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Comparative study of WCSPH, EISPH and Explicit Incompressible-Compressible SPH (EICSPH) for Multi-Phase Flow with High Density Difference J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-12 Hee Sang Yoo, Young Beom Jo, Eung Soo Kim
This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian-Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and
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Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-12 Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and
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Correcting model misspecification in physics-informed neural networks (PINNs) J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-09 Zongren Zou, Xuhui Meng, George Em Karniadakis
Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed neural networks (PINNs) have also been employed to learn governing equations given data across diverse scientific disciplines, e.g., in biology and fluid dynamics.
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Efficient implementation of complex equations of state in a high-order framework J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-08 E. Mantecca, A. Colombo, A. Ghidoni, G. Noventa
In the last decades, the interest in non-ideal compressible fluid dynamics (NICFD) flows and high-order accurate numerical methods, such as discontinuous Galerkin (dG), has quickly grown. In fact, advanced simulation capabilities are of paramount importance to develop new sustainable technologies with higher efficiency and low environmental impact, and to decrease the use of expensive experimental
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Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-08 Eleni D. Koronaki, Nikolaos Evangelou, Cristina P. Martin-Linares, Edriss S. Titi, Ioannis G. Kevrekidis
This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of Approximate Inertial Manifolds (AIMs); the particular motivation is the so-called post-processing Galerkin method of Garcia-Archilla, Novo and Titi. Its applicability
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A unified stochastic particle method with spatiotemporal adaptation for simulating multiscale gas flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-08 Kaikai Feng, Ziqi Cui, Peng Tian, Jun Zhang
Recently, the Unified Stochastic Particle (USP) method has emerged as a promising approach for multiscale particle simulations, tailored specifically for non-equilibrium gas flow scenarios. However, in typical simulations of multiscale flow fields, the time step and grid size of the original USP method remain constrained by the smallest spatiotemporal scale of local flow field, limiting its true multiscale
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Robust and accurate Roe-type Riemann solver with compact stencil: Rotated-RoeM scheme J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-08 Seongyu Choi, Donguk Kim, Jaehyong Park, Jin Seok Park
In this study, we aim to develop a robust and accurate Riemann solver to resolve strong shock waves with compact stencil information by applying the rotated hybrid concept to the RoeM scheme. The original RoeM scheme offers good robustness from the perspective of avoiding shock instability, also called the carbuncle phenomenon, in hypersonic flows by introducing Mach-number-based functions. These functions
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Cell-centered indirect Arbitrary Lagrangian-Eulerian numerical strategy for solving 3D gas dynamics equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-08 S. Guisset, G. Damour, J. Breil
Solving the Euler equations under the Lagrangian formalism enables to simulate various complex engineering applications. However, the use of this formalism can lead to significant mesh deformations as the mesh follows the fluid velocity. The mesh quality may be considerably deteriorated requiring a regularization procedure. In the present document, it is shown that the ideas presented by and (2016)
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Canonical variables based numerical schemes for hybrid plasma models with kinetic ions and massless electrons J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-07 Yingzhe Li, Florian Holderied, Stefan Possanner, Eric Sonnendrücker
We study the canonical variables based numerical schemes of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented with the vector potentials in different gauges and the distribution functions depending on canonical momentum (not velocity), which constitutes a pair of canonical variables with the position variable. Particle-in-cell methods
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Joint-mode diffusion analysis of discontinuous Galerkin methods: Towards superior dissipation estimates for nonlinear problems and implicit LES J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-07 R.C. Moura, L.D. Fernandes, A.F.C. da Silva, S.J. Sherwin
We present a new linear eigensolution analysis technique that provides superior estimates of dissipation distribution in wavenumber space for the discontinuous Galerkin (DG) method. The technique builds upon traditional dispersion-diffusion analyses that have been applied to spectral/hp element methods, but in particular is an improvement upon the non-modal eigenanalysis approach proposed by Fernandez
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Efficient and stable SAV-based methods for gradient flows arising from deep learning J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-07 Ziqi Ma, Zhiping Mao, Jie Shen
The optimization algorithm plays an important role in deep learning and significantly affects the stability and efficiency of the training process, and consequently the accuracy of the neural network approximation. A suitable (initial) learning rate is crucial for the optimization algorithm in deep learning. However, a small learning rate is usually needed to guarantee the convergence of the optimization
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Robust domain decomposition methods for high-contrast multiscale problems on irregular domains with virtual element discretizations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-07 Juan G. Calvo, Juan Galvis
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling coefficients with high-contrast and multiscale properties, and ii) accommodating irregular domains in the original problem, the coarse mesh, and the subdomain partition.
