Journal of Computational Physics最新文献_第10页

A positivity-preserving Active Flux method for the Vlasov-Poisson system

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-20 DOI: 10.1016/j.jcp.2024.113693

Yanick Kiechle, Erik Chudzik, Christiane Helzel

引用次数: 0

Projection based summation-by-parts methods, embeddings and the pseudoinverse

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-20 DOI: 10.1016/j.jcp.2024.113689

Pelle Olsson , Gustav Eriksson , Ken Mattsson

{"title":"Projection based summation-by-parts methods, embeddings and the pseudoinverse","authors":"Pelle Olsson , Gustav Eriksson , Ken Mattsson","doi":"10.1016/j.jcp.2024.113689","DOIUrl":"10.1016/j.jcp.2024.113689","url":null,"abstract":"<div><div>In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and practical implications; the theory applies even if the boundary operator is rank deficient, or near rank deficient. If desired, the pseudoinverse can be implemented directly using standard tools like Matlab. We also introduce a new and simplified version of the semidiscrete approximation of the linear PDE system, which completely avoids taking the time derivative of the boundary data, cf. <span><span>[1]</span></span>. The 2D stability results of the projection method in <span><span>[2]</span></span> are extended to nondiagonal summation-by-parts norms, which introduce boundary terms that require special attention in case of the projection method (equivalence of diagonal and nondiagonal boundary norms), see <span><span>[3]</span></span> for details. Another key result is the extension of summation-by-parts operators to multidomains by means of carefully crafted embedding operators. No extra numerical boundary conditions are required at the grid interfaces. The pseudoinverse allows for a compact representation of these multiblock operators, which preserves all relevant properties of the single-block operators. The embedding operators can be constructed for multiple space dimensions. Numerical results for the two-dimensional Maxwell's equations are presented, and they show very good agreement with theory.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113689"},"PeriodicalIF":3.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132205","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}

引用次数: 0

A sixth-order finite difference model coupled with the matched interface and boundary method for underwater acoustic propagation simulations

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-19 DOI: 10.1016/j.jcp.2024.113694

Wei Liu, Guojun Xu, Xinghua Cheng, Yongxian Wang

{"title":"A sixth-order finite difference model coupled with the matched interface and boundary method for underwater acoustic propagation simulations","authors":"Wei Liu, Guojun Xu, Xinghua Cheng, Yongxian Wang","doi":"10.1016/j.jcp.2024.113694","DOIUrl":"10.1016/j.jcp.2024.113694","url":null,"abstract":"<div><div>To improve the accuracy of seabed processing in finite difference (FD) models for ocean acoustic field simulations, a nominal fifth-order matched interface and boundary (MIB) method is developed, which can automatically determine the highest achievable order of accuracy near boundaries or complex seabed interfaces. Since the MIB method can separate the discretization of partial differential equations from the implementation of interface conditions, a sixth-order FD scheme is also developed to discretize the acoustic Helmholtz equation coupled with the fifth-order MIB method. This FD scheme is applied to each grid line segment whose end nodes are either the physical boundary nodes or the MIB ghost nodes, and the FD scheme near the MIB ghost nodes is designed to be consistent with that at the boundary nodes. Furthermore, the accuracy of the present FD model has been numerically verified using two- and three-dimensional acoustic benchmarks, including a newly designed C-shaped atoll acoustic propagation case. Compared with the fourth-order FD model using the smoothing approximation method to handle the seabed, which requires a <em>PPW</em> (points per wavelength) of 30∼60 for the accurate computation of a general non-flat ocean acoustic field, the proposed sixth-order FD model coupled with the MIB method requires only a <em>PPW</em> of 8 with the comparable solution accuracy, leading to a significant improvement in the computational efficiency of three-dimensional ocean acoustic field simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113694"},"PeriodicalIF":3.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132203","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}

引用次数: 0

Input gradient annealing neural network for solving Fokker-Planck equations with low temperature

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-19 DOI: 10.1016/j.jcp.2024.113688

Liangkai Hang, Dan Hu, Zhi-Qin John Xu

引用次数: 0

Scalable resolvent analysis for three-dimensional flows

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-19 DOI: 10.1016/j.jcp.2024.113695

Ali Farghadan , Eduardo Martini , Aaron Towne

{"title":"Scalable resolvent analysis for three-dimensional flows","authors":"Ali Farghadan , Eduardo Martini , Aaron Towne","doi":"10.1016/j.jcp.2024.113695","DOIUrl":"10.1016/j.jcp.2024.113695","url":null,"abstract":"<div><div>Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and other large systems has been hindered by the computational cost of computing resolvent modes. In particular, the CPU and memory requirements of state-of-the-art algorithms scale poorly with the problem dimension, <em>i.e.</em>, the number of discrete degrees of freedom. In this paper, we present RSVD-Δ<em>t</em>, a novel approach that overcomes these limitations by combining randomized singular value decomposition with an optimized time-stepping method for computing the action of the resolvent operator. Critically, the CPU cost and memory requirements of the algorithm scale linearly with the problem dimension. We develop additional strategies to minimize these costs and control errors. We validate the algorithm using a Ginzburg-Landau test problem and demonstrate RSVD-Δ<em>t</em>'s low cost and improved scaling using a three-dimensional discretization of a turbulent jet. Lastly, we use it to study the impact of low-speed streaks on the development of Kelvin-Helmholtz wavepackets in the jet via secondary stability analysis, a problem that would have been intractable using previous algorithms.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113695"},"PeriodicalIF":3.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132175","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}

