Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113516
Magnus Svärd, Henrik Kalisch
Many Boussinesq models suffer from nonlinear instabilities, especially in the context of rapid variations in the bed topography. In this work, a Boussinesq system is put forward which is derived in such a way as to be both linearly and nonlinearly energy-stable.
The proposed system is designed to be robust for coastal simulations with sharply varying bathymetric features while maintaining the dispersive accuracy at any constant depth. For constant bathymetries, the system has the same linear dispersion relation as Peregrine's system ([22]). Furthermore, the system transitions smoothly to the shallow-water system as the depth goes to zero.
In the one-dimensional case, we design a stable finite-volume scheme and demonstrate its robustness, accuracy and stability under grid refinement in a suite of test problems including Dingemans's wave experiment.
Finally, we generalise the system to the two-dimensional case.
{"title":"A novel energy-bounded Boussinesq model and a well balanced and stable numerical discretisation","authors":"Magnus Svärd, Henrik Kalisch","doi":"10.1016/j.jcp.2024.113516","DOIUrl":"10.1016/j.jcp.2024.113516","url":null,"abstract":"<div><div>Many Boussinesq models suffer from nonlinear instabilities, especially in the context of rapid variations in the bed topography. In this work, a Boussinesq system is put forward which is derived in such a way as to be both linearly and nonlinearly energy-stable.</div><div>The proposed system is designed to be robust for coastal simulations with sharply varying bathymetric features while maintaining the dispersive accuracy at any constant depth. For constant bathymetries, the system has the same linear dispersion relation as Peregrine's system (<span><span>[22]</span></span>). Furthermore, the system transitions smoothly to the shallow-water system as the depth goes to zero.</div><div>In the one-dimensional case, we design a stable finite-volume scheme and demonstrate its robustness, accuracy and stability under grid refinement in a suite of test problems including Dingemans's wave experiment.</div><div>Finally, we generalise the system to the two-dimensional case.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113516"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113509
Tim Wegmann , Ansgar Niemöller , Matthias Meinke , Wolfgang Schröder
An Eulerian-Lagrangian coupling method based on hierarchical meshes is presented, which allows an efficient parallelization on high-performance computing hardware. It features an interleaved execution pattern with non-blocking communication, where the hierarchical mesh structure facilitates the redistribution of the computational load. The Lagrangian and Eulerian solvers use hierarchical Cartesian meshes which share a common coarse mesh level. The domain decomposition is based on a space-filling curve defined on the joint computational mesh, where the load is projected to a coarse mesh level used for the partitioning. The performance of the coupled method is evaluated for the problem of spray modeling in turbulent flow. A solution adaptive mesh is utilized for the large-eddy simulation of the flow field and the Lagrangian tracking method is used for the spray particles. Static and dynamic workload estimators are compared with respect to the alleviation of load imbalances. Liquid fuel spray injection in a constant pressure chamber and in an internal combustion engine serves as applications with varying scale resolution and localized computational load. The parallel efficiency of the approach on high performance systems is demonstrated for meshes with up to cells and particles. Detailed performance analyses show a performance gain of the novel algorithm of approx. 20% compared to a non-interleaved time step execution for two-way coupled spray injection simulations. Results of strong scaling experiments at different injection phases show a good parallel performance with an efficiency of up to 81% using 262000 MPI processes.
