三维对流扩散方程的高精度全隐式多重网格方法

Multigrid method based on high accuracy full implicit schemeof 3D convection diffusion equation

提出了数值求解三维非定常变系数对流扩散方程的一种高精度全隐紧致差分格式,该格式在空间上具有四阶精度,时间具有二阶精度。为了克服传统迭代法在每一个时间步上迭代求解隐格式时收敛速度慢的缺点,采用多重网格加速技术,建立了适用于本文高精度全隐紧致格式的多重网格算法,从而大大加快了迭代收敛速度。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。

A high order compact finite difference scheme is proposed to solve the three-dimensional unsteady convection diffusion equation with variable convection coefficients. The scheme is of fourth order in space and second order in time. A multigrid algorithm is presented to overcome the difficulties when traditional relaxation methods are used to treat the implicit difference schemes at each time step and a fast solution is obtained. Numerical experiments are employed to show that the present method is stable and yields accurate solutions for high Reynolds number problems.