双曲守恒律方程的一种熵相容格式

An Entropy-consistent Scheme for Hyperbolic Conservation Laws

提出了一种求解双曲守恒律方程的熵相容数值通量。在熵守恒通量中添加一个二阶迎风项和一个三阶的差商项来保持熵稳定并且抵消解在跨过激波时所产生的激波强度立方倍的熵增,从而实现熵相容。新的数值通量能精确保持定常的接触间断、消除非物理的膨胀激波及负压力等现象。通过采用近年发展起来的WENO方法在单元交界面处进行高阶重构,得到高阶精度的熵相容格式。数值算例采用空间半离散格式,并结合显式三步三阶Runge-Kutta(RK3)方法进行时间推进。不同的算例结果表明,格式具有稳定性、高分辨率和无振荡性等特点。

An entropy-consistent flux is developed for the hyperbolic conservation laws.To preserve entropy-stability and offset the entropy production of the order of cube of the shock strength across the shock waves,a second-order upwind term and a third-order differential term are added to the entropy-conservation flux,so as to achieve entropy consistency.The new flux exactly preserves the stationary contact discontinuity and does not capture the unphysical rarefaction shock and negative pressure.By using WENO reconstruction at cell interfaces,a high order accurate entropy consistent scheme is adopted.Numerical experiments use the semi-discrete scheme with the explicit three-stage third-order Runge-Kutta（RK3） time evolution.Several different numerical examples were implemented with the entropy consistent scheme.The results showed that the scheme is stable,high resolution and non-oscillation.