中文摘要：

研究二维散乱点集上数值求解非线性扩散方程的有限方向差分方法。利用五个邻点信息构造具有最小模板的离散格式,并且离散系数具有显式表达式。另外,利用五点公式获得了间断问题物质界面的离散格式,该格式对界面流的计算具有近似二阶精度。不同计算区域及不同类型的离散点集上的计算结果验证了方法的有效性。

英文摘要：

An approach for numerically solving nonlinear diffusion equations on 2D scattered point distributions is developed with finite directional difference method. The approach yields stencils of minimal size using five neighboring points. And coefficients of discretization have explicit expressions. A scheme employing five-point formulae is proposed to discretize multimedia interface condition for discontinuous problems in which approximation to flux on interface is second-order accurate. The discretization methods show good performance in numerical examples with different computational domains and different point distributions.