一个三阶基本无振荡的差分格式

A Third-order Non-oscillatory Difference Scheme

利用待定系数法推导了一阶空间变量导数的三阶差分逼近,进而将通常对流通量的逼近方法推广到对通量导数的逼近.通过引入TVD限制器函数,对导数的三阶差分逼近进行校正,并结合三阶Runge-Kutta时间离散方法,构造了求解双曲型守恒律方程的一个三阶基本无振荡差分格式.该格式具有形式简单、计算量小且易于推广到非均匀网格等优点.通过给出的两个标准数值算例,验证了格式的有效性.

In this paper,a third-order approximation of the first-order space derivative is deduced by applying an undetermined coefficient method.Then the general approximation method for the convection flux to the derivative of the flux is extended.After introducing the TVD limiter function,we correct the third-order derivative difference approximation.Then we propose a third-order essential non-oscillatory difference scheme for solving hyperbolic conservation laws by employing the third-order Runge-Kutta method to discretize the time variable.This scheme has the advantages of simple form,less computational cost and easiness to extend the case of non-uniform grid.Finally,two standard numerical examples are given to verify the effectiveness of the scheme.