Well-balanced schemes and path-conservative numerical methods
In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …
schemes for hyperbolic system with nonconservative products and/or source terms. We …
A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
R Abgrall - Journal of Computational Physics, 2018 - Elsevier
We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …
Hyperbolic balance laws: residual distribution, local and global fluxes
R Abgrall, M Ricchiuto - Numerical Fluid Dynamics: Methods and …, 2022 - Springer
This review 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 splitting schemes”. They are a generalization of Roe's numerical flux in …
[HTML][HTML] Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws
The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …
Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries
M Ricchiuto, AG Filippini - Journal of Computational Physics, 2014 - Elsevier
In this paper we consider the solution of the enhanced Boussinesq equations of Madsen
and Sørensen (1992)[55] by means of residual based discretizations. In particular, we …
and Sørensen (1992)[55] by means of residual based discretizations. In particular, we …
High order methods for CFD
R Abgrall, M Ricchiuto - Encyclopedia of Computational Mechanics, 2017 - inria.hal.science
We provide a review of high order methods for CFD. Besides recalling some classical
methods, we show a framework allowing on one hand to see and work with these methods …
methods, we show a framework allowing on one hand to see and work with these methods …
A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems
R Abgrall, C Dobrzynski… - International Journal for …, 2014 - Wiley Online Library
We propose and analyze an algorithm for the robust construction of curved meshes in two
and three dimensions. The meshes are made of curved simplexes. The algorithm starts from …
and three dimensions. The meshes are made of curved simplexes. The algorithm starts from …
Reconstructed discontinuous Galerkin methods for linear advection–diffusion equations based on first-order hyperbolic system
Abstract Newly developed reconstructed Discontinuous Galerkin (rDG) methods are
presented for solving linear advection–diffusion equations on hybrid unstructured grids …
presented for solving linear advection–diffusion equations on hybrid unstructured grids …
Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier–Stokes equations
R Abgrall, D De Santis - Journal of computational physics, 2015 - Elsevier
A robust and high order accurate Residual Distribution (RD) scheme for the discretization of
the steady Navier–Stokes equations is presented. The proposed method is very flexible: it is …
the steady Navier–Stokes equations is presented. The proposed method is very flexible: it is …
First, second, and third order finite-volume schemes for advection–diffusion
H Nishikawa - Journal of Computational Physics, 2014 - Elsevier
In this paper, we present first, second, and third order implicit finite-volume solvers for
advection–diffusion problems based on the first-order hyperbolic system method. In …
advection–diffusion problems based on the first-order hyperbolic system method. In …