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Multi-component electro-hydro-thermodynamic model with phase-field method. I. Dielectric J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-07 Haodong Zhang, Fei Wang, Britta Nestler
We derive a multi-component electro-hydro-thermodynamic (EHTD) model for both leaky and perfect dielectric materials via the principle of energy dissipation. Differing from previous electro-hydrodynamic (EHD) models focusing on fluid mechanics, the electrochemical potential expression is revised and the electric field related term is added to the mass and momentum conservation equations. Resulting
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Multi-species kinetic-fluid coupling for high-energy density simulations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-05 Thomas Chuna, Irina Sagert, Michael S. Murillo, Jeffrey R. Haack
Many physics problems are subject to a mix of continuum and non-equilibrium flows or conditions where one transition into the other, as a function of time and/or space. Numerically, such flows could be described with a purely kinetic method which, in the limit of small particle mean free paths, reproduces a continuum regime. However, from a computational perspective, such approaches are usually very
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A positivity preserving and oscillation-free entropy stable discontinuous Galerkin scheme for the reactive Euler equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-05 Hujian Zuo, Weifeng Zhao, Ping Lin
The reactive Euler equations are a basic model for fluid flows with chemical reactions. In this work, we construct a high order positivity preserving and oscillation-free entropy stable discontinuous Galerkin (DG) scheme for the reactive Euler equations. The main ingredients of the scheme include (i) entropy preserving and entropy stable fluxes to achieve entropy stability, (ii) artificial damping
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Gas-kinetic scheme for partially ionized plasma in hydrodynamic regime J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-05 Zhigang Pu, Chang Liu, Kun Xu
Most plasmas are only partially ionized. To better understand the dynamics of these plasmas, the behaviors of a mixture of neutral species and plasma in ideal magnetohydrodynamic states are investigated. The current approach is about the construction of coupled kinetic models for the neutral gas, electron, and proton, and the development of the corresponding gas-kinetic scheme (GKS) for the solution
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Zero coordinate shift: Whetted automatic differentiation for physics-informed operator learning J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-02 Kuangdai Leng, Mallikarjun Shankar, Jeyan Thiyagalingam
Automatic differentiation (AD) is a critical step in physics-informed machine learning, required for computing the high-order derivatives of network output w.r.t. coordinates of collocation points. In this paper, we present a novel and lightweight algorithm to conduct AD for physics-informed operator learning, which we call the trick of Zero Coordinate Shift (ZCS). Instead of making all sampled coordinates
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Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes I: Steady flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-01 Yaqing Yang, Liang Pan, Kun Xu
In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit non-compact and compact HGKSs are developed. For non-compact scheme, the simple weighted essentially non-oscillatory (WENO) reconstruction is used to achieve the spatial
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Theoretical link in numerical shock thickness and shock-capturing dissipation J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Ryosuke Ida, Yoshiharu Tamaki, Soshi Kawai
This paper presents a theoretical link between numerical shock thickness and shock-capturing dissipation. The link is derived rigorously from the compressible flow governing equations involving explicitly added shock-capturing numerical dissipation terms. The derivation employs only a natural assumption that the shock-capturing dissipation takes its maximum at the maximum velocity gradient location
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Uncertain data in initial boundary value problems: Impact on short and long time predictions J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 J, a, n, , N, o, r, d, s, t, r, ö, m
We investigate the influence of uncertain data on solutions to initial boundary value problems with well posed boundary conditions. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for short and long time calculations. For short time calculations, uncertainty in the initial data dominates. As time grows, the influence
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Stochastic modelling of symmetric positive definite material tensors J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Sharana Kumar Shivanand, Bojana Rosić, Hermann G. Matthies
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive definite tensors, as they appear often in the description of materials, and one wants to be able to prescribe certain classes of spatial symmetries and invariances for
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Finite difference and finite volume ghost multi-resolution WENO schemes with increasingly higher order of accuracy J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Yan Zhang, Jun Zhu
This article provides the high-order finite difference and finite volume ghost multi-resolution weighted essentially non-oscillatory (GMR-WENO) schemes for solving hyperbolic conservation laws on structured meshes. We only utilize the information defined on one big central spatial stencil without introducing any equivalent multi-resolution representations. These GMR-WENO schemes utilize orthogonal