{"title":"Parallel Eulerian-Lagrangian coupling method on hierarchical meshes","authors":"Tim Wegmann , Ansgar Niemöller , Matthias Meinke , Wolfgang Schröder","doi":"10.1016/j.jcp.2024.113509","DOIUrl":"10.1016/j.jcp.2024.113509","url":null,"abstract":"<div><div>An Eulerian-Lagrangian coupling method based on hierarchical meshes is presented, which allows an efficient parallelization on high-performance computing hardware. It features an interleaved execution pattern with non-blocking communication, where the hierarchical mesh structure facilitates the redistribution of the computational load. The Lagrangian and Eulerian solvers use hierarchical Cartesian meshes which share a common coarse mesh level. The domain decomposition is based on a space-filling curve defined on the joint computational mesh, where the load is projected to a coarse mesh level used for the partitioning. The performance of the coupled method is evaluated for the problem of spray modeling in turbulent flow. A solution adaptive mesh is utilized for the large-eddy simulation of the flow field and the Lagrangian tracking method is used for the spray particles. Static and dynamic workload estimators are compared with respect to the alleviation of load imbalances. Liquid fuel spray injection in a constant pressure chamber and in an internal combustion engine serves as applications with varying scale resolution and localized computational load. The parallel efficiency of the approach on high performance systems is demonstrated for meshes with up to <span><math><mn>2.8</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup></math></span> cells and <span><math><mn>21</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup></math></span> particles. Detailed performance analyses show a performance gain of the novel algorithm of approx. 20% compared to a non-interleaved time step execution for two-way coupled spray injection simulations. Results of strong scaling experiments at different injection phases show a good parallel performance with an efficiency of up to 81% using 262000 MPI processes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113509"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Phase-field has been effectively applied to many complex problems according to the mesh based method. However, the computational speed of the numerical method based on phase-field still needs improved. In this paper, an improved localized radial basis function collocation method (LRBFCM) based on the adaptive support domain is employed to the phase-field methods. The proposed adaptive support domain can increase the stability of the LRBFCM, and the improved LRBFCM is much more efficient than the traditional finite element method (FEM) in coupling with phase-field methods. The proposed approach is further applied to the single-phase dendrite solidification, two-phase sintering, and three-phase wetting phenomena. We compare the efficiency of the proposed LRBFCM with different numerical methods, which show that the LRBFCM combined with the Fourier spectral method can deal with the three-phase model with more than ten million nodes easily.
{"title":"The localized radial basis function collocation method for dendritic solidification, solid phase sintering and wetting phenomenon based on phase field","authors":"Pengfei Jiang , Hui Zheng , Jingang Xiong , Timon Rabczuk","doi":"10.1016/j.jcp.2024.113515","DOIUrl":"10.1016/j.jcp.2024.113515","url":null,"abstract":"<div><div>Phase-field has been effectively applied to many complex problems according to the mesh based method. However, the computational speed of the numerical method based on phase-field still needs improved. In this paper, an improved localized radial basis function collocation method (LRBFCM) based on the adaptive support domain is employed to the phase-field methods. The proposed adaptive support domain can increase the stability of the LRBFCM, and the improved LRBFCM is much more efficient than the traditional finite element method (FEM) in coupling with phase-field methods. The proposed approach is further applied to the single-phase dendrite solidification, two-phase sintering, and three-phase wetting phenomena. We compare the efficiency of the proposed LRBFCM with different numerical methods, which show that the LRBFCM combined with the Fourier spectral method can deal with the three-phase model with more than ten million nodes easily.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113515"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142536281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.jcp.2024.113510
David Sidilkover
Lagrangian methods for computational continuum mechanics, since their inception, traditionally relied on staggered meshes. This feature, while facilitating their robustness and reliability, presented some difficulties. The latter motivated the search for collocated Lagrangian schemes. One of the attempts to develop such a scheme was the CAVEAT method/code. Numerical solutions produced by this method suffered sometimes from large vorticity errors, which could lead to mesh entanglement and premature run termination. The efforts to devise a more robust collocated scheme began to bear fruit a couple of decades later starting from the groundbreaking method GLACE, closely followed by EUCCLHYD and later on by CCH and others.
One of the aims of this paper is to present a novel Lagrangian collocated factorizable scheme. The notion of a factorizable method was introduced more than two decades ago within the Eulerian approach. It designates a numerical scheme that reflects/preserves the mixed character of the Euler equations, i.e. does not introduce non-physical coupling between the different factors of the system of equations - advection and acoustics operators.
Another aim of this paper is to explore the connection between the factorizability property of a Lagrangian method and whether or not it suffers from spurious vorticity. Several existing schemes are surveyed for this purpose. A conjecture summarizing our findings is formulated.
