A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation
This work provides a high-order accurate and efficient numerical method for solving nonlinear Burgers' equations, which are important in fluid dynamics and other fields.
The authors propose a CCD-TVD finite difference method for solving multidimensional coupled Burgers' equation, achieving sixth-order spatial and third-order temporal accuracy. Numerical experiments on 2D and 3D problems demonstrate high efficiency and accuracy.
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.