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

In this paper, we survey our recent work on designing high order positivitypreserving well-
balanced finite difference and finite volume WENO (weighted essentially non-oscillatory) …

In this paper, we develop bound-preserving modified exponential Runge–Kutta (RK)
discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source …

In this paper, we construct a family of modified Patankar Runge–Kutta methods, which is
conservative and unconditionally positivity-preserving, for production–destruction equations …

In this paper, we propose a fifth order well-balanced positivity-preserving finite difference
scale-invariant AWENO scheme for the compressible Euler equations with gravitational …

In this paper, we develop an oscillation-free discontinuous Galerkin (OFDG) method for
solving the shallow water equations with a non-flat bottom topography. Due to the nonlinear …

We present a novel high-order discontinuous Galerkin discretization for the spherical
shallow water equations, able to handle wetting/drying and non-conforming, curved meshes …

We extend the entropy stable high order nodal discontinuous Galerkin spectral element
approximation for the non-linear two dimensional shallow water equations presented by …

By revisiting the basic Godunov approach for system of linear hyperbolic Partial Differential
Equations (PDEs) we show that it is hybridizable. As such, it is a natural recipe for us to …

A non-staggered second-order accurate central scheme based on new hydrostatic
reconstruction (HR) for the shallow water equation (SWE) with dry–wet fronts is presented …