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Numerical approximation of the shallow water equations with coriolis source term 具有科里奥利源项的浅水方程的数值逼近
Pub Date : 2021-03-26 DOI: 10.1051/PROC/202107003
E. Audusse, V. Dubos, A. Duran, Noémie Gaveau, Y. Nasseri, Y. Penel
We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.
在这项工作中,我们研究了一类专门用于具有地形和科里奥利力的非线性浅水方程的数值格式。所提出的算法依赖于在配置和交错网格上制定的有限体积近似,涉及数值通量中的适当扩散项,表示为线性地转平衡的离散版本。由此可见,与标准有限体积方法相反,所提出方案的线性版本提供了地转平衡的相关近似。我们还证明了所得到的方法保证了半离散的能量估计。数值实验表明,在接近地转平衡的科里奥利力存在下,特别是在低弗劳德数状态下,该方法是有效的。
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引用次数: 1
Simulation of complex free surface flows 复杂自由表面流动的模拟
Pub Date : 2021-03-03 DOI: 10.1051/PROC/202107004
K. Benyo, A. Charhabil, Mohamed Ali Debyaoui, Y. Penel
We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].
我们研究了Serre-Green-Naghdi体系下的非流体静力公式,模拟了浅水状态下不可压缩的自由表面流动。与众所周知的(非线性)Saint-Venant方程不同,该系统考虑了非静水压力项的影响以及色散现象。设计了基于有限体积-有限差分型分割格式和迭代校正算法的两种数值格式。通过模拟孤立波解的传播,对这两种方法进行了比较。该模型也用Favre次波实验数据进行了评估[12]。
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引用次数: 1
Goal-oriented adaptive sampling under random field modelling of response probability distributions 响应概率分布随机场模型下目标导向自适应抽样
Pub Date : 2021-02-15 DOI: 10.1051/proc/202171108
Ath'enais Gautier, D. Ginsbourger, G. Pirot
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation.
在自然和人工复杂系统的研究中,不完全由所考虑的决策变量决定的响应通常是概率建模的,导致响应分布在决策空间中变化。我们考虑的情况是,这些响应分布的空间变化不仅涉及它们的平均值和/或方差,还涉及其他特征,例如形状或单模态与多模态。我们的贡献建立在非参数贝叶斯方法的基础上,以模拟由此引起的概率分布场,特别是逻辑高斯模型的空间扩展。所考虑的模型提供候选点响应分布的概率预测,例如允许执行概率密度函数的(近似)后验模拟,联合预测目标分布的多个矩和其他函数,以及量化收集新样本对感兴趣的分布领域的知识状态的影响。特别是,我们引入了自适应采样策略,利用所考虑的随机分布场模型的潜力,以面向目标的方式指导系统评估,以期从非线性(随机)反演和全局优化中简洁地解决校准和相关问题。
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引用次数: 3
Comparison of models for the simulation of landslide generated Tsunamis 滑坡海啸模拟模型的比较
Pub Date : 2021-01-01 DOI: 10.1051/PROC/202107002
Emmanuel Audusse, Joao Guilherme, Caldas Steinstraesser, Louis Emerald, Philippe Heinrich, A. Paris, Martin Parisot, J. G. C. Steinstraesser
In this paper, we analyze the relevance of the use of the shallow water model and the Boussinesq model to simulate tsunamis generated by a landslide. In a first part, we determine if the two models are able to reproduce waves generated by a landslide. Each model has drawbacks but it seems that it is possible to use them together to improve the simulations. In a second part we try to recover the landslide displacement from the generated wave. This problem is formulated as a minimization problem and we limit the number of parameters to determine assuming that the bottom can be well described by an empirical law.
