Conjugate filter approach for solving Burgers' equation

Authors:
G. W. Wei;Yun Gu
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, MI;Department of Computational Science, National University of Singapore, Singapore 117543, Singapore
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 6
Cited 6

Uniformly high order accurate essentially non-oscillatory schemes, 111

Journal of Computational Physics
Ten lectures on wavelets

Ten lectures on wavelets
A self-adaptive domain decomposition for the viscous/inviscid coupling. I: Burgers equation

Journal of Computational Physics
Space-time spectral element methods for one-dimensional nonlinear advection-diffusion problems

Journal of Computational Physics
Efficient implementation of weighted ENO schemes

Journal of Computational Physics
An efficient numerical scheme for Burgers' equation

Applied Mathematics and Computation

High resolution conjugate filters for the simulation of flows

Journal of Computational Physics
DSC time-domain solution of Maxwell's equations

Journal of Computational Physics
A windowed Fourier pseudospectral method for hyperbolic conservation laws

Journal of Computational Physics
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

Journal of Computational Physics
Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach

Journal of Computational and Applied Mathematics
An oscillation-free high order TVD/CBC-based upwind scheme for convection discretization

Numerical Algorithms

Quantified Score

Hi-index	7.31

Visualization

Abstract

We propose a novel scheme for solving Burgers' equation with all possible values of Reynolds numbers. A low-pass filter is introduced to intelligently eliminate the high frequency errors produced by its conjugate high-pass filters. All conjugate filters are derived from one generating function and have essentially the same degree of regularity, smoothness, time-frequency localization, effective support and bandwidth. Computational accuracy is tested by using both a linear hyperbolic equation and Burgers' equation at a moderately high Reynolds number for which analytical solution is available. The ability of shock-capturing is validated by using discontinuous initial values. Excellent numerical results indicate that the proposed scheme is efficient, robust and reliable for solving Burgers' equation and for shock capturing.