Comparison of second-order accurate TVD scheme and p-version space-time least-squares finite-element method for nonlinear hyperbolic problems

Author

Tseng, Ming Hseng ; Liang, Shin-Jye

Author_Institution

Nat. Center for High-Performance Comput., Taiwan

fYear

1997

fDate

28 Apr-2 May 1997

Firstpage

289

Lastpage

294

Abstract

The 2nd-order accurate total variation diminishing (TVD2) finite-difference method and p-version based space-time least-squares finite-element method (STLSFEM) are presented in this study. Both methods are applied to 1D unsteady Burgers´ and shallow-water equations which contain sharp gradients. The computed results demonstrate that both methods are capable of resolving the sharp gradients without generating spurious oscillations. The methods provide the basis for the extension of TVD2 and p-version STLSFEM to multi-dimensional unsteady problems and appear to have great potential in computational fluid dynamics

Keywords

finite difference methods; finite element analysis; fluid dynamics; hyperbolic equations; least squares approximations; mechanical engineering computing; 1D unsteady Burgers´ equations; 2nd-order accurate total variation diminishing finite-difference method; computational fluid dynamics; multi-dimensional unsteady problems; nonlinear hyperbolic problems; p-version space-time least-squares finite-element method; shallow-water equations; sharp gradients; Boundary conditions; Computational fluid dynamics; Convergence; Differential equations; Finite difference methods; Finite element methods; Partial differential equations; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

High Performance Computing on the Information Superhighway, 1997. HPC Asia '97

Conference_Location

Seoul

Print_ISBN

0-8186-7901-8

Type

conf

DOI

10.1109/HPC.1997.592162

Filename

592162