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Summation-by-parts operators for general function spaces: The second derivative J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Jan Glaubitz, Simon-Christian Klein, Jan Nordström, Philipp Öffner
Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developing stable, high-order accurate numerical methodologies for such problems. Conventionally, SBP operators are tailored to the assumption that polynomials accurately approximate the solution, and SBP operators should thus be
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A compact simple HWENO scheme with ADER time discretization for hyperbolic conservation laws I: Structured meshes J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Dongmi Luo, Shiyi Li, Jianxian Qiu, Jun Zhu, Yibing Chen
In this paper, a compact and high order ADER (Arbitrary high order using DERivatives) scheme using the simple HWENO method (ADER-SHWENO) is proposed for hyperbolic conservation laws. The newly-developed method employs the Lax-Wendroff procedure to convert time derivatives to spatial derivatives, which provides the time evolution of the variables at the cell interfaces. This information is required
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An electromechanics-driven fluid dynamics model for the simulation of the whole human heart J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Alberto Zingaro, Michele Bucelli, Roberto Piersanti, Francesco Regazzoni, Luca Dede', Alfio Quarteroni
We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 active contraction model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then,
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On the grid convergence of wall-modeled large-eddy simulation J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-29 Xiaohan Hu, Xiang Yang, George Ilhwan Park
At first glance, grid convergence and wall modeling appear to be competing objectives that require reconciliation in inherently underresolved wall-modeled large-eddy simulation (LES). The understanding of which flow quantities can converge at typical wall-modeled LES resolution, as well as what parameters of wall models affect the convergence trend, is currently limited. Motivated by the attached eddy
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Towards a genuinely stable boundary closure for pentadiagonal compact finite difference schemes J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-28 Long Wu, Jae Wook Kim
A new optimisation strategy to develop high-order and genuinely stable boundary closure schemes for a pentadiagonal, seven-point stencil, compact finite difference system is proposed. Previous approaches to developing boundary compact schemes often yielded either potential instabilities or non-optimal accuracy in the numerical solutions. In the present optimisation, the numerical accuracy and stability
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Well-balanced positivity-preserving high-order discontinuous Galerkin methods for Euler equations with gravitation J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-28 Jie Du, Yang Yang, Fangyao Zhu
In this paper, we develop high order discontinuous Galerkin (DG) methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. Such problems may yield steady-state solutions and the density and pressure are positive. There were plenty of previous works developing either well-balanced (WB) schemes to preserve the steady states or positivity-preserving (PP) schemes to get positive
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High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-28 Jesse Chan, Khemraj Shukla, Xinhui Wu, Ruofeng Liu, Prani Nalluri
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of discretization parameters. This work extends high order entropy stable schemes to the quasi-1D
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A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-28 Michael Dumbser, Olindo Zanotti, Elena Gaburro, Ilya Peshkov
In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Z4 system, which is composed of 59 equations, is analyzed and proven to be strongly hyperbolic for a
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Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part I: The one-dimensional case J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-28 Eric J. Ching, Ryan F. Johnson, Andrew D. Kercher
In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting, compressible Euler equations with complex thermodynamics. The proposed formulation is an extension of the fully conservative, high-order numerical method previously developed by Johnson and Kercher (2020) that maintains pressure
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A new re-redistribution scheme for weighted state redistribution with adaptive mesh refinement J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-27 I. Barrio Sanchez, A.S. Almgren, J.B. Bell, M.T. Henry de Frahan, W. Zhang
State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow problems. When used in conjunction with adaptive mesh refinement (AMR), additional steps are needed to preserve the accuracy and conservation properties of the solution
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A hybrid continuum surface tension force for the three-phase VOF method J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-27 Chunheng Zhao, Jacob Maarek, Seyed Mohammadamin Taleghani, Stephane Zaleski
We propose a hybrid continuum surface tension force (CSF) formulation to model the interface interaction within the three-phase volume of fluid (VOF) method. Instead of employing the height function globally, we compute the curvature based on a smooth fraction function near the region of the triple contact point. In addition, we apply the isotropic finite difference method to calculate derivatives
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Vertically averaged and moment equations: New derivation, efficient numerical solution and comparison with other physical approximations for modeling non-hydrostatic free surface flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-27 C. Escalante, T. Morales de Luna, F. Cantero-Chinchilla, O. Castro-Orgaz