引用次数: 0

Sapphire++: A particle transport code combining a spherical harmonic expansion and the discontinuous Galerkin method

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-19 DOI: 10.1016/j.jcp.2024.113690

Nils W. Schween, Florian Schulze, Brian Reville

引用次数: 0

Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-19 DOI: 10.1016/j.jcp.2024.113669

Liu Liu, Yating Wang, Xueyu Zhu, Zhenyi Zhu

{"title":"Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems","authors":"Liu Liu, Yating Wang, Xueyu Zhu, Zhenyi Zhu","doi":"10.1016/j.jcp.2024.113669","DOIUrl":"10.1016/j.jcp.2024.113669","url":null,"abstract":"<div><div>In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational challenges of conventional numerical methods and multiple scales of the model. To guarantee the network can operate uniformly in different regimes, it is desirable to carry the Asymptotic-Preservation (AP) property in the learning process. In a micro-macro decomposition framework, we design such an AP formulation of loss function. The convergence analysis of both the loss function and its neural network is shown, based on the Universal Approximation Theorem and hypocoercivity theory of the model equation. We show a series of numerical tests for forward and inverse problems of both the semiconductor Boltzmann and the Boltzmann-Poisson system to validate the effectiveness of our proposed method, which addresses the significance of the AP property when dealing with inverse problems of multiscale Boltzmann equations especially when only sparse or partially observed data are available.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113669"},"PeriodicalIF":3.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150620","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}

引用次数: 0

Undisturbed velocity recovery with transient and weak inertia effects in volume-filtered simulations of particle-laden flows

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-18 DOI: 10.1016/j.jcp.2024.113684

Fabien Evrard , Akshay Chandran , Ricardo Cortez , Berend van Wachem

{"title":"Undisturbed velocity recovery with transient and weak inertia effects in volume-filtered simulations of particle-laden flows","authors":"Fabien Evrard , Akshay Chandran , Ricardo Cortez , Berend van Wachem","doi":"10.1016/j.jcp.2024.113684","DOIUrl":"10.1016/j.jcp.2024.113684","url":null,"abstract":"<div><div>In volume-filtered Euler-Lagrange simulations of particle-laden flows, the fluid forces acting on a particle are estimated using reduced models, which rely on the knowledge of the local <em>undisturbed flow</em> for that particle. Since the two-way coupling between the particle and the fluid creates a local flow perturbation, the filtered fluid velocity interpolated to the particle location must be corrected prior to estimating the fluid forces, so as to subtract the contribution of this perturbation and recover the local undisturbed flow with good accuracy. In this manuscript, we present a new model for estimating a particle's self-induced flow disturbance that accounts for its transient development and for inertial effects related to finite particle Reynolds numbers. The model also does not require the direction of the momentum feedback to align with the direction of the particle's relative velocity, allowing force contributions other than the steady drag force to be considered. It is based upon the linearization of the volume-filtered equations governing the particle's self-induced flow disturbance, such that their solution can be expressed as a linear combination of regularized transient Stokeslet contributions. Tested on a range of numerical cases, the model is shown to consistently estimate the particle's self-induced flow disturbance with high accuracy both in steady and highly transient flow environments, as well as for finite particle Reynolds numbers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113684"},"PeriodicalIF":3.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150618","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}

引用次数: 0

Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-18 DOI: 10.1016/j.jcp.2024.113686

Alexander Rothkopf , W.A. Horowitz , Jan Nordström

{"title":"Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems","authors":"Alexander Rothkopf , W.A. Horowitz , Jan Nordström","doi":"10.1016/j.jcp.2024.113686","DOIUrl":"10.1016/j.jcp.2024.113686","url":null,"abstract":"<div><div>We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is formulated in an abstract parameter space and an energy density scale associated with the space-time coordinates separates the dynamics of the coordinate maps and of the propagating fields. Treating coordinates as dependent, i.e. dynamical quantities, offers the opportunity to discretize the action while retaining all space-time symmetries and also provides the basis for automatic adaptive mesh refinement (AMR). The presence of unbroken space-time symmetries after discretization also ensures that the associated continuum Noether charges remain exactly conserved. The presence of coordinate maps in addition provides new freedom in the choice of boundary conditions. An explicit numerical example for wave propagation in <span><math><mn>1</mn><mo>+</mo><mn>1</mn></math></span> dimensions is provided, using recently developed regularized summation-by-parts finite difference operators.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113686"},"PeriodicalIF":3.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132204","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}

引用次数: 0

Ensemble variational Fokker-Planck methods for data assimilation

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2024-12-18 DOI: 10.1016/j.jcp.2024.113681

Amit N. Subrahmanya, Andrey A. Popov, Adrian Sandu

{"title":"Ensemble variational Fokker-Planck methods for data assimilation","authors":"Amit N. Subrahmanya, Andrey A. Popov, Adrian Sandu","doi":"10.1016/j.jcp.2024.113681","DOIUrl":"10.1016/j.jcp.2024.113681","url":null,"abstract":"<div><div>Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itô process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itô process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean-Vlasov-Itô processes. The effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz'63, Lorenz'96 and the quasi-geostrophic equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113681"},"PeriodicalIF":3.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150617","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}

引用次数: 0