在本文中,我们分析了使用浅水模型和Boussinesq模型来模拟滑坡引起的海啸的相关性。在第一部分中,我们确定这两个模型是否能够再现滑坡产生的波浪。每种模型都有缺点,但似乎可以将它们结合起来使用以改进模拟。在第二部分中,我们试图从产生的波中恢复滑坡位移。这个问题是一个最小化问题,我们限制参数的数量来确定假设底部可以很好地描述经验定律。
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引用次数: 4
Numerical investigations of the compressible Navier-Stokes system 可压缩Navier-Stokes系统的数值研究
Pub Date : 2021-01-01 DOI: 10.1051/PROC/202107001
Bilal Al-Taki, Kevin Atsou, Jean-J'erome Casanova, T. Goudon, P. Lafitte, F. Lagoutière, S. Minjeaud
In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: a staggered scheme based on the Rusanov one for the inviscid (Euler) system,a staggered pseudo-Lagrangian scheme in which the mesh “follows” the fluid,the Eulerian projection (on a fixed mesh) of the preceding scheme. All these schemes only involve the resolution of linear systems (all the nonlinear terms are solved in an explicit way). We propose numerical illustrations of their behaviors on particular solutions in which the density has discontinuities (hereafter called Hoff solutions). We show that the three schemes seem to converge to the same solutions, and we compare the evolution of the amplitude of the discontinuity of the numerical solution (with the pseudo-Lagrangian scheme) with the one predicted by Hoff and observe a good agreement.
在本文中,我们编写、分析并实验比较了三种专门用于一维正压性Navier-Stokes方程的不同数值格式:一种基于鲁萨诺夫格式的无粘(欧拉)系统的交错格式,一种网格“遵循”流体的交错伪拉格朗日格式,前一种格式的欧拉投影(在固定网格上)。所有这些方案只涉及线性系统的解析(所有的非线性项都以显式的方式求解)。我们提出了它们在密度具有不连续的特殊解(以下称为霍夫解)上的行为的数值说明。我们证明了这三种格式似乎收敛于相同的解,并且我们比较了数值解(使用伪拉格朗日格式)的不连续振幅的演变与Hoff预测的不连续振幅的演变,并观察到很好的一致性。
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引用次数: 0
Editorial CEMRACS 2019
Pub Date : 2021-01-01 DOI: 10.1051/proc/202107000
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引用次数: 0
Adaptive wavelet schemes and finite volumes 自适应小波方案和有限体积
Pub Date : 2021-01-01 DOI: 10.1051/PROC/202107007
D. Sarto, Erwan Deriaz, Xavier Lhébrard, Mathieu Rigal
We consider a procedure for combining high order finite volumes and tree-based nonuniform grids. Especially, we focus on efficient algorithms for third order multidimensional volume interpolation and communication between levels of refinement. In the end, numerical results are reviewed to validate our approach.
我们考虑了一种结合高阶有限体积和基于树的非均匀网格的方法。我们特别关注三阶多维体插值和精化层次之间通信的高效算法。最后对数值结果进行了验证。
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引用次数: 0
A lubrication equation for a simplified model of shear-thinning fluid 剪切变稀流体简化模型的润滑方程
Pub Date : 2021-01-01 DOI: 10.1051/PROC/202107010
F. James, Meissa M'Baye, K. Msheik, D. Nguyen
A lubrication equation is obtained for a simplified shear-thinning fluid. The simplified rheology consists of a piecewise linear stress tensor, resulting in a two-viscosity model. This can be interpreted as a modified Bingham fluid, which can be recovered in a specific limit. The lubrication equation is obtained in two steps. First two scalings are performed on the incompressible Navier-Stokes equations, namely the long-wave scaling and the slow motion scaling. Second, the resulting equations are averaged along the vertical direction. Numerical illustrations are provided, bringing to light the different possible behaviours.
得到了简化剪切-稀化流体的润滑方程。简化后的流变学由一个分段线性应力张量组成,形成一个双粘度模型。这可以解释为一种改良的宾厄姆流体,它可以在特定的限制下恢复。润滑方程分两步得到。首先对不可压缩的Navier-Stokes方程进行了两种尺度变换,即长波尺度变换和慢动作尺度变换。其次,所得方程沿垂直方向取平均值。提供了数值插图,揭示了不同可能的行为。
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引用次数: 1
Partial differential equations for oceanic artificial intelligence 海洋人工智能的偏微分方程
Pub Date : 2021-01-01 DOI: 10.1051/PROC/202107009
Jules Guillot, Guillaume Koenig, Kadi Minbashian, E. Frénod, Hélène Flourent, J. Brajard
The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities. On the one hand, standard physical methods for forecasting SST use coupled ocean- atmosphere prediction systems, based on the Navier-Stokes equations. These models rely on multiple physical hypotheses and do not optimally exploit the information available in the data. On the other hand, despite the availability of large amounts of data, direct applications of machine learning methods do not always lead to competitive state of the art results. Another approach is to combine these two methods: this is data-model coupling. The aim of this paper is to use a model in another domain. This model is based on a data-model coupling approach to simulate and predict SST. We first introduce the original model. Then, the modified model is described, to finish with some numerical results.