{"title":"Spurious vorticity in Eulerian and Lagrangian methods","authors":"David Sidilkover","doi":"10.1016/j.jcp.2024.113510","DOIUrl":"10.1016/j.jcp.2024.113510","url":null,"abstract":"<div><div>Lagrangian methods for computational continuum mechanics, since their inception, traditionally relied on staggered meshes. This feature, while facilitating their robustness and reliability, presented some difficulties. The latter motivated the search for collocated Lagrangian schemes. One of the attempts to develop such a scheme was the CAVEAT method/code. Numerical solutions produced by this method suffered sometimes from large vorticity errors, which could lead to mesh entanglement and premature run termination. The efforts to devise a more robust collocated scheme began to bear fruit a couple of decades later starting from the groundbreaking method GLACE, closely followed by EUCCLHYD and later on by CCH and others.</div><div>One of the aims of this paper is to present a novel Lagrangian collocated <em>factorizable</em> scheme. The notion of a <em>factorizable</em> method was introduced more than two decades ago within the Eulerian approach. It designates a numerical scheme that reflects/preserves the mixed character of the Euler equations, i.e. does not introduce non-physical coupling between the different factors of the system of equations - advection and acoustics operators.</div><div>Another aim of this paper is to explore the connection between the <em>factorizability</em> property of a Lagrangian method and whether or not it suffers from spurious vorticity. Several existing schemes are surveyed for this purpose. A conjecture summarizing our findings is formulated.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113510"},"PeriodicalIF":3.8,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-17DOI: 10.1016/j.jcp.2024.113504
Mengdi Wang , Matthew Cong , Bo Zhu
This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.
{"title":"An interface tracking method with triangle edge cuts","authors":"Mengdi Wang , Matthew Cong , Bo Zhu","doi":"10.1016/j.jcp.2024.113504","DOIUrl":"10.1016/j.jcp.2024.113504","url":null,"abstract":"<div><div>This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via <em>triangle edge cuts</em> which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113504"},"PeriodicalIF":3.8,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-17DOI: 10.1016/j.jcp.2024.113508
David A. Kopriva , Andrew R. Winters , Jan Nordström
We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter is bounded by data only for fixed polynomial order, mesh, and time. In the absence of dissipation, coupling of the overlapping domains is destabilizing by allowing positive eigenvalues in the system to be integrated in time. This coupling can be stabilized in one space dimension by using the upwind numerical flux. To help provide additional dissipation, we introduce a novel penalty method that applies dissipation at arbitrary points within the overlap region and depends only on the difference between the solutions. We present numerical experiments in one space dimension to illustrate the implementation of the well-posed penalty formulation, and show spectral convergence of the approximations when sufficient dissipation is applied.
