In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

This paper presents a well-balanced numerical scheme for simulating frictional shallow
flows over complex domains involving wetting and drying. The proposed scheme solves, in …

Numerical modelling of transoceanic tsunami propagation, together with the detailed
modelling of inundation of small-scale coastal regions, poses a number of algorithmic …

Shallow water equations with a non-flat bottom topography have been widely used to model
flows in rivers and coastal areas. An important difficulty arising in these simulations is the …

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is
proposed that works for general conservative and non-conservative systems of hyperbolic …

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 are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid
dynamics, and, for solutions containing shock waves, we investigate the convergence of …

We consider in this work the discontinuous Galerkin discretization of the nonlinear shallow
water equations on unstructured triangulations. In the recent years, several improvements …

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 …