94 citations · 439 across the 45 of their papers we have counts for
47 papers
Novel well-balanced continuous interior penalty stabilizations
Lorenzo Micalizzi, Mario Ricchiuto, Rémi Abgrall
In this work, the high order accuracy and the well-balanced (WB) properties of some novel continuous interior penalty (CIP) stabilizations for the Shallow Water (SW) equations are…
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 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…
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…
\textit{A Posteriori} local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids
François Vilar, Rémi Abgrall
We present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [52]. The technique is…
Evaluating a distance function
Rémi Abgrall
Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, usi…
A hybrid finite element - finite volume method for conservation laws
Rémi Abgrall, Wasilij Barsukow
We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point v…
Extensions of Active Flux to arbitrary order of accuracy
Rémi Abgrall, Wasilij Barsukow
Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These…
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…
Spectral analysis of high order continuous FEM for hyperbolic PDEs on triangular meshes: influence of approximation, stabilization, and time-stepping
Sixtine Michel, Davide Torlo, Mario Ricchiuto +1
In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on eq…
On the discrete equation model for compressible multiphase fluid flows
Marco Petrella, Remi Abgrall, Siddhartha Mishra
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discret…
A discontinuous Galerkin spectral element method for a nonconservative compressible multicomponent flow model
Rémi Abgrall, Pratik Rai, Florent Renac
In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where…
Conservative scheme compatible with some other conservation laws: conservation of the local angular momentum
Rémi Abgrall, Fatemeh Nassajian Mojarrad
We are interested in building schemes for the compressible Euler equations that are also locally conserving the angular momentum. We present a general framework, describe a few exa…
Staggered schemes for compressible flow: a general construction
Rémi Abgrall
This paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the veloci…
Hyperbolic balance laws: residual distribution, local and global fluxes
Remi Abgrall, Mario Ricchiuto
This paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux in fluctuation fo…
A pressure-based method for weakly compressible two-phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium
Barbara Re, Rémi Abgrall
Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily dea…
Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
Rémi Abgrall, Elise Le Mélédo, Philipp Öffner +1
In [1] is proposed a simplified DeC method, that, when combined with the residual distribution (RD) framework, allows to construct a high order, explicit FE scheme with continuous…
Assessment of a non-conservative four-equation multiphase system with phase transition
Paola Bacigaluppi, Julien Carlier, Marica Pelanti +2
This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consi…
High Order Residual Distribution Conservative Finite Difference HWENO Scheme for Steady State Problems
Jianfang Lin, Yupeng Ren, Rémi Abgrall +1
In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO)…
Spectral analysis of continuous FEM for hyperbolic PDEs: influence of approximation, stabilization, and time-stepping
Sixtine Michel, Davide Torlo, Mario Ricchiuto +1
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete s…
THINC scaling method that bridges VOF and level set schemes
Ronit Kumar, Lidong Cheng, Yunong Xiong +3
We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two different approaches wi…
A combination of Residual Distribution and the Active Flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations
Rémi Abgrall
We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form.…
On the simulation of multicomponent and multiphase compressible flows
Rémi Abgrall, Paola Bacigaluppi, Barbara Re
The following paper presents two simulation strategies for compressible two-phase or multicomponent flows. One is a full non-equilibrium model in which the pressure and velocity ar…