underlying system of equations. Numerical examples demonstrate the accuracy for a quadratic plate under standard, but also under complex loading. For constant or linear loading functions only one element is sufficient to receive the exact solution – a general advantage of using higher order basis functions. The correct convergence behaviour of the proposed formulation is proved by the -error norm for a complex load situation. Here, only a few refinement steps yield a good approximation with a very small error of the stresses.","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131084782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12324
J. Both, Nicolas A. Barnafi
Sequential block-partitioned solvers have in the recent past been quite popular for multi-physics and in particular poroelasticity models. Such enable tailored solver technology for the respective single-physics problems via iterative coupling, as well as suggest suitable block-preconditioners for monolithic solvers.In this talk, we focus on a thermodynamically consistent poroelasticity model recently proposed. It extends the classical quasi-static Biot equations by incoporating inertia contributions in both solid and fluid equations, aiming at biomedical applications; for instance, the perfusion of the heart.Following ideas and techniques from previous works, we present block-partitioned solvers for the fully dynamic poroelasticity model supported by theoretical convergence analysis.
{"title":"ITERATIVE QUASI-NEWTON SOLVERS FOR POROMECHANICS APPLIED TO HEART PERFUSION","authors":"J. Both, Nicolas A. Barnafi","doi":"10.4995/yic2021.2021.12324","DOIUrl":"https://doi.org/10.4995/yic2021.2021.12324","url":null,"abstract":"Sequential block-partitioned solvers have in the recent past been quite popular for multi-physics and in particular poroelasticity models. Such enable tailored solver technology for the respective single-physics problems via iterative coupling, as well as suggest suitable block-preconditioners for monolithic solvers.In this talk, we focus on a thermodynamically consistent poroelasticity model recently proposed. It extends the classical quasi-static Biot equations by incoporating inertia contributions in both solid and fluid equations, aiming at biomedical applications; for instance, the perfusion of the heart.Following ideas and techniques from previous works, we present block-partitioned solvers for the fully dynamic poroelasticity model supported by theoretical convergence analysis.","PeriodicalId":406819,"journal":{"name":"Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134488419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-07DOI: 10.4995/yic2021.2021.12389
Arooj Fatima, S. Turek, A. Ouazzi, M. Afaq
Developing a numerical and algorithmic tool which correctly identifies unyielded region in the yield stress fluid flow is a challenging task. Two approaches are commonly used to handle the singular behaviour at the yield surface, i.e. Augmented Lagrangian approach and the regularization approach, respectively. Generally in the regularization approach, solvers do not perform efficiently when the regularization parameter gets very small. In this work, we use a formulation introducing a new auxiliary stress [1]. The three field formulation of yield stress fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations arising from the three field formulation is solved efficiently and accurately by a monolithic finite element method. The velocity and pressure are discretized by higher order stable FEM pair $Q_2/P^{text{disc}}_1$ and the auxiliary stress is discretized by $Q_2$ element.Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear solver. We developed a new adaptive discrete Newton's method, which evaluates the Jacobian with the directional divided difference approach [2]. The step length in this process is an important key: We relate this length to the rate of the actual nonlinear reduction for achieving a robust adaptive Newton's method. The resulting linear sub problems are solved using the geometrical multigrid solver. We analyse the solvability of the problem along with the adaptive Newton method for Bingham fluids by doing numerical studies for two different prototypical configurations, i.e. "Viscoplastic fluid flow in a channel" and "Lid Driven Cavity", respectively [2].REFERENCES[1] Aposporidis, A., Haber, E., Olshanskii, M. A. and Veneziani, A. A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution. Comput. Methods Appl. Mech. Engrg, Vol. 200, pp. 2434–2446, (2011).[2] Fatima, A., Turek, S., Ouazzi, A. and Afaq, M. A. An adaptive discrete Newton method for regularization-free Bingham model. Ergebnisberichte des Instituts fuer Angewandte Mathematik Nummer 635, Fakultaet fuer Mathematik, TU Dortmund University, 635, 2021.
开发一种能够正确识别屈服应力流体流动中未屈服区域的数值和算法工具是一项具有挑战性的任务。通常有两种方法用于处理屈服面上的奇异行为，即增广拉格朗日方法和正则化方法。通常在正则化方法中，当正则化参数非常小时，求解器不能有效地执行。在这项工作中，我们使用了一个引入新的辅助应力的公式[1]。屈服应力流体的三场公式对应于无正则化的Bingham公式。用整体有限元法高效、准确地求解了由三种场公式产生的方程组。速度和压力采用高阶稳定有限元对$Q_2/P^{text{disc}}_1$进行离散，辅助应力采用$Q_2$单元进行离散。此外，该问题是高度非线性的，对任何非线性求解器都提出了很大的挑战。我们开发了一种新的自适应离散牛顿方法，该方法使用方向除差法评估雅可比矩阵[2]。这个过程中的步长是一个重要的关键:我们将这个长度与实现鲁棒自适应牛顿方法的实际非线性缩减率联系起来。所得到的线性子问题用几何多重网格求解器求解。本文采用自适应牛顿法对Bingham流体进行了数值研究，分析了该问题的可解性。分别为“粘塑性流体在通道中流动”和“盖驱动腔”[2]。[1] Aposporidis, A, Haber, E, Olshanskii, M. A.和Veneziani, A. Bingham流体流动问题的混合公式:分析和数值解。第一版。方法:。动力机械。工程学报，Vol. 200, pp. 2434-2446， (2011).[2]Fatima, A.， Turek, S.， Ouazzi, A.和Afaq, M. A.一种无正则化Bingham模型的自适应离散牛顿方法。德国多特蒙德大学数学研究所(635)，德国多特蒙德大学数学研究所(635)，2021。
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