4 papers
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…
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
Rémi Abgrall, Mária Lukácova-Medvid'ová, Philipp Öffner
In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution sc…