A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation
Abstract
In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge-Kutta total variation diminishing (TVD) scheme is employed for the time discretization, and the three-point combined compact difference (CCD) scheme is used for spatial discretization. Our method is third-order accurate in time and sixth-order accurate in space. The CCD-TVD method treats the nonlinear term explicitly thus it is very efficient and easy to implement. In addition, we prove the unique solvability of the CCD system under non-periodic boundary conditions. Numerical experiments including both two-dimensional and three-dimensional problems have been conducted to demonstrate the high efficiency and accuracy of the proposed method.
Cite
@article{arxiv.1805.08407,
title = {A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation},
author = {Kejia Pan and Xiaoxin Wu and Xiaoqiang Yue and Runxin Ni},
journal= {arXiv preprint arXiv:1805.08407},
year = {2018}
}
Comments
16 pages, 0 figures, 4 tables