三维扩散方程基于Richardson外推法的高阶紧致差分方法
High-Order Compact Difference Method Based on Richardson Extrapolation for Three-Dimensional Diffusion Equations
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摘要: 基于Richardson外推法提出了一种求解三维扩散方程的高阶紧致差分方法.该方法首先利用截断误差为O(τ2+h4)的四阶紧致交替方向隐式(ADI)差分格式在不同尺寸的网格上对原方程进行求解,然后利用Richardson外推技术外推一次,得到了三维扩散方程具有O(τ4+h6)精度的数值解.数值实验验证了该方法的高阶精度及有效性.Abstract: A high-order compact difference method based on the Richardson extrapolation technique is proposed to solve the unsteady three-dimensional diffusion equations. For a particular implementation, firstly, numerical results are obtained on meshes of different sizes using a high order alternating direction implicit (ADI) difference scheme, which are fourth order in space and second order in time. Then, the Richardson extrapolation method is used to get an accuracy solution for three-dimensional problems, which is six order in space and fourth order in time. Numerical experiments are made to demonstrate the high accuracy and validity of this method.
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