WENO Scheme Based on Lax-Wendroff Time Discretization to Solving Hyperbolic Conservation Laws - LI Xing-hua; SUN Yang; AI Xiao-hui (Journal of Harbin University of Science and Technology)
The research of high accuracy and high resolution schemes have been a hot topic in computational mathematics． According to low resolution and large amount of calculation of the original WENO-JS scheme，we propose a simple new limiter fifth order upwind WENO scheme to reconstruct the numerical flux of the simple structure to improve the computational efficiency． Compared with other efficient high accuracy schemes such as ENO and WENO，it is shown that the computational cost of this scheme is less than that of WENO-JS in the same accuracy． By use of MATLAB software，we compared and analyzed computational efficiencies and computational accuracies of Lax-Wendroff WENO-JS scheme，Lax-Wendroff simple limiter WENO scheme，Ｒunge-Kutta simple limiter WENO scheme and Ｒunge-Kutta WENO-JS scheme． The numerical results show that the new Lax-Wendroff simple limiter WENO scheme can improve the computing speed and reduce the computing time by 20% while maintaining the original WENO resolution