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We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to the Euler equations of compressible gas dynamics. Two key…

Numerical Analysis · Mathematics 2025-12-01 Michael Dumbser , Mária Lukáčová-Medvid'ová , Andrea Thomann

Integrable self-adaptive moving mesh schemes for short pulse type equations (the short pulse equation, the coupled short pulse equation, and the complex short pulse equation) are investigated. Two systematic methods, one is based on…

Exactly Solvable and Integrable Systems · Physics 2014-04-03 Bao-Feng Feng , Ken-ichi Maruno , Yasuhiro Ohta

In this work, we present the Domain of Dependence (DoD) stabilization for systems of hyperbolic conservation laws in one space dimension. The base scheme uses a method of lines approach consisting of a discontinuous Galerkin scheme in space…

Numerical Analysis · Mathematics 2021-07-09 Sandra May , Florian Streitbürger

In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations \cite{guo2016transport,…

Numerical Analysis · Mathematics 2020-02-25 Juntao Huang , Yingda Cheng

In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…

Numerical Analysis · Mathematics 2026-02-03 Elena Gaburro , Mario Ricchiuto , Michael Dumbser

We present a modified Front Tracking (mFT) scheme for hyperbolic systems of conservation laws in one space dimension, in which we allow arbitrarily large nonlinear waves. We build the scheme by introducing and solving a ``generalized…

Analysis of PDEs · Mathematics 2025-04-30 Manas Bhatnagar , Robin Young

This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…

Numerical Analysis · Mathematics 2025-03-18 Shumo Cui , Kailiang Wu , Linfeng Xu

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…

Cosmology and Nongalactic Astrophysics · Physics 2014-11-20 Peng Wang , Tom Abel , Ralf Kaehler

We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with the Poisson equation, which is a {classical mean-field} primary model for collisional plasmas. Two subproblems, i.e. the…

Computational Physics · Physics 2017-06-19 Chenglong Zhang , Irene M. Gamba

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…

Numerical Analysis · Mathematics 2022-04-20 Tarik Dzanic , Will Trojak , Freddie D. Witherden

Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…

Computational Physics · Physics 2021-07-16 Alan A. Kaptanoglu , Kyle D. Morgan , Chris J. Hansen , Steven L. Brunton

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…

Analysis of PDEs · Mathematics 2021-10-01 Benjamin Boutin , Frédéric Coquel , Philippe G. LeFloch

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

Analysis of PDEs · Mathematics 2024-07-02 Timothée Crin-Barat , Yue-Jun Peng , Ling-Yun Shou , Jiang Xu

We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly…

Numerical Analysis · Mathematics 2025-10-23 Giuseppe Orlando , Tommaso Benacchio , Luca Bonaventura

This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here…

Astrophysics · Physics 2009-11-07 John C. Hayes , Michael L. Norman

In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…

Numerical Analysis · Mathematics 2021-04-12 M. Siebenborn , V. Schulz , S. Schmidt

In this paper we present a class of high order accurate cell-centered Arbitrary-Eulerian-Lagrangian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured…

Computational Physics · Physics 2015-06-17 Walter Boscheri , Michael Dumbser , Dinshaw Balsara

We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based…

Numerical Analysis · Mathematics 2023-05-18 Giuseppe Orlando , Tommaso Benacchio , Luca Bonaventura

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…

Numerical Analysis · Computer Science 2021-08-04 Thomas C. Clevenger , Timo Heister , Guido Kanschat , Martin Kronbichler

This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population…

Fluid Dynamics · Physics 2025-04-08 Ruben M. Strässle , S. A. Hosseini , I. V. Karlin