MHD模拟中的一些困难问题的数值方法研究

Usual difference schemes are constructed basing on Taylor expansion of the solution. The difference schemes based on approximate Taylor expansion of the solution function don't be suited to the problems with sharp functions partly (e.g. boundary layer, highly oscillation), because the method requires the solution to be slow variance relative to mesh scale. The difference schemes of coefficient approximation that we propose are constructed basing on Taylor expansion of the coefficient. The coefficient approximate method is a robust solution method for boundary layer as well as high oscillatory in linear boundary value and eigen-value problems.

等离子体丰富的物理现象提出了一些至今求仍然很困难的数值问题，如奇扰动问题、高荡问题、反向点及多尺度问题等。本工作将用解函数的局部特征构造函数的局部基，导出几种新的差分格式。新格式避免了传统差分求解引起的非物理振荡和解的畸变，因而新式能有效地求解一些困难的数值问题，从而研究相关的物理问题提供了强有力的手段。