{"title":"Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems","authors":"David A. Kopriva , Andrew R. Winters , Jan Nordström","doi":"10.1016/j.jcp.2024.113508","DOIUrl":"10.1016/j.jcp.2024.113508","url":null,"abstract":"<div><div>We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter is bounded by data only for fixed polynomial order, mesh, and time. In the absence of dissipation, coupling of the overlapping domains is destabilizing by allowing positive eigenvalues in the system to be integrated in time. This coupling can be stabilized in one space dimension by using the upwind numerical flux. To help provide additional dissipation, we introduce a novel penalty method that applies dissipation at arbitrary points within the overlap region and depends only on the difference between the solutions. We present numerical experiments in one space dimension to illustrate the implementation of the well-posed penalty formulation, and show spectral convergence of the approximations when sufficient dissipation is applied.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113508"},"PeriodicalIF":3.8,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1016/j.jcp.2024.113507
Wei Chen , Shumo Cui , Kailiang Wu , Tao Xiong
Physical solutions to the widely used Aw–Rascle–Zhang (ARZ) traffic model and the adapted pressure ARZ model should satisfy the positivity of density, the minimum and maximum principles with respect to the velocity v and other Riemann invariants. Many numerical schemes suffer from instabilities caused by violating these bounds, and the only existing bound-preserving (BP) numerical scheme (for ARZ model) is random, only first-order accurate, and not strictly conservative. This paper introduces arbitrarily high-order provably BP discontinuous Galerkin (DG) schemes for these two models, preserving all the aforementioned bounds except the maximum principle of v, which has been rigorously proven to conflict with the consistency and conservation of numerical schemes. Although the maximum principle of v is not directly enforced, we find that the strictly preserved maximum principle of another Riemann invariant w actually enforces an alternative upper bound on v. At the core of this work, analyzing and rigorously proving the BP property is a particularly nontrivial task: the Lax–Friedrichs (LF) splitting property, usually expected for hyperbolic conservation laws and employed to construct BP schemes, does not hold for these two models. To overcome this challenge, we formulate a generalized version of the LF splitting property, and prove it via the geometric quasilinearization approach (Wu and Shu, 2023 [47]). To suppress spurious oscillations in the DG solutions, we incorporate the oscillation-eliminating technique, recently proposed in (Peng et al., 2024 [34]), which is based on the solution operator of a novel damping equation. Several numerical examples are included to demonstrate the effectiveness, accuracy, and BP properties of our schemes, with applications to traffic simulations on road networks.
广泛使用的 Aw-Rascle-Zhang (ARZ) 交通模型和经调整的压力 ARZ 模型的物理解应满足密度的正性、速度 v 的最小和最大原则以及其他黎曼不变式。许多数值方案都存在因违反这些约束而导致的不稳定性，而现有的唯一一种（针对 ARZ 模型的）保边（BP）数值方案是随机的，只有一阶精度，而且不是严格保守的。本文针对这两个模型引入了任意高阶的可证明 BP 非连续伽勒金（DG）方案，保留了上述所有约束，但 v 的最大值原则除外，该原则已被严格证明与数值方案的一致性和守恒性相冲突。虽然 v 的最大值原则没有被直接执行，但我们发现严格保留的另一个黎曼不变式 w 的最大值原则实际上执行了 v 的另一个上界。在这项工作的核心中，分析和严格证明 BP 特性是一项特别非难的任务：Lax-Friedrichs（LF）分裂特性通常是对双曲守恒定律的预期，并用于构建 BP 方案，但在这两个模型中并不成立。为了克服这一难题，我们提出了 LF 分裂性质的广义版本，并通过几何准线性化方法加以证明（Wu 和 Shu，2023 [47]）。为了抑制 DG 解中的虚假振荡，我们采用了最近在（Peng 等，2024 [34]）中提出的振荡消除技术，该技术基于新型阻尼方程的解算子。我们还列举了几个数值示例来证明我们方案的有效性、准确性和 BP 特性，并将其应用于道路网络的交通模拟。
{"title":"Bound-preserving OEDG schemes for Aw–Rascle–Zhang traffic models on networks","authors":"Wei Chen , Shumo Cui , Kailiang Wu , Tao Xiong","doi":"10.1016/j.jcp.2024.113507","DOIUrl":"10.1016/j.jcp.2024.113507","url":null,"abstract":"<div><div>Physical solutions to the widely used Aw–Rascle–Zhang (ARZ) traffic model and the adapted pressure ARZ model should satisfy the positivity of density, the minimum and maximum principles with respect to the velocity <em>v</em> and other Riemann invariants. Many numerical schemes suffer from instabilities caused by violating these bounds, and the only existing bound-preserving (BP) numerical scheme (for ARZ model) is random, only first-order accurate, and not strictly conservative. This paper introduces arbitrarily high-order provably BP discontinuous Galerkin (DG) schemes for these two models, preserving all the aforementioned bounds except the maximum principle of <em>v</em>, which has been rigorously proven to conflict with the consistency and conservation of numerical schemes. Although the maximum principle of <em>v</em> is not directly enforced, we find that the strictly preserved maximum principle of another Riemann invariant <em>w</em> actually enforces an