Journal of Computational Physics最新文献

{"title":"An interface tracking method with triangle edge cuts","authors":"Mengdi Wang ,&nbsp;Matthew Cong ,&nbsp;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}

{"title":"Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems","authors":"David A. Kopriva ,&nbsp;Andrew R. Winters ,&nbsp;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}

{"title":"Bound-preserving OEDG schemes for Aw–Rascle–Zhang traffic models on networks","authors":"Wei Chen ,&nbsp;Shumo Cui ,&nbsp;Kailiang Wu ,&nbsp;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}

{"title":"Non-radiating sources in elastodynamics and their applications in the exterior cloaking","authors":"Shuxiang Chen ,&nbsp;Jue Wang ,&nbsp;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}

{"title":"Preconditioning elliptic operators in high-performance all-scale atmospheric models on unstructured meshes","authors":"Mike Gillard ,&nbsp;Joanna Szmelter ,&nbsp;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}

{"title":"Structural topology optimization based on deep learning","authors":"Yingning Gao,&nbsp;Sizhu Zhou,&nbsp;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}

{"title":"Multi-body mesh deformation using a multi-level localized dual-restricted radial basis function interpolation","authors":"Hong Deng ,&nbsp;Haifeng Hong ,&nbsp;Chunsheng Nie ,&nbsp;Hong Fang ,&nbsp;Liang Xie","doi":"10.1016/j.jcp.2024.113502","DOIUrl":"10.1016/j.jcp.2024.113502","url":null,"abstract":"<div><div>Multi-body dynamic problems with moving boundaries are prevalent in the computational fluid dynamics. In these problems, the original mesh is unsuitable for subsequent solution steps and is needed to be deformed. The radial basis function (RBF) interpolation is a common algorithm for the mesh deformation task. However, the multi-body mesh may contain numerous individuals and volume nodes, which will harm the computational efficiency. In order to optimize this process, we propose a new method for the mesh deformation of the multi-body configuration. In this new approach, each individual is deformed separately. Thus the global problem is decomposed into a series of local mesh deformation problems. As the computational cost to construct the interpolation system in RBF algorithm is proportional to the cube of the number of support points on the surface, converting it into multiple local mesh deformation problems can effectively reduce the CPU cost. To treat each local problem, we employ a dual-restricted RBF interpolation technique which could avoid the influence of moving individual on the other individuals. This new localized approach effectively improves the computational efficiency to construct the interpolation system but sometimes will increase the CPU cost of the mesh updating procedure. To avoid this drawback, the existed multi-level restricted RBF strategy is coupled with the new localized method to further reduce the CPU cost to update the mesh. The combination of the two techniques could enhance their advantages and avoid their drawbacks. Some numerical examples have demonstrated the abilities of the new algorithm. For instance, in the case of the three-dimensional birds flock, the CPU time to construct the interpolation system and deform the volume mesh was respectively reduced by three and two orders of magnitude compared to the global single-level method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113502"},"PeriodicalIF":3.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442030","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}

{"title":"The jump filter in the discontinuous Galerkin method for hyperbolic conservation laws","authors":"Lei Wei ,&nbsp;Lingling Zhou ,&nbsp;Yinhua Xia","doi":"10.1016/j.jcp.2024.113498","DOIUrl":"10.1016/j.jcp.2024.113498","url":null,"abstract":"<div><div>When simulating hyperbolic conservation laws with discontinuous solutions, high-order linear numerical schemes often produce undesirable spurious oscillations. In this paper, we propose a jump filter within the discontinuous Galerkin (DG) method to mitigate these oscillations. This filter operates locally based on jump information at cell interfaces, targeting high-order polynomial modes within each cell. Besides its localized nature, our proposed filter preserves key attributes of the DG method, including conservation, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stability, and high-order accuracy. We also explore its compatibility with other damping techniques, and demonstrate its seamless integration into a hybrid limiter. In scenarios featuring strong shock waves, this hybrid approach, incorporating this jump filter as the low-order limiter, effectively suppresses numerical oscillations while exhibiting low numerical dissipation. Additionally, the proposed jump filter maintains the compactness of the DG scheme, which greatly aids in efficient parallel computing. Moreover, it boasts an impressively low computational cost, given that no characteristic decomposition is required and all computations are confined to physical space. Numerical experiments validate the effectiveness and performance of our proposed scheme, confirming its accuracy and shock-capturing capabilities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113498"},"PeriodicalIF":3.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433048","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}

{"title":"General synthetic iterative scheme for non-equilibrium dense gas flows","authors":"Zheng Shi,&nbsp;Yanbing Zhang,&nbsp;Lei Wu","doi":"10.1016/j.jcp.2024.113501","DOIUrl":"10.1016/j.jcp.2024.113501","url":null,"abstract":"<div><div>The recently-developed general synthetic iterative scheme (GSIS), which is tailored for non-equilibrium dilute gas, has been extended to find the steady-state solutions of the non-equilibrium dense gas flows based on the Shakhov-Enskog model, resolving the problems of slow convergence and requirement of ultra-fine grids in near-continuum flows that exist in the conventional iterative scheme. The key ingredient of GSIS is the tight coupling of the mesoscopic kinetic equation and the macroscopic synthetic equations that are exactly derived from the kinetic equation. On the one hand, high-order terms computed from the velocity distribution function provide the higher-order constitutive relations describing the non-equilibrium effects for the macroscopic synthetic equations. On the other hand, the macroscopic quantities obtained from the macroscopic synthetic equations are used to guide the evolution of the velocity distribution function in the kinetic equation. The efficiency and accuracy of GSIS are demonstrated in several test cases, including the shock wave passing through a cylinder and the pressure-driven dense gas flows passing through parallel plates and porous media. The effects of denseness are analyzed in a wide range of gas rarefaction.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113501"},"PeriodicalIF":3.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441919","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}

{"title":"A semi-analytical transient undisturbed velocity correction scheme for wall-bounded two-way coupled Euler-Lagrange simulations","authors":"Akshay Chandran ,&nbsp;Fabien Evrard ,&nbsp;Berend van Wachem","doi":"10.1016/j.jcp.2024.113496","DOIUrl":"10.1016/j.jcp.2024.113496","url":null,"abstract":"<div><div>Force closure models employed in Euler-Lagrange (EL) point-particle simulations rely on the accurate estimation of the undisturbed fluid velocity at the particle center to evaluate the fluid forces on each particle. Due to the self-induced velocity disturbance of the particle in the fluid, two-way coupled EL simulations only have access to the disturbed velocity. The undisturbed velocity can be recovered if the particle-generated disturbance is estimated. In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof <span><span>[1]</span></span>) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed in the Stokes regime on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"520 ","pages":"Article 113496"},"PeriodicalIF":3.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433047","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}