In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for the 5-equation model of compressible multi-component flows with Mie-Grüneisen equation of state. The method mainly consists of three steps: firstly, the DG method with the non-oscillatory kinetic flux is used to solve the conservative equations of the model; secondly, inspired by Abgrall’s idea, we derive a DG scheme for the volume fraction equation which can avoid the unphysical oscillations near the material interfaces; finally, a multi-resolution weighted essentially non-oscillatory limiter and a maximum-principle-satisfying limiter are employed to ensure oscillation-free near the discontinuities, and preserve the physical bounds for the volume fraction, respectively. Numerical tests show that the method can achieve high order for smooth solutions and keep non-oscillatory at discontinuities. Moreover, the velocity and pressure are oscillation-free at the interface and the volume fraction can stay in the interval [0,1].

本文针对具有Mie-Grüneisen状态方程的可压缩多组分流的5方程模型，提出了一种采用非振荡动量的高阶准保守不连续Galerkin（DG）方法。该方法主要包括三个步骤：首先，采用非振荡动量的DG方法求解模型的保守方程。其次，受阿布格拉（Abgrall）的思想启发，我们为体积分数方程推导了DG方案，该方案可以避免材料界面附近的非物理振动。最后，采用多分辨率加权基本非振荡限制器和最大原理满足限制器，以确保在不连续点附近无振荡，并分别保留体积分数的物理界限。数值测试表明，该方法可以实现高阶平滑解，并保持非振荡的不连续性。此外，速度和压力在界面处无振荡，体积分数可以保持在[0,1]区间内。