任意精度的三点紧致显格式及其在CFD中的应用

通过在泰勒级数展开中运用逐阶迭代的方法，推导出了空间任意精度的三点紧致显格式的表达式，又由Fourier分析法得到了格式的数值弥散和耗散特性．与以往的高精度紧致差分格式不同，提出的格式不用隐式求解代数方程组并且可以达到任意精度．通过方波问题和顶盖方腔流的算例表明，格式在稀疏网格下可以得到很高的精度，不仅能节省计算量，而且易于编程，有很高的计算效率．

Three-Point Explicit Compact Difference Scheme With Arbitrary Order of Accuracy and Its Applicatin in CFD

Based on the successive iterative approach in the taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived, and the numerical characteristic of the scheme was studied by the Fourier analysis. Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convection-diffusion problem with a sharp front gradient and the typical lid-driven cavity flow were given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.