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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…