A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers' system

This paper introduces a modification of n-dimensional Hopf-Cole transformation to the n-dimensional Burgers' system. We obtain the n-dimensional heat conduction equation through the modification of the Hopf-Cole transformation. Then the high-order exponential time differencing precise integration method (PIM) based on fourth-order Taylor approximation in combination with a spatially global sixth-order compact finite difference (CFD) scheme is presented to solve the equation with high accuracy. Moreover, coupling with the Strang splitting method, the scheme is extended to multi-dimensional (two,three-dimensional) Burgers' system, which also possesses high computational efficiency and accuracy. Several numerical examples verify the performance and capability of the proposed scheme. Numerical results show that the proposed method appreciably improves the computational accuracy compared with the existing numerical method. In addition, the two-dimensional and three-dimensional examples demonstrate excellent adaptability, and the numerical simulation results also have very high accuracy in medium Reynolds numbers