一维双曲系统高分辨率波传播算法研究

High resolution wave propagation algorithm for one dimensional hyperbolic system

本文发展了波传播理论算法,通过Riemann求解器和高阶WENO空间重构得到间断跳跃.根据波传播的物理性质能够处理双曲系统的振荡以及各物理量的守恒问题,相比于其他的高分辨率数值模拟方法,不仅合理降低了耗散,清晰地捕捉到激波间断,并且提出间断判断因子,在保持精度的前提下,使计算效率显著提高.通过数值模拟欧拉方程的Sod问题和Lax问题,验证该方法在处理双曲系统间断问题上有广泛适用性和优越性.通过比较CPU时间,验证了加入判断因子后计算效率明显提高.

In this paper, wave propagation algorithm was developed and discontinuity was solved by the Riemann solver and high order WENO spatial reconstruction. This method is able to handle the oscillation and the physical variables conservation of the hyperbolic systems on the basis of the physical properties of wave propagation. It can not only reduce the dissipation and capture the shock wave and discontinuity clearly compared to other high resolution numerical methods, but also make the calculation efficiency improving obviously through putting forward the discontinuous judgment factors on the premise of accuracy unchanged. This method has demonstrated the wide applicability and advantageous properties when dealing with hyperbolic system through numerical examples, including Sod problem and Lax problem of Euler equations. Calculation efficiency was obviously improved after introducing judgment factors.