In an earlier study (Zhang & Shu 2010 b J. Comput. Phys. 229, 3091–3120 (doi: 10.1016/j.
jcp. 2009.12. 030)), genuinely high-order accurate finite volume and discontinuous Galerkin …

For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …

Strong Stability Preserving Explicit Runge—Kutta Methods | Strong Stability Preserving
Runge-Kutta and Multistep Time Discretizations World Scientific Search This Book Anywhere …

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the
potential applications of POD reduced-order numerical methods in increasing computational …

Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this
paper proposes a 2D well-balanced shallow water model for unstructured grids. In this …

Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

The aim of this paper is to present a novel monotone upstream scheme for conservation law
(MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to …

We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green–
Naghdi equations over varying topography. These new Green–Naghdi systems share the …

Hyperbolic conservation laws with source terms often admit steady state solutions where the
fluxes and source terms balance each other. To capture this balance and near-equilibrium …