alternative upper bound on <em>v</em>. At the core of this work, analyzing and rigorously proving the BP property is a particularly nontrivial task: the Lax–Friedrichs (LF) splitting property, usually expected for hyperbolic conservation laws and employed to construct BP schemes, does not hold for these two models. To overcome this challenge, we formulate a generalized version of the LF splitting property, and prove it via the geometric quasilinearization approach (Wu and Shu, 2023 <span><span>[47]</span></span>). To suppress spurious oscillations in the DG solutions, we incorporate the oscillation-eliminating technique, recently proposed in (Peng et al., 2024 <span><span>[34]</span></span>), which is based on the solution operator of a novel damping equation. Several numerical examples are included to demonstrate the effectiveness, accuracy, and BP properties of our schemes, with applications to traffic simulations on road networks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113507"},"PeriodicalIF":3.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-16DOI: 10.1016/j.jcp.2024.113505
Shuxiang Chen , Jue Wang , Lei Zhang
In this work, we develop a mathematical framework on constructed general non-radiating sources of elastic waves governed by the Navier equation via the approach of Helmholtz decomposition and potential theory in elastodynamics. Our study offers a rather comprehensive analysis. We first provide a rigorous justification of the general non-radiating sources. Based on the complete destructive interference of external elastic fields generated by specific radiating sources, a general non-radiating elastic source is derived and shown to possess a hidden interior wave field. For an incident wave, targets remain invisible within non-radiating source regions, and the geometry and boundary conditions of obstacles can be very general, which holds significant practical implications. Moreover, we introduce an effective novel method for designing such generalized non-radiating sources. To avoid the complex structure, we propose to use radiating source overlay construction on specific nodes at the boundary of non-radiating regions construction and derive sharp error estimates to evaluate the cloaking performance. The proposed scheme is capable of nearly cloaking arbitrary obstacles with a high accuracy. Numerical verifications validate the precision of our analytical findings.
{"title":"Non-radiating sources in elastodynamics and their applications in the exterior cloaking","authors":"Shuxiang Chen , Jue Wang , Lei Zhang","doi":"10.1016/j.jcp.2024.113505","DOIUrl":"10.1016/j.jcp.2024.113505","url":null,"abstract":"<div><div>In this work, we develop a mathematical framework on constructed general non-radiating sources of elastic waves governed by the Navier equation via the approach of Helmholtz decomposition and potential theory in elastodynamics. Our study offers a rather comprehensive analysis. We first provide a rigorous justification of the general non-radiating sources. Based on the complete destructive interference of external elastic fields generated by specific radiating sources, a general non-radiating elastic source is derived and shown to possess a hidden interior wave field. For an incident wave, targets remain invisible within non-radiating source regions, and the geometry and boundary conditions of obstacles can be very general, which holds significant practical implications. Moreover, we introduce an effective novel method for designing such generalized non-radiating sources. To avoid the complex structure, we propose to use radiating source overlay construction on specific nodes at the boundary of non-radiating regions construction and derive sharp error estimates to evaluate the cloaking performance. The proposed scheme is capable of nearly cloaking arbitrary obstacles with a high accuracy. Numerical verifications validate the precision of our analytical findings.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113505"},"PeriodicalIF":3.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.jcp.2024.113503
Mike Gillard , Joanna Szmelter , Francesco Cocetta
Effective simulation of all-scale atmospheric flows – e.g., cloud-resolving global weather – involves semi-implicit integration of the non-hydrostatic compressible Euler equations under gravity on a rotating sphere. Such integrations depend on complex non-symmetric elliptic solvers. The condition number of the underlying sparse linear operator is , which necessitates bespoke operator preconditioning. This paper highlights the development and implementation on unstructured meshes of specialised preconditioners for the non-symmetric Krylov-subspace solver. These developments are set in the context of a massively-parallel high-performance computing environment, aimed at architectures evolving towards exascale.
