Colloquium

Starts: November 20, 2009 at 3:00 PM
Location: Jones Hall 131
Contact: Junping Shi, Paul Tian

Summary

Speaker: Anne Fernando (Norfolk State University)

Full Description

Title: DGM-FD: A Finite Difference Scheme Based on the Discontinuous Galerkin Method

Abstract: Accurate and efficient numerical wave propagation is important in many areas of study such as computational aero-acoustics (CAA). While dissipation and dispersion errors influence the accuracy of a method, efficiency can be assessed by convergence rates and effective adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. In this research we formulate a numerical method that has advantages of both, high-order convergence, with strong accuracy for numerical wave numbers, and is adaptive to non-uniform grids. The propsed schemes, DGM-FD, is developed based on the Discontinuous Galerkin Method (DGM) applied to the hyperbolic equation. These schemes inherit, naturally, some features of the DGM, such as high-order approximations, applicability to non-uniform grids and super-accuracy for wave propagations. The structure presented has a regular, but non-uniform, finite difference type grid and fourth-order upwind and third order central schemes. For non-linear equations, flux finite difference formula are given where no explicit upwind and downwind split of the flux is needed. Stability of the scheme with boundary closures and the super-accuracy for wave propagation problems are investigated and validated. The new scheme is demonstrated by numerical examples including the linearized acoustic waves, the solution of non-linear Burger's equation and the flat-plate boundary layer problem.