[BOOK][B] Hyperbolic Systems of Conservation Laws: The theory of classical and nonclassical shock waves

PG LeFloch - 2002 - books.google.com
This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the
Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would …

GPU computing for shallow water flow simulation based on finite volume schemes

MJ Castro, S Ortega, M De la Asuncion… - Comptes Rendus …, 2011 - Elsevier
This article is a review of the work that we are carrying out to efficiently simulate shallow
water flows. In this paper, we focus on the efficient implementation of path-conservative Roe …

On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas

JM Gallardo, C Parés, M Castro - Journal of Computational Physics, 2007 - Elsevier
We present a finite volume scheme for solving shallow water equations with source term due
to the bottom topography. The scheme has the following properties: it is high-order accurate …

Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

MJ Castro, PG LeFloch, ML Muñoz-Ruiz… - Journal of Computational …, 2008 - Elsevier
We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid
dynamics, and, for solutions containing shock waves, we investigate the convergence of …

ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

M Dumbser, M Castro, C Parés, EF Toro - Computers & Fluids, 2009 - Elsevier
We develop a new family of well-balanced path-conservative quadrature-free one-step
ADER finite volume and discontinuous Galerkin finite element schemes on unstructured …

Numerical modeling of two-phase flows using the two-fluid two-pressure approach

T Gallouët, JM Hérard, N Seguin - Mathematical Models and …, 2004 - World Scientific
The present paper is devoted to the computation of two-phase flows using the two-fluid
approach. The overall model is hyperbolic and has no conservative form. No instantaneous …

An existence and uniqueness result for two nonstrictly hyperbolic systems

P Le Floch - Nonlinear evolution equations that change type, 1990 - Springer
We prove a result of existence and uniqueness of entropy weak solutions for two nonstrictly
hyperbolic systems, both a nonconservative system of two equations\partial_t u+\partial_x f …

Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique

MJ Castro, A Pardo Milanés, C Parés - Mathematical Models and …, 2007 - World Scientific
The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in
Ref. 2 for the shallow water system to more general hyperbolic systems with source term …

Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

S Rhebergen, O Bokhove, JJW van der Vegt - Journal of Computational …, 2008 - Elsevier
We present space-and space–time discontinuous Galerkin finite element (DGFEM)
formulations for systems containing nonconservative products, such as occur in dispersed …

A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime

PG LeFloch, MD Thanh - Journal of Computational Physics, 2011 - Elsevier
We investigate the Riemann problem for the shallow water equations with variable and
(possibly) discontinuous topography and provide a complete description of the properties of …