Journal of Computational Physics最新文献

{"title":"Mesh optimization for the virtual element method: How small can an agglomerated mesh become?","authors":"Tommaso Sorgente ,&nbsp;Fabio Vicini ,&nbsp;Stefano Berrone ,&nbsp;Silvia Biasotti ,&nbsp;Gianmarco Manzini ,&nbsp;Michela Spagnuolo","doi":"10.1016/j.jcp.2024.113552","DOIUrl":"10.1016/j.jcp.2024.113552","url":null,"abstract":"<div><div>We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups of elements are agglomerated to optimize the global mesh quality. A user-set parameter regulates the percentage of mesh elements, and consequently of faces, edges, and vertices, to be removed. This significantly reduces the total number of degrees of freedom associated with a discrete problem defined over the mesh with the VEM, particularly for high-order formulations. We show how the VEM convergence rate is preserved in the optimized meshes, and the approximation errors are comparable with those obtained with the original ones. We observe that the optimization has a regularization effect over low-quality meshes, removing the most pathological elements. In such cases, these “badly-shaped” elements yield a system matrix with very large condition number, which may cause the VEM to diverge, while the optimized meshes lead to convergence. We conclude by showing how the optimization of a real CAD model can be used effectively in the simulation of a time-dependent problem.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113552"},"PeriodicalIF":3.8,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587081","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":"A pseudo-spectral time-domain method for ultrasound wave propagation in soft biological tissue","authors":"Carlos Spa,&nbsp;Josep de la Puente","doi":"10.1016/j.jcp.2024.113527","DOIUrl":"10.1016/j.jcp.2024.113527","url":null,"abstract":"<div><div>We introduce a Pseudo-Spectral Time-Domain (PSTD) method to simulate acoustic wave propagation in soft biological tissues, incorporating frequency-dependent power-law absorption and dispersion. A comprehensive Von-Neumann stability analysis highlights the influence of material parameters, time step, and spatial discretization on numerical stability. Validation is conducted through one-dimensional tests comparing numerical results with theoretical predictions for dispersion and attenuation, and two-dimensional simulations benchmarked against analytical Green's functions. Additionally, forward simulations on a breast phantom model using typical ultrasound parameters demonstrate the method's accuracy in modeling wave attenuation and dispersion. This PSTD method provides a reliable and efficient computational tool for advanced biomedical ultrasonics research.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113527"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553769","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":"Entropy-stable in- and outflow boundary conditions for the compressible Euler equations","authors":"Magnus Svärd","doi":"10.1016/j.jcp.2024.113543","DOIUrl":"10.1016/j.jcp.2024.113543","url":null,"abstract":"<div><div>We propose general inflow and outflow boundary conditions for the Euler equations and prove that they are both linearly well-posed and lead to entropy-bounded solutions. Furthermore, we provide numerical boundary fluxes that enforce these boundary conditions and prove entropy stability for (entropy-stable) finite-volume schemes. The method is generalisable to most entropy-stable summation-by-parts schemes. Finally, we demonstrate their performance in various flow regimes using a second-order accurate entropy-stable finite-volume scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113543"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561368","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":"Reduced order modeling of turbulent reacting flows on low-rank matrix manifolds","authors":"Aidyn Aitzhan ,&nbsp;Arash G. Nouri ,&nbsp;Peyman Givi ,&nbsp;Hessam Babaee","doi":"10.1016/j.jcp.2024.113549","DOIUrl":"10.1016/j.jcp.2024.113549","url":null,"abstract":"<div><div>A new low-rank approximation, referred to as time-dependent principal component analysis (t-PCA), is developed for reduced-order modeling (ROM) of scalar transport in turbulent reactive flows. In t-PCA, the evolution of the composition matrix is constrained to a low-rank matrix manifold, similar to that in standard PCA. Specifically, the t-PCA approximates the composition matrix through the multiplication of two thin, time-dependent matrices that represent spatial and composition subspaces. The evolution equations for these subspaces are derived by projecting the composition transport equation onto the tangent space of the low-rank matrix manifold. While the evolution equations for the spatial subspace in both PCA and t-PCA are similar, there are differences in how the composition subspace is obtained: (i) In t-PCA, the composition subspace is time-dependent, whereas in PCA, it is static. (ii) The t-PCA does not require any prior data, and an evolution equation for the composition subspace is derived. In PCA, the composition subspace is obtained from data. The t-PCA can be regarded as an on-the-fly low-rank approximation that can adapt to changes in the flow instantaneously. It is shown that the low-rank t-PCA approximations achieve residual levels lower than those obtained via PCA. For demonstrations and a comparative assessment of the ROMs, simulations are conducted of a non-premixed CO/H₂ flame in a temporally evolving jet. Two cases are considered, based on the mechanisms previously suggested for combustion kinetics of this flame: (i) the GRI-Mech 3.0 model involving 53 species for a two-dimensional flame, (ii) the skeletal syngas model involving 11 species for a three-dimensional turbulent flame. The results are appraised via <em>a posteriori</em> comparisons against data generated via full-rank direct numerical simulation (DNS) of the same flame, and also with the PCA-reduced data from the DNS. It is shown that t-PCA yields excellent predictions of various features of the thermo-chemistry field.