The baroclinic instability benchmark bearing representative features relevant to numerical weather prediction (NWP) has been selected to study the performance of the preconditioning options. The reported results illustrate the improved performance with the new preconditioning options. In particular, the Jacobi based option, for the computational meshes tested in this study, provides an excellent time to solution improvement.
{"title":"Preconditioning elliptic operators in high-performance all-scale atmospheric models on unstructured meshes","authors":"Mike Gillard , Joanna Szmelter , Francesco Cocetta","doi":"10.1016/j.jcp.2024.113503","DOIUrl":"10.1016/j.jcp.2024.113503","url":null,"abstract":"<div><div>Effective simulation of all-scale atmospheric flows – e.g., cloud-resolving global weather – involves semi-implicit integration of the non-hydrostatic compressible Euler equations under gravity on a rotating sphere. Such integrations depend on complex non-symmetric elliptic solvers. The condition number of the underlying sparse linear operator is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mo>)</mo></math></span>, which necessitates bespoke operator preconditioning. This paper highlights the development and implementation on unstructured meshes of specialised preconditioners for the non-symmetric Krylov-subspace solver. These developments are set in the context of a massively-parallel high-performance computing environment, aimed at architectures evolving towards exascale.</div><div>The baroclinic instability benchmark bearing representative features relevant to numerical weather prediction (NWP) has been selected to study the performance of the preconditioning options. The reported results illustrate the improved performance with the new preconditioning options. In particular, the Jacobi based option, for the computational meshes tested in this study, provides an excellent time to solution improvement.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113503"},"PeriodicalIF":3.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-15DOI: 10.1016/j.jcp.2024.113506
Yingning Gao, Sizhu Zhou, Meiqiu Li
In the mechanical design of structures, traditional topology optimization methods involve numerous finite element iterative analyses, leading to a significant expenditure of computational resources. Therefore, the improved multi-scale gradient generative adversarial networks topology optimization technique is proposed. The topology optimization condition parameters are compressed into a low-dimensional latent space feature representation using the encoder, allowing the model to better extract features from these parameters. To speed up model training, the generator and discriminator networks use lightweight residual convolutional blocks. The hybrid attention mechanism extracts prominent region features from the topology optimization structure map. The model training process is guided by a multi-dimensional fusion loss function to enhance the quality of generated model samples. Finally, transferring the parameters of the low-resolution topology optimization model to the high-resolution model enables complete training on a limited amount of high-resolution topology optimization datasets. The experimental data on the low- and high-resolution topology optimization datasets demonstrate that, when compared to alternative methods, this method produces better-quality topology optimization structure maps. Additionally, it can generate high-resolution topology optimization structure maps in minimal time, enabling real-time topology optimization.
{"title":"Structural topology optimization based on deep learning","authors":"Yingning Gao, Sizhu Zhou, Meiqiu Li","doi":"10.1016/j.jcp.2024.113506","DOIUrl":"10.1016/j.jcp.2024.113506","url":null,"abstract":"<div><div>In the mechanical design of structures, traditional topology optimization methods involve numerous finite element iterative analyses, leading to a significant expenditure of computational resources. Therefore, the improved multi-scale gradient generative adversarial networks topology optimization technique is proposed. The topology optimization condition parameters are compressed into a low-dimensional latent space feature representation using the encoder, allowing the model to better extract features from these parameters. To speed up model training, the generator and discriminator networks use lightweight residual convolutional blocks. The hybrid attention mechanism extracts prominent region features from the topology optimization structure map. The model training process is guided by a multi-dimensional fusion loss function to enhance the quality of generated model samples. Finally, transferring the parameters of the low-resolution topology optimization model to the high-resolution model enables complete training on a limited amount of high-resolution topology optimization datasets. The experimental data on the low- and high-resolution topology optimization datasets demonstrate that, when compared to alternative methods, this method produces better-quality topology optimization structure maps. Additionally, it can generate high-resolution topology optimization structure maps in minimal time, enabling real-time topology optimization.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113506"},"PeriodicalIF":3.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号