1 citations · 1 across the 4 of their papers we have counts for
6 papers
Positivity-preserving Well-balanced PAMPA Schemes with Global Flux quadrature for One-dimensional Shallow Water Models
Remi Abgrall, Yongle Liu, Mario Ricchiuto
We present a novel hydrostatic and non-hydrostatic equilibria preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) method for solving the one-dimensional hyperbolic balan…
An active-flux-type scheme for ideal MHD with provable positivity and discrete divergence-free property
Mengqing Liu, Dongwen Pang, Remi Abgrall +1
We develop a positivity-preserving (PP) PAMPA (Point-Average-Moment PolynomiAl-interpreted) scheme that enforces a discrete divergence-free (DDF) magnetic field for ideal MHD on Ca…
Bound preserving {P}oint-{A}verage-{M}oment {P}olynomi{A}l-interpreted ({PAMPA}) on polygonal meshes
Rémi Abgrall, Yongle Liu, Walter Boscheri
We present a novel discretisation strategy, strongly inspired from Roe's Active Flux scheme. It can use polygonal meshes and is provably bound preserving for scalar problems and th…
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…
Virtual finite element and hyperbolic problems: the PAMPA algorithm
Rémi Abgrall, Yongle Liu, Walter Boscheri
In this paper, we explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the ac…
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…