  This paper modifies a 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
fourth-order precise integration method (PIM) 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. Numerical results show that the proposed method appreciably
improves the computational accuracy compared with the existing numerical
method.Moreover, the two-dimensional and three-dimensional examples demonstrate
excellent adaptability, and the numerical simulation results also have very
high accuracy in medium Reynolds numbers.
