关键词: 无网格, 有限方向差分方法, 非线性扩散方程, 多介质界面, 最小模板

Abstract: 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.

Key words: meshless, finite directional difference method, nonlinear diffusion equations, multimedia interface, minimal stencil