双曲守恒律方程的Lax-Wendroff时间离散WENO格式

WENO Scheme Based on Lax-Wendroff Time Discretization to Solving Hyperbolic Conservation Laws

双曲守恒型方程的高精度、高分辨率计算格式的研究一直是计算流体力学的热点问题。针对原WENO-JS格式分辨率较低和计算量偏大的不足问题,提出利用简单的重构数值通量的方法以提高计算效率,构造了新的简单限制器的5阶迎风型WENO格式。通过MATLAB软件的仿真对Lax-Wendroff WENO-JS格式、Lax-Wendroff简单限制器WENO格式、Runge-Kutta WENO-JS格式、Runge-Kutta简单限制器的WENO格式的实验结果进行了分析,并比较了这四种计算格式的计算效率和计算精度。数值实验表明:新格式Lax-Wendroff简单限制器WENO格式在保持原WENO分辨率的前提下,计算速度有明显提高,减少了20%的计算时间。

The research of high accuracy and high resolution schemes have been a hmathematics. According to low resolution and large amount of calculation of the original WENO-JIS scheme, wepropose a simple new limiter fiftli order upwind WENO scheme to reconstruct the numerical flux of the simplestructure to improve the computational efficiency. Compared with other efficient high ENOand WENO, it is shown that the computational cost of this scheme is less than that of WENO-JS accuracy. By use of MATLAB software,we compared and analyzed computational efficiencies accuracies of Lax-Wendroff WENO-JS scheme,Lax-Wendroff simple limiter WENO scheme,Runge-Kutta simple limiter WENOscheme and Runge-Kutta WENO-JS scheme. The numerical results showthat the newLax-Wendroff simple limiter WENO scheme can improve the computing speed and reduce the computing time by 20% whilemaintaining the original WENO resolution.