Efficient modeling of flow physics is a prerequisite for a reliable computation of free-surface environmental flows. Non-hydrostatic flows are often present in shallow water environments, making the task challenging. In this work, we use the method of weighted residuals for modeling non-hydrostatic free surface flows in a depth-averaged framework. In particular, we focus on the Vertically Averaged
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Conservative correction procedures utilizing artificial dissipation operators J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-27 A, y, a, b, o, e, , K, ., , E, d, o, h
The conservative correction procedure of Abgrall is studied from the perspective of filter-based artificial dissipation methods, which motivates the ability to tailor the behavior of the method in both physical and spectral space. Compared to the original formulation, employing diffusion operators biases the correction towards smaller scales and better controls discretization errors when seeking to
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Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part II: The multidimensional case J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-27 Eric J. Ching, Ryan F. Johnson, Andrew D. Kercher
In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the chemically reacting Euler equations. Our primary objective is to enable robust and accurate solutions to complex reacting-flow problems using the high-order discontinuous
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Learning fast, accurate, and stable closures of a kinetic theory of an active fluid J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Suryanarayana Maddu, Scott Weady, Michael J. Shelley
Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present
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A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Alexandre Caboussat, Julien Hess, Alexandre Masserey, Marco Picasso
We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces between phases, and contact angles. The volume-of-fluid approach is used to track the interfaces and the free surfaces between the various phases and
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A finite element-inspired hypergraph neural network: Application to fluid dynamics simulations J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Rui Gao, Indu Kant Deo, Rajeev K. Jaiman
An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two nodes. Inspired by the data connectivity in the finite element method, we present a method to construct a hypergraph by connecting the nodes by elements rather than edges
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Initialisation from lattice Boltzmann to multi-step Finite Difference methods: Modified equations and discrete observability J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Thomas Bellotti
Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data.
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Second-order accurate and unconditionally stable algorithm with unique solvability for a phase-field model of 3D volume reconstruction J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Yi Zhao, Dongting Cai, Junxiang Yang
Three-dimensional (3D) volume reconstruction is an important technique in the fields of 3D printing, artificial limb, and medical diagnostic. This work aims to develop an unconditionally stable algorithm with desired accuracy and unique solvability for a phase-field model of 3D volume reconstruction. Based on scattered points of a target object, a smooth narrow volume is reconstructed by solving a
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A highly efficient and accurate numerical method for the electromagnetic scattering problem with rectangular cavities J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 Xiaokai Yuan, Peijun Li
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at the open aperture of the cavity to transform the problem from an unbounded domain into that of bounded cavities. By employing Fourier series expansion of the solution
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Midpoint geometric integrators for inertial magnetization dynamics J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-23 M. d'Aquino, S. Perna, C. Serpico
We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines a higher-order nonlinear dynamical system with very different nature compared to the classical LLG equation, requiring twice as many degrees of freedom for space-time
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Stochastic and self-consistent 3D modeling of streamer discharge trees with Kinetic Monte Carlo J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-20 Robert Marskar
This paper contains the foundation for a new Particle-In-Cell model for gas discharges, based on Îto diffusion and Kinetic Monte Carlo (KMC). In the new model the electrons are described with a microscopic drift-diffusion model rather than a macroscopic one. We discuss the connection of the Îto-KMC model to the equations of fluctuating hydrodynamics and the advection-diffusion-reaction equation which
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Artificial viscosity-based shock capturing scheme for the Spectral Difference method on simplicial elements J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-20 Nadir-Alexandre Messaï, Guillaume Daviller, Jean-François Boussuge
An artificial viscosity-based shock capturing scheme is extended to the context of high-order triangular Spectral Difference method for solving gas dynamics problems featuring discontinuities and shock waves. The equations are regularised thanks to an artificial diffusivity method combined with a shock sensor based on dilatation and vorticity fields valid for any polynomial order of approximation.
