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 …

This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin
schemes with subcell finite volume limiters applied to a new class of first order hyperbolic …

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 …

In this paper we propose a new high order accurate centered path-conservative method on
unstructured triangular and tetrahedral meshes for the solution of multi-dimensional non …

In this paper we propose a new reformulation of the first order hyperbolic model for unsteady
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …

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 …

In this work, we present a class of fast first order finite volume solvers, called PVM
(polynomial viscosity matrix), for balance laws or, more generally, for nonconservative …

We present a novel staggered semi-implicit hybrid finite volume/finite element method for the
numerical solution of the shallow water equations at all Froude numbers on unstructured …

Abstract The Tsunami-HySEA model is used to perform some of the numerical benchmark
problems proposed and documented in the “Proceedings and results of the 2011 NTHMP …

Mud/debris flows are among the most challenging gravity-driven flows in environmental and
geophysical processes. Natural muddy slurries and debris are solid-laden fluids where the …