径向基函数插值的有限体积方法

Finite Volume Method of Radial Basis Functions Interpolation

构造了一类基于径向基函数插值思想的有限体积格式。依据ENO思想建立自适应模板,在选定的模板上利用Multiquadric函数逼近控制单元边界处的守恒变量,再构造高阶数值通量。对经典的一维和二维问题的数值模拟结果表明,这种格式具有高阶精度和高分辨率。

A kind of finite volume methods based radial basis function （RBF） is presented. The adaptive stencils are formed according to essentially non-oscillatory （EN0） method, then multiquadric radial basis function （MQRBF） is used to approximate the numerical flux terms on the adaptive stencils, Finally it is generalized to one and two dimensional problems of aerodynamics, and the numerical experiments show that it has high accuracy and resolution.