一类逆风ENO线方法的构造及其对Euler方程的应用

本文利用ENO(essentially-non-oscillatory)插值思想,对非线性双曲型守恒律=0提出了一类逆风ENO线方法,使用这种格式其计算量比C.Shu在文6]中提出的通量分裂方法明显减少,进而同Runge-kutta时间离散相结合,提出了时空高精度差分格式。本文还把这类方法推广到方程组并用于计算Euler方程组的黎曼问题和拟一维喷管问题,得到了比较满意的数值结果。

A Class of Upwind ENO Methods of Lines with Applications of Systems of Euler Equation

In this paper, a class of upwind ENO (essentially non-oscillatory) methods of lines are constructed by applying ENO interpolation method to nonlinear hyperbolic laws. The amount of computation of these methods is less than that of the method in 6]. Moreover, on the basis of this class of schemes, using Runge-Kutta time-discretization, we construct a new class of second order accurate schemes in space and time. At last these methods are applied to systems of Euler equation, Riemann problem and quasi-one dimensional nozzle problem. The numerical results are quite satisfactory.