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This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…

Numerical Analysis · Mathematics 2025-05-20 Kunal Bahuguna , Ramesh Kolluru , S. V. Raghurama Rao

We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences…

Quantum Physics · Physics 2026-04-28 Sreemayee Aditya , Emanuele Tirrito , Piotr Sierant , Xhek Turkeshi

This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate…

Numerical Analysis · Mathematics 2016-09-07 Christophe Berthon , Marianne Bessemoulin-Chatard , Hélène Mathis

This paper proposes a hierarchy of numerical fluxes for the compressible flow equations which are kinetic-energy and pressure equilibrium preserving and asymptotically entropy conservative, i.e., they are able to arbitrarily reduce the…

Fluid Dynamics · Physics 2024-08-08 Carlo De Michele , Gennaro Coppola

Results of numerical simulation constructed before strict mathematical model of an establishment of thermodynamic equilibrium in originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with any acceleration in the…

General Relativity and Quantum Cosmology · Physics 2013-10-09 Yu. G. Ignatyev

The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an…

Analysis of PDEs · Mathematics 2018-03-07 Fabio Ancona , Laura Caravenna , Andrea Marson

We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…

Numerical Analysis · Mathematics 2025-10-02 Boris D. Andrews , Patrick E. Farrell

In this work, we devise a model adaptation strategy for a class of model hierarchies consisting of two levels of model complexity. In particular, the fine model consists of a system of hyperbolic balance laws with stiff reaction terms and…

Numerical Analysis · Mathematics 2023-02-23 Jan Giesselmann , Hrishikesh Joshi , Siegfried Müller , Aleksey Sikstel

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

Analysis of PDEs · Mathematics 2017-09-29 Martin Gugat , Vincent Perrollaz , Lionel Rosier

A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…

Computational Physics · Physics 2007-05-23 A. G. Kulikovskii , N. V. Pogorelov , A. Yu Semenov

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…

Statistical Mechanics · Physics 2009-10-31 I. P. Omelyan , I. M. Mryglod , R. Folk

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

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…

Analysis of PDEs · Mathematics 2026-05-04 Alberto Bressan , Laura Caravenna , Wen Shen

High-order entropy stable summation-by-parts (SBP) schemes are a class of robust and accurate numerical methods for hyperbolic conservation laws that are numerically stable at arbitrary order without the need for artificial stabilization.…

Numerical Analysis · Mathematics 2024-12-18 Christina G. Taylor , Jesse Chan

A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…

Numerical Analysis · Mathematics 2025-12-03 Tommaso Tenna

Numerical simulations of compressible real-fluid flows are notoriously plagued by spurious pressure oscillations arising in regions of abrupt flow variations. As a possible remedy, several numerical formulations enforce the pressure…

Fluid Dynamics · Physics 2026-05-27 Gennaro Coppola , Alessandro Aiello , Carlo De Michele

Entropy-conserving numerical fluxes are a cornerstone of modern high-order entropy-dissipative discretizations of conservation laws. In addition to entropy conservation, other structural properties mimicking the continuous level such as…

Numerical Analysis · Mathematics 2022-04-25 Hendrik Ranocha

This paper is devoted to hyperbolic systems of balance laws with non local source terms. The existence, uniqueness and Lipschitz dependence proved here comprise previous results in the literature and can be applied to physical models, such…

Analysis of PDEs · Mathematics 2007-12-13 Rinaldo M. Colombo , Graziano Guerra

We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while…

Fluid Dynamics · Physics 2022-05-18 David I. Ketcheson , Manuel Quezada de Luna

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…

Numerical Analysis · Mathematics 2020-08-05 Jonas P. Berberich , Praveen Chandrashekar , Christian Klingenberg