7 papers · 1 filter
A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case
Rémi Abgrall, Miaosen Jiao, Yongle Liu +1
The PAMPA (Point-Average-Moment PolynomiAl-interpreted) method, proposed in [R. Abgrall, Commun. Appl. Math. Comput., 5: 370-402, 2023], combines conservative and non-conservative…
A positive- and bound-preserving vectorial lattice Boltzmann method in two dimensions
Gauthier Wissocq, Yongle Liu, Rémi Abgrall
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We foc…
A new local and explicit kinetic method for linear and non-linear convection-diffusion problems with finite kinetic speeds: I. One-dimensional case
Gauthier Wissocq, Rémi Abgrall
We propose a numerical approach, of the BGK kinetic type, that is able to approximate with a given, but arbitrary, order of accuracy the solution of linear and non-linear convectio…
A personal discussion on conservation, and how to formulate it
Remi Abgrall
Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form.…
An arbitrarily high order and asymptotic preserving kinetic scheme in compressible fluid dynamic
Rémi Abgrall, Fatemeh Nassajian Mojarrad
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes b…
A Monte-Carlo ab-initio algorithm for the multiscale simulation of compressible multiphase flows
Marco Petrella, Remi Abgrall, Siddhartha Mishra
We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorith…