【摘要】 在紧致格式的基础上 ,提出了在 3个网格结点的框架下构造各阶奇次偏导数与偶次偏导数以及混合偏导数的高精度差分逼近方法和通用表达式 .首次提出了边界条件处理的具体方法 .本格式在构造时所涉及的网格结点数少 ,而且内点与边界点处具有相同的格式精度 .另外 ,由于内点与边界点处的各阶导数均采用统一求解块三对角阵的快速求解措施 ,因此该方法具有简捷、高效和通用的特点 ,并且易于推广到多维流场计算 .更多还原

【Abstract】 A new higher order accurate strongly compact scheme with three-point stencil dimensions is presented. This scheme has several advantages over those now in use. Firstly, the stencil dimension for the scheme is less than the traditional compact schemes and involves only three grid points. Secondly, finite difference approximations for odd partial derivatives, even partial derivatives and mixed partial derivatives are obtained by the scheme. It can reach arbitrary order of accuracy. The strongly compact scheme considers as unknowns not only the value of the function itself, but also those of its odd or even derivatives at each discretization point. The system is closed by considering auxiliary relationships between the function and its partial derivatives in some successive discretization points. It has block tridiagonal structure and can be sovled by using the block tridiagonal solver. Thirdly, the scheme ensures the same accuracy at the boundary points and the interior grid points. Numerical experiments suggest that the scheme not only has a fairly rapid convergence rate, but also can keep high-order accuracy. Besides, it also can be straightforward in the case of extensions to multidimensional problems.更多还原