A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented. The space-time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution. The dispersion and dissipation errors of the scheme are investigated and the algorithm is demonstrated...

CCHE3D model is developed at the National Center for Computational Hydroscience and Engineering, The University of Mississippi, for simulating unsteady, free surface, three-dimensional turbulent flows and sediment/pollutant transport and water quality. This model is based on Efficient Element Method, a collocation version of the Galerkin approach. The basic element is a cube with twenty-seven n...

This paper presents a Galerkin boundary element method for solving crack problems governed by potential theory in nonhomogeneous media. In the simple boundary element method, the nonhomogeneous problem is reduced to a homogeneous problem using variable transformation. Cracks in heat conduction problem in functionally graded materials are investigated. The thermal conductivity varies parabolical...

In this note, we reinterpret a discontinuous Galerkin method originally developed by Huand Shu [1] (see also [2]) for solving Hamilton-Jacobi equations. By this reinterpretation,numerical solutions will automatically satisfy the curl-free property of the exact solutionsinside each element. This new reinterpretation allows a method of lines formulation, whichrenders a more na...

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact ni...