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.

翻译：本文对n维Burgers系统的Hopf-Cole变换进行了修正。通过修正Hopf-Cole变换，我们得到了n维热传导方程。随后，提出了一种结合空间全局六阶紧致有限差分格式的四阶精细积分法，以高精度求解该方程。此外，结合Strang分裂方法，将该格式推广至多维（二维、三维）Burgers系统。数值结果表明，与现有数值方法相比，所提方法显著提高了计算精度。同时，二维和三维算例展现了优异的适应性，且在中雷诺数下数值模拟结果亦具有极高的精度。