[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 …

[ספר][B] Interacting multiagent systems: kinetic equations and Monte Carlo methods

L Pareschi, G Toscani - 2013‏ - books.google.com
The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

Monte carlo and quasi-monte carlo methods

RE Caflisch - Acta numerica, 1998‏ - cambridge.org
Monte Carlo is one of the most versatile and widely used numerical methods. Its
convergence rate, O (N− 1/2), is independent of dimension, which shows Monte Carlo to be …

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 …

Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations

S ** - SIAM Journal on Scientific Computing, 1999‏ - SIAM
Many kinetic models of the Boltzmann equation have a diffusive scaling that leads to the
Navier--Stokes type parabolic equations as the small scaling parameter approaches zero. In …

[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 …

Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries

L Mieussens - Journal of Computational Physics, 2000‏ - Elsevier
We present new numerical models for computing transitional or rarefied gas flows as
described by the Boltzmann-BGK and BGK-ES equations. We first propose a new discrete …

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 …

Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics

L Mieussens - Mathematical Models and Methods in Applied …, 2000‏ - World Scientific
We present a numerical method for computing transitional flows as described by the BGK
equation of gas kinetic theory. Using the minimum entropy principle to define a discrete …

Kinetic models for epidemic dynamics with social heterogeneity

G Dimarco, B Perthame, G Toscani… - Journal of Mathematical …, 2021‏ - Springer
We introduce a mathematical description of the impact of the number of daily contacts in the
spread of infectious diseases by integrating an epidemiological dynamics with a kinetic …