Numerical Shallow Water Simulation Using Godunov-Type Scheme on Quadtree Grids

Shallow Flow Simulation on Dynamically Adaptive Cut-cell Quadtree Grids

A computationally efficient, high-resolution numerical model of shallow flow hydrodynamics is described, based on boundary-fitted adaptive quadtree grids. The numerical model solves the two-dimensional non-linear shallow water equations by means of an explicit second-order MUSCL-Hancock Godunov-type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. T...

Numerical Approximation of the Nonlinear Shallow Water Equations with Topography and Dry Beds: A Godunov-Type Scheme

A fast adaptive quadtree scheme for a two-layer shallow water model

This paper presents a dynamically adaptive quadtree grid generation system for the solution of a two-dimensional two-layer shallow water model. Roe-type two-layer shallow water solvers require numerical approximation of the system eigenvalues as well as numerical balancing, which increase computational cost considerably when a regular grid is used. In order to improve computational efficiency, ...

An Adaptive Order Godunov Type Central Scheme

1 Department of Mathematics, Institute for Physical Science & Technology and Center for Scientific Computation And Mathematical Modeling (CSCAMM), University of Maryland College Park, MD 20742-3289 [email protected] 2 Department of Mathematics University of California Davis, CA 95616 [email protected] “Hyperbolic Problems: Theory, Numerics, Applications”, Proceedings of the 9th Inter...

Central-Upwind Scheme on Triangular Grids for the Saint-Venant System of Shallow Water Equations

We consider a novel second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids which was originally introduced in [3] . Here, in several numerical experiments we demonstrate accuracy, high resolution and robustness of the proposed method.