[PDF][PDF] Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review

S ** - Lecture notes for summer school on methods and …, 2010‏ - researchgate.net
Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

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 …

Asymptotic-preserving schemes for multiscale physical problems

S ** - Acta Numerica, 2022‏ - cambridge.org
We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

[ספר][B] Direct modeling for computational fluid dynamics: construction and application of unified gas-kinetic schemes

K Xu - 2014‏ - books.google.com
Computational fluid dynamics (CFD) studies the flow motion in a discretized space. Its basic
scale resolved is the mesh size and time step. The CFD algorithm can be constructed …

A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources

F Filbet, S ** - Journal of Computational Physics, 2010‏ - Elsevier
In this paper, we propose a general time-discrete framework to design asymptotic-
preserving schemes for initial value problem of the Boltzmann kinetic and related equations …

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 …

Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations

S **, Z Ma, K Wu - Journal of Scientific Computing, 2023‏ - Springer
In this paper we develop a neural network for the numerical simulation of time-dependent
linear transport equations with diffusive scaling and uncertainties. The goal of the network is …

A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit

M Lemou, L Mieussens - SIAM Journal on Scientific Computing, 2008‏ - SIAM
We propose a new numerical scheme for linear transport equations. It is based on a
decomposition of the distribution function into equilibrium and nonequilibrium parts. We also …

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 …