ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves

A Well–Balanced Stable GRP Scheme for Shallow Water Equations for Adaptive Unstructured Triangular Meshes

Visual simulation of shallow-water waves

A commodity-type graphics card (GPU) is used to simulate nonlinear water waves described by a system of balance laws called the shallow-water system. To solve this hyperbolic system we use explicit high-resolution central-upwind schemes, which are particularly well suited for exploiting the parallel processing power of the GPU. In fact, simulations on the GPU are found to run 15–30 times faster...

Numerical discretizations for shallow water equations with source terms on unstructured meshes

In the following lines we introduce two frictional schemes for the discretization of the 2D Shallow Water system, on unstructured meshes. The starting point consists in writing both of them as convex combinations of 1D schemes. Then, we propose to include the resistance effects proceeding to a slight adaptation of the gathered convex components, using the frictional approach recently developed ...

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In [36], the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the nonnegativity of the water height without...

Optimization-based Fluid Simulation on Unstructured Meshes

We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable si...