A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation

TL;DR

This paper introduces a high-order finite difference method combining CCD and TVD schemes for efficiently solving multidimensional nonlinear Burgers' equations with proven stability and demonstrated high accuracy through numerical experiments.

Contribution

The paper presents a novel third-order TVD scheme combined with a sixth-order CCD spatial discretization for multidimensional Burgers' equations, ensuring efficiency and high accuracy.

Findings

The method achieves third-order accuracy in time.

The method achieves sixth-order accuracy in space.

Numerical experiments confirm high efficiency and accuracy.

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.