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MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-19 Hendrik Fischer, Julian Roth, Thomas Wick, Ludovic Chamoin, Amelie Fau
In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (odel rder duction with ual-eighted esidual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation
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Multi-stage neural networks: Function approximator of machine precision J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-19 Yongji Wang, Ching-Yao Lai
Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the
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Domain-decomposed Bayesian inversion based on local Karhunen-Loève expansions J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 Zhihang Xu, Qifeng Liao, Jinglai Li
In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is governed by complex partial differential equations (PDEs). The challenge is particularly severe when the spatial domain is large and the unknown random field needs to be represented by a high-dimensional parameter. In this
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Biquadratic element discrete duality finite volume method for solving elliptic equations on quadrilateral mesh J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 Kejia Pan, Xiaoxin Wu, Yufeng Xu
Nowadays numerical methods for handling partial differential equations is so vast that it is almost taken for granted. In this paper, we propose a discrete duality finite volume scheme with biquadratic elements and its application in solving two-dimensional elliptic equation on quadrilateral meshes. To test the robustness and efficiency of this method, we investigate several examples from physical
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Faster is Slower effect for evacuation processes: A granular standpoint J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 F. Al Reda, S. Faure, B. Maury, E. Pinsard
The so-called Faster is Slower (FIS) effect is observed in some particular real-life or experimental situations. In the context of an evacuation process, it expresses that increasing the speed (or, more generally, the competitiveness) of individuals may induce a reduction of the flow through the exit door. We propose here a parameter-free model to reproduce and investigate this effect (more precisely
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A duality-preserving adjoint method for segregated Navier–Stokes solvers J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 Lean Fang, Ping He
Adjoint methods efficiently compute gradients for systems with many inputs and have been widely used for large-scale gradient-based optimization in fluid mechanics. To ensure optimization's numerical robustness, we need to develop an adjoint solution algorithm that has a similar, if not the same, convergence rate as the primal flow solver at each optimization iteration. This consistent primal-adjoint
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A finite volume method to solve the Poisson equation with jump conditions and surface charges: Application to electroporation J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 Thomas Bonnafont, Delphine Bessieres, Jean Paillol
Efficient numerical schemes for solving the Poisson equation with jump conditions are of great interest for a variety of problems, including the modeling of electroporation phenomena and filamentary discharges. In this paper, we propose a modification to a finite volume scheme, namely the discrete dual finite volume method, in order to account for jump conditions with surface charges, i.e. with a source
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Score-based transport modeling for mean-field Fokker-Planck equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-15 Jianfeng Lu, Yue Wu, Yang Xiang
We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach. Besides, we provide an error analysis for the algorithm. In numerical experiments, we study three types
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High order conservative Lagrangian schemes for two-dimensional radiation hydrodynamics equations in the equilibrium-diffusion limit J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-13 Nuo Lei, Juan Cheng, Chi-Wang Shu
Radiation hydrodynamics equations (RHE) refer to the study of how interactions between radiation and matter influence thermodynamic states and dynamic flow, which has been widely applied to high temperature hydrodynamics, such as inertial confinement fusion (ICF) and astrophysical gaseous stars. Solving RHE accurately and robustly even under the equilibrium diffusion approximation is a challenging
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A radial basis function partition of unity method for steady flow simulations J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-13 Francisco Bernal, Ali Safdari-Vaighani, Elisabeth Larsson
A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The compressed domain is then discretised, regardless of its final shape, via the radial basis function partition of unity method. Finally, the system of nonlinear algebraic
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Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-13 Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella
The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a natural extension of the classical Direct Simulation Monte Carlo (DSMC) method devised for the Boltzmann equation. One way to overcome this problem is to consider the design of Monte Carlo algorithms that are robust in the
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Uncertainty quantification in the Henry problem using the multilevel Monte Carlo method J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-13 Dmitry Logashenko, Alexander Litvinenko, Raul Tempone, Ekaterina Vasilyeva, Gabriel Wittum
We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain Henry saltwater intrusion problem. Unknown porosity, permeability and recharge parameters are modelled by using random fields. The classical deterministic Henry problem
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A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-02-12 Hanzhi Zhao, Suming Weng, Zhengming Sheng, Shi Jin, Jie Zhang
A Vlasov-Fokker-Planck-Landau (VFPL) code is developed for the study of colliding supersonic dense plasma flows, in which the VFPL equations for both electrons and ions are solved by the time splitting strategy in the two-dimensional Cartesian coordinate space and the two-dimensional velocity space (2D2V). To accurately handle two colliding supersonic plasma flows with their velocities even much higher