中文摘要：

讨论抛物型方程的离散差分格式的构造．对九点差分格式进行了适用范围的讨论，并在此基础上提出辅助网格差分方法，用于处理因网格长宽比大且扭曲较大的网格引起的计算精度与计算效率降低的问题．该方法从守恒方程出发，将九点差分格式应用于按某种合适的方式进行重分之后的网格上，减少由于网格正则性差以及网格节点上的物理量采用周围网格量的加权平均等原因所引起的计算误差，得到一个新的但其解仍然逼近原来网格上的物理量的方程组．所构造的方法便于实施，且更适合于对实际物理模型的模拟，能比较好地适应流体大变形导致的网格扭曲．数值试验表明它有较好的数值精度和稳定性．

英文摘要：

Construction of difference schemes for parabolic equations on distorted meshes with large aspect ratio is discussed. The limitation of 9-point scheme is provided. An assistant mesh difference method is proposed for distorted meshes with large aspect ratio to improve precision and efficiency. Based on the conservation law, applying appropriate rezone methods for meshes we modify the 9-peint method to reduce computation error due to poor regularity of the meshes and low precision due to the approximation to vertices values by an average of neighboring cell values. The nonlinear system obtained is a different system from the 9-peint scheme. Its solution approximates to the solution with the original meshes. The designed scheme is implemented easily and adapts well to distorted meshes. Numerical experiments show good precision and stability.