双曲型守恒律的一个4阶精度差分格式

A Fourth-order Accurate Difference Scheme of Hyperbolic Conservation Laws

基于TVD限制器函数方法选取数值导数,在空间方向用分段3次多项式进行重构,对时间积分用Simpson求积公式,并用四阶Runge-Kutta NCE方法求中间时间点的值,得到求解一维非线性双曲型守恒律方程的4阶精度差分格式;之后给出2个经典数值算例,以验证格式的高精度高分辨率优点。

By applying piecewise cubic polynomial reconstruction in spacial direction and Simpson quadrature formulae about the time integral and fourth-order Runge-Kutta Natural Continuous Exten- sion method for solving the intermediate value of time point, a new fourth-order accurate difference scheme, which based on the total variation diminishing limiter function method to choose numerical derivative, is obtained for the one dimensional equation of hyperbolic conservation laws. And then, two typical numerical examples are given to show the advantages of high-accuracy and high-resolu- tion.