高精度WENO和MWENO格式溃坝波模拟

采用高精度WENO和MWENO格式对二维浅水方程变量进行数值重构,研究分析高精度格式捕捉溃坝波的能力和分辨率.对浅水方程,采用Roe-Riemann格式和波传算法进行数值离散,并与以上2种重构方法两两结合成4种计算方法.采用Fortran语言分别对其进行编程计算.计算结果显示,高精度格式在捕捉溃坝瞬时基波延续推进的过程较好.在4种计算方法计算结果中,MWENO型波传格式模拟结果最好,捕捉溃坝波能力强,分辨率很高.

High accuracy WENO and MWENO schemes for dam break simulation

Variables for the two-dimensional shallow water equations were reconstructed based on the high accuracy WENO and MWENO schemes.The ability of capturing dam break waves and resolutions were analyzed by use of the high accuracy schemes.The two-dimensional shallow water equations were discretized by means of the RoeRiemann scheme and wave propagation algorithms.These two schemes combined with the above two reconstructed methods resulted in 4 computational methods.The relevant programs were compiled by use of the Fortran language.The numerical results show that the high accuracy schemes are satisfactory in capturing the continuous propagation process of instantaneous fundamental waves due to the dam break.The comparison among the 4 methods reveals that the simulated results by the wave propagation MWENO scheme are the best.It has strong ability of capturing dam break waves and high resolutions.