求解三维对流扩散方程的高精度隐式紧致差分方法

Compact Difference Method Based on High-Order Implicit Scheme for Solving the 3D Steady Convection-Diffusion Equation

首先利用一阶和二阶导数的Padé型四阶紧致差分格式,并结合原方程本身,构造了三维定常对流扩散方程的四阶隐式紧致差分格式;然后采用Richardson外推技术外推一次,得到了三维定常对流扩散方程具有六阶精度的数值解;最后通过数值实验验证了该方法的高阶精度及有效性.

Based on the Pad6 schemes of first-and second-order partial derivatives and combined with the original differential equation, a fourth-order implicit compact difference method is proposed for solving the 3D steady convection-diffusion equation. Then, the Richardson extrapolation method is used to further im prove the computational accuracy and a sixth-order accurate solution is obtained. Lastly, numerical experi ments are conducted to demonstrate the high accuracy and validity of this method.