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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…