Comparison of Two Sixth-Order Compact Finite Difference Schemes for Burgers' Equation

Abstract:

In this study, two sixth-order compact finite difference schemes have been considered for solving the Burgers equation. The main difference of these schemes lies in the calculation of second-order derivative terms, which is obtained by applying the first-order operator twice and the method of undetermined coefficients. The aim is to comparison these schemes in terms of computational accuracy for solving the Burgers equation with difference viscosity values, especially for very small viscosity values. The results show that both schemes achieve almost the same accuracy for large viscosity values and second method is more accurate for moderate viscosity values, but both schemes are failed for very small viscosity values. However, when both schemes coupled low-pass filter for very small viscosity values, both schemes can well inhibit the problem.

• Periodical: Applied Mechanics and Materials (Volumes 444-445)
• Pages: 681-686
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.444-445.681
• Online since: October 2013
• Authors: Xiao Gang He, Ying Yang, Ping Zhang, Xiao Hua Zhang
• Keywords: Burgers’ Equation, Compact Finite Difference, Low-Pass Filter

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