1 citations · 1 across the 10 of their papers we have counts for
12 papers
On the involution preserving properties of semi-discrete Active Flux methods on simplex
Remi Abgrall, Yongle Liu, Mario Ricchiuto
We study the involution-preserving properties of the Active Flux method on unstructured triangular meshes. Two model problems are considered: the two-dimensional linear acoustic sy…
Construction of entropy satisfying Active Flux-type methods
Remi Abgrall, Yongle Liu
This paper is devoted to the analysis of the entropy stability properties of Active Flux\yolo{-type} scheme for a hyperbolic system equipped with one entropy inequality. This type…
Robust PAMPA Scheme in the DG Formulation on Unstructured Triangular Meshes: bound preservation, oscillation elimination, and boundary conditions
Rémi Abgrall, Yongle Liu
We propose an improved version of the PAMPA algorithm where the solution is sought as globally continuous. The scheme is locally conservative, and there is no mass matrix to invert…
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…
Some new properties of an Active flux type scheme: PamPa
Rémi Abgrall, Philipp Öffner, Yongle Liu
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pam…
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…
Bound preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: one-dimensional case
Rémi Abgrall, Miaosen Jiao, Yongle Liu +1
We propose a bound-preserving (BP) Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme by blending third-order and first-order constructions. The originality of the present…
Active flux for triangular meshes for compressible flows problems
Rémi Abgrall, Jianfang Lin, Yongle Liu
In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and th…
A New Approach for Designing Well-Balanced Schemes for the Shallow Water Equations: A Combination of Conservative and Primitive Formulations
Remi Abgrall, Yongle Liu
In this paper, we introduce a new approach for constructing robust well-balanced numerical methods for the one-dimensional Saint-Venant system with and without the Manning friction…