爆轰波模拟中一个保正的有限体积WENO格式

A Positive Preserving Finite Volume WENO Scheme in Detonation Wave Simulation

对一维爆轰波的数值模拟设计了一种保正的有限体积WENO格式.以一维反应欧拉方程组作为描述爆轰波的控制方程,对方程组在空间离散上采用三阶WENO重构的有限体积法,时间离散上采用Strang分裂法和二阶龙格库塔法.从爆轰波的数值模拟中可以观察到,在压力快速变化的区域使用一般的WENO重构方法会使得压力出现负值.提出了一种简单且有效的策略,使得重构的压力具有保正性.通过数值算例验证了所提出的数值格式的稳定性和收敛性,以及对爆轰波结构变化捕捉的良好能力.

In this paper,a positive preserving finite volume WENO scheme is designed for the numerical simulation of one-dimensional detonation waves.The one-dimensional reaction Euler equations are used as the control equations for describing detonation waves.The equations are discretized using the third-order WENO reconstruction finite volume method in space,and the Strang splitting method and second-order Runge Kutta method in time.From the numerical simulation of detonation waves,it can be observed that using the general WENO reconstruction method in areas with rapid pressure changes can result in negative pressure values.A simple and effective strategy is proposed to ensure that the reconstructed pressure maintains positivity.The stability and convergence of the proposed numerical scheme were verified through numerical examples,as well as its good ability to capture changes in detonation wave structure.