海表温度(SST)在分析和评估天气和生物系统的动态方面起着重要作用。它有各种各样的应用,如天气预报或沿海活动的规划。一方面,预测海温的标准物理方法使用基于纳维-斯托克斯方程的耦合海洋-大气预报系统。这些模型依赖于多种物理假设,不能最佳地利用数据中可用的信息。另一方面,尽管有大量数据的可用性,但机器学习方法的直接应用并不总是会产生具有竞争力的最新结果。另一种方法是将这两种方法结合起来:这是数据模型耦合。本文的目的是在另一个领域中使用模型。该模型基于数据模型耦合的方法来模拟和预测海温。我们首先介绍原始模型。然后,对修正后的模型进行了描述,最后给出了一些数值结果。
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引用次数: 1
A diffuse interface approach for disperse two-phase flows involving dual-scale kinematics of droplet deformation based on geometrical variables 基于几何变量的涉及液滴变形双尺度运动学的分散两相流扩散界面方法
Pub Date : 2020-06-24 DOI: 10.1051/PROC/202069024
Pierre Cordesse, R. D. Battista, Quentin Chevalier, L. Matuszewski, T. Ménard, S. Kokh, M. Massot
The purpose of this contribution is to derive a reduced-order two-phase flow model in- cluding interface subscale modeling through geometrical variables based on Stationary Action Principle (SAP) and Second Principle of Thermodynamics in the spirit of [6, 14]. The derivation is conducted in the disperse phase regime for the sake of clarity but the resulting paradigm can be used in a more general framework. One key issue is the definition of the proper potential and kinetic energies in the Lagrangian of the system based on geometrical variables (Interface area density, mean and Gauss curvatures...), which will drive the subscale kinematics and dissipation, and their coupling with large scales of the flow. While [14] relied on bubble pulsation, that is normal deformation of the interface with shape preservation related to pressure changes, we aim here at tackling inclusion deformation at constant volume, thus describing self-sustained oscillations. In order to identify the proper energies, we use Direct Numerical Simulations (DNS) of oscillating droplets using ARCHER code and recently devel- oped library, Mercur(v)e, for mean geometrical variable evaluation and analysis preserving topological invariants. This study is combined with historical analytical studies conducted in the small perturba- tion regime and shows that the proper potential energy is related to the surface difference compared to the spherical minimal surface. A geometrical quasi-invariant is also identified and a natural definition of subscale momentum is proposed. The set of Partial Differential Equations (PDEs) including the conservation equations as well as dissipation source terms are eventually derived leading to an original two-scale diffuse interface model involving geometrical variables.
本贡献的目的是在[6,14]的精神下,基于静止作用原理(SAP)和热力学第二原理,通过几何变量推导出包含界面亚尺度建模的降阶两相流模型。为了清楚起见,推导是在分散相体系中进行的,但所得的范式可以在更一般的框架中使用。其中一个关键问题是基于几何变量(界面面积密度、平均曲率和高斯曲率等)在系统拉格朗日量中定义合适的势能和动能,这将驱动亚尺度运动和耗散,以及它们与大尺度流动的耦合。虽然[14]依赖于气泡脉动,即与压力变化相关的具有形状保持的界面的正常变形,但我们在这里的目标是解决恒定体积下的夹杂变形,从而描述自持续振荡。为了确定合适的能量,我们使用ARCHER代码和最近开发的Mercur(v)e库对振荡液滴进行直接数值模拟(DNS),以进行平均几何变量的评估和分析,并保持拓扑不变量。本研究结合在小摄动区进行的历史分析研究,表明与球面最小表面相比,适当的势能与表面差有关。在此基础上,给出了子尺度动量的几何拟不变量,并给出了子尺度动量的自然定义。最后导出了包含守恒方程和耗散源项的一组偏微分方程(PDEs),得到了包含几何变量的原始双尺度扩散界面模型。
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引用次数: 3
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ESAIM Proceedings and Surveys
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