Numerical methods for kinetic equations

G Dimarco, L Pareschi - Acta Numerica, 2014‏ - cambridge.org
In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

[ספר][B] Nonlinear stability of finite Volume Methods for hyperbolic conservation laws: And Well-Balanced schemes for sources

F Bouchut - 2004‏ - books.google.com
This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It
differs from previous expositions on the subject in that the accent is put on the development …

Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

M Dumbser, C Enaux, EF Toro - Journal of Computational Physics, 2008‏ - Elsevier
In this article, we propose a new class of finite volume schemes of arbitrary accuracy in
space and time for systems of hyperbolic balance laws with stiff source terms. The new class …

Implicit-explicit Runge--Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit

S Boscarino, L Pareschi, G Russo - SIAM Journal on Scientific Computing, 2013‏ - SIAM
We consider implicit-explicit (IMEX) Runge--Kutta (RK) schemes for hyperbolic systems with
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …

Uniformly accurate diffusive relaxation schemes for multiscale transport equations

S **, L Pareschi, G Toscani - SIAM Journal on Numerical Analysis, 2000‏ - SIAM
Many transport equations, such as the neutron transport, radiative transfer, and transport
equations for waves in random media, have a diffusive scaling that leads to the diffusion …

Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review

S Boscarino, G Russo - SeMA Journal, 2024‏ - Springer
Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial
differential equations which describe several physical phenomena, ranging from gas …

Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations

S **, L Pareschi, G Toscani - SIAM Journal on Numerical Analysis, 1998‏ - SIAM
Many kinetic models of the Boltzmann equation have a diffusive scaling that leads to the
Navier--Stokes-type parabolic equations, such as the heat equation, the porous media …

On thermodynamically compatible finite volume schemes for continuum mechanics

S Busto, M Dumbser, I Peshkov, E Romenski - SIAM Journal on Scientific …, 2022‏ - SIAM
In this paper we present a new family of semidiscrete and fully discrete finite volume
schemes for overdetermined, hyperbolic, and thermodynamically compatible PDE systems …

Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

G Bertaglia, L Pareschi - ESAIM: Mathematical Modelling and …, 2021‏ - esaim-m2an.org
We consider the development of hyperbolic transport models for the propagation in space of
an epidemic phenomenon described by a classical compartmental dynamics. The model is …

A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics

W Boscheri, M Dumbser, M Ioriatti, I Peshkov… - Journal of …, 2021‏ - Elsevier
We propose a new pressure-based structure-preserving (SP) and quasi asymptotic
preserving (AP) staggered semi-implicit finite volume scheme for the unified first order …