In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions for low Mach flows. High order accuracy in time is obtained by semi-implicit temporal integrator based on the IMEX Runge-Kutta (IMEX-RK) framework. High order in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions adapted to the semi-implicit IMEX-RK time discretization. Type A IMEX schemes are constructed to handle not well-prepared initial conditions. Besides, these schemes are proven to be asymptotic preserving and asymptotically accurate as the Mach number vanishes for well-prepared initial conditions. Divergence-free property of the time-discrete schemes is proved. The proposed scheme can also well capture discontinuous solutions in the compressible regime, especially for two dimensional Riemann problems. Numerical tests in one and two space dimensions will illustrate the effectiveness of the proposed schemes.
翻译:在本文中,我们提出了一个新的高顺序半隐性计划,用于所有马赫公司全部气动电动电动等方程式。材料波得到明确处理,而声波得到暗中处理,从而避免了对低马赫流动的严重的CFL限制。基于IMEX Runge-Kutta(IMEX-Kutta)框架的半隐含时间集成器获得了较高的时间顺序精确度。空间高度秩序是通过有限的差异WENO计划实现的,这些差异计划具有与半隐含的IMEX-RK时间分解的特性的重建。AMEX计划是用来处理准备不完善的初始条件的。此外,这些计划被证明是简单的保护,并且与精心准备的初始条件的Mach数字消失一样,也是不精确的。证明了时间分解办法的无差异性属性。拟议的计划还可以在压缩制度中捕捉不连续的解决方案,特别是针对两个维度的Riemann问题。一个和两个空间层面的数值测试将说明拟议计划的有效性。