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113549"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578700","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":"An asymptotic-preserving and exactly mass-conservative semi-implicit scheme for weakly compressible flows based on compatible finite elements","authors":"E. Zampa ,&nbsp;M. Dumbser","doi":"10.1016/j.jcp.2024.113551","DOIUrl":"10.1016/j.jcp.2024.113551","url":null,"abstract":"<div><div>We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an <span><math><mi>H</mi><mo>(</mo><mrow><mi>div</mi></mrow><mo>)</mo></math></span>-conforming space, ensuring exact pointwise mass conservation at the discrete level. We use an explicit discontinuous Galerkin-based discretization for the nonlinear convective terms, while treating the pressure and viscous terms implicitly, so that the CFL condition depends only on the fluid velocity. To handle shocks and damp spurious oscillations in the compressible regime, we incorporate an <em>a posteriori</em> limiter that employs artificial viscosity and is based on a discrete maximum principle. By using hybridization, the final algorithm requires solving only symmetric positive definite linear systems. As the Mach number approaches zero and the density remains constant, the method naturally converges to an <span><math><mi>H</mi><mo>(</mo><mrow><mi>div</mi></mrow><mo>)</mo></math></span>-based discretization of the incompressible Navier-Stokes equations in the vorticity-velocity-pressure formulation. Several numerical tests validate the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113551"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578703","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":"Democratizing uncertainty quantification","authors":"Linus Seelinger ,&nbsp;Anne Reinarz ,&nbsp;Mikkel B. Lykkegaard ,&nbsp;Robert Akers ,&nbsp;Amal M.A. Alghamdi ,&nbsp;David Aristoff ,&nbsp;Wolfgang Bangerth ,&nbsp;Jean Bénézech ,&nbsp;Matteo Diez ,&nbsp;Kurt Frey ,&nbsp;John D. Jakeman ,&nbsp;Jakob S. Jørgensen ,&nbsp;Ki-Tae Kim ,&nbsp;Benjamin M. Kent ,&nbsp;Massimiliano Martinelli ,&nbsp;Matthew Parno ,&nbsp;Riccardo Pellegrini ,&nbsp;Noemi Petra ,&nbsp;Nicolai A.B. Riis ,&nbsp;Katherine Rosenfeld ,&nbsp;Robert Scheichl","doi":"10.1016/j.jcp.2024.113542","DOIUrl":"10.1016/j.jcp.2024.113542","url":null,"abstract":"<div><div>Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale.</div><div>In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113542"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660646","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":"Dynamically regularized Lagrange multiplier schemes with energy dissipation for the incompressible Navier-Stokes equations","authors":"Cao-Kha Doan ,&nbsp;Thi-Thao-Phuong Hoang ,&nbsp;Lili Ju ,&nbsp;Rihui Lan","doi":"10.1016/j.jcp.2024.113550","DOIUrl":"10.1016/j.jcp.2024.113550","url":null,"abstract":"<div><div>In this paper, we present efficient numerical schemes based on the Lagrange multiplier approach for the Navier-Stokes equations. By introducing a dynamic equation (involving the kinetic energy, the Lagrange multiplier, and a regularization parameter), we form a new system which incorporates the energy evolution process but is still equivalent to the original equations. Such nonlinear system is then discretized in time based on the backward differentiation formulas, resulting in a dynamically regularized Lagrange multiplier (DRLM) method. First- and second-order DRLM schemes are derived and shown to be unconditionally energy stable with respect to the original variables. The proposed schemes require only the solutions of two linear Stokes systems and a scalar quadratic equation at each time step. Moreover, with the introduction of the regularization parameter, the Lagrange multiplier can be uniquely determined from the quadratic equation, even with large time step sizes, without affecting accuracy and stability of the numerical solutions. Fully discrete energy stability is also proved with the Marker-and-Cell (MAC) discretization in space. Various numerical experiments in two and three dimensions verify the convergence and energy dissipation as well as demonstrate the accuracy and robustness of the proposed DRLM schemes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113550"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578702","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":"IGA-Graph-Net: Isogeometric analysis-reuse method based on graph neural networks for topology-consistent models","authors":"Gang Xu ,&nbsp;Jin Xie ,&nbsp;Weizhen Zhong ,&nbsp;Masahiro Toyoura ,&nbsp;Ran Ling ,&nbsp;Jinlan Xu ,&nbsp;Renshu Gu ,&nbsp;Charlie C.L. Wang ,&nbsp;Timon Rabczuk","doi":"10.1016/j.jcp.2024.113544","DOIUrl":"10.1016/j.jcp.2024.113544","url":null,"abstract":"<div><div>This paper introduces a novel isogeometric analysis-reuse framework called IGA-Graph-Net, which combines <em>Graph Neural Networks</em> with <em>Isogeometric Analysis</em> to overcome the limitations of Convolutional Neural Networks when dealing with B-spline data. Our network architecture incorporates ResNetV2 and PointTransformer for enhanced performance. We transformed the dataset creation process from using <em>Convolutional Neural Networks</em> to <em>Graph Neural Networks</em>. Additionally, we proposed a new loss function tailored for Dirichlet boundary conditions and enriched the input features. Several examples are presented to demonstrate the effectiveness of the proposed framework. In terms of accuracy when tested on the same set of <em>partial differential equation</em> data, our framework demonstrates significant improvements compared to the reuse method based on Convolutional Neural Networks for Isogeometric Analysis on topology-consistent geometries with complex boundaries.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113544"},"PeriodicalIF":3.8,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578699","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":"Particulate transport in porous media at pore-scale. Part 1: Unresolved-resolved four-way coupling CFD-DEM","authors":"Laurez Maya Fogouang ,&nbsp;Laurent André ,&nbsp;Cyprien Soulaine","doi":"10.1016/j.jcp.2024.113540","DOIUrl":"10.1016/j.jcp.2024.113540","url":null,"abstract":"<div><div>Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is a powerful approach to simulate particulate flow in porous media at the pore-scale, and hence decipher the complex interplay between particle transport and retention. Two separate CFD-DEM approaches are commonly used in the literature: the unresolved (particle smaller than the grid cell size) and the resolved (particle bigger than the grid cell size) approach. In this paper, we propose a novel CFD-DEM coupling approach that combines both unresolved and resolved coupling. Our new modeling technique allows for the simulation of particulate flows in complex pore morphology characteristic of porous materials. It relies on an efficient searching strategy to find grid cells covered by the particles and on an appropriate calculation of the fluid-solid momentum exchange term. The robustness and efficiency of the computational model are demonstrated using cases for which reference solutions – analytical or experimental – exist. The new unresolved-resolved four-way coupling CFD-DEM is used to investigate pore-clogging and permeability reduction due to the sieving and bridging of particles.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113540"},"PeriodicalIF":3.8,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560648","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":"Quantifying the checkerboard problem to reduce numerical dissipation","authors":"J.A. Hopman ,&nbsp;D. Santos ,&nbsp;À. Alsalti-Baldellou ,&nbsp;J. Rigola ,&nbsp;F.X. Trias","doi":"10.1016/j.jcp.2024.113537","DOIUrl":"10.1016/j.jcp.2024.113537","url":null,"abstract":"<div><div>This work provides a comprehensive exploration of various methods in solving incompressible flows using a projection method, and their relation to the occurrence and management of checkerboard oscillations. It employs an algebraic symmetry-preserving framework, clarifying the derivation and implementation of discrete operators while also addressing the associated numerical errors. The lack of a proper definition for the checkerboard problem is addressed by proposing a physics-based coefficient. This coefficient, rooted in the disparity between the compact- and wide-stencil Laplacian operators, is able to quantify oscillatory solution fields with a physics-based, global, normalised, non-dimensional value. The influence of mesh and time-step refinement on the occurrence of checkerboarding is highlighted. Therefore, single measurements using this coefficient should be considered with caution, as the value presents little use without any context and can either suggest mesh refinement or use of a different solver. In addition, an example is given on how to employ this coefficient, by establishing a negative feedback between the level of checkerboarding and the inclusion of a pressure predictor, to dynamically balance the checkerboarding and numerical dissipation. This method is tested for laminar and turbulent flows, demonstrating its capabilities in obtaining this dynamical balance, without requiring user input. The method is able to achieve low numerical dissipation in absence of oscillations or diminish oscillation on skew meshes, while it shows minimal loss in accuracy for a turbulent test case. Despite its advantages, the method exhibits a slight decrease in the second-order relation between time-step size and pressure error, suggesting that other feedback mechanisms could be of interest.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113537"},"PeriodicalIF":3.8,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560645","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}