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.

Septic B-spline collocation method for numerical solution of the coupled Burgers’ equations

“…Implicit logarithmic finite-difference method (Srivastava et al, 2014), and collocation of local radial basis functions (Islam et al, 2012). For more about Burgers' equation see (Bonkile et al, 2018;Lashkarian et al, 2019;Pana et al, 2018;Prakasha et al, 2015;Shi et al, 2017;Wang and Kara, 2018;Karakoc et al, 2014).…”

Method of lines for multi-dimensional coupled viscous Burgers’ equations via nodal Jacobi spectral collocation method

“…In table 13 we compare the error norms obtained by applying our numerical scheme with [11], for = = = = a b c d 1 3 1at = t 1.…”

“…Flethcer [9] and Gao and Zou [10] extend the Hopf-Cole transformation to solve 2D and 3D Burgers' equations. Similar transformations could solve the 2D and 3D coupled versions [11,12]. The exact approaches usually use the Hopf-Cole transformations or construct solutions in the series form, e.g.…”

“…They use the Crank-Nicolson finite difference scheme to discretize the temporal variable and then solve the ODE system by the improved backward substitution. Pan et al in [11] propose a numerical scheme for 2D and 3D coupled Burgers' equations using third-order accuracy total variation diminishing RungeKutta scheme in time, and sixth-order accuracy combined compact difference scheme for spatial discretization. Shukla et al [15] propose an unconditionally stable method to solve 3D coupled Burgers' equations.…”