论文标题
使用非振荡动力学通量
A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux
论文作者
论文摘要
在本文中，提出了使用非振荡动力学通量的高阶准保守不连续的戈尔金（DG）方法，该方法是针对具有Mie-Grüneisen状态方程的可压缩多组分流量的5个方程模型。该方法主要由三个步骤组成：首先，使用非振荡动力学通量的DG方法用于求解模型的保守方程。其次，受Abgrall的想法的启发，我们得出了用于体积分数方程的DG方案，该方案可以避免材料接口附近的非物理振荡。最后，采用了多分辨率的WENO限制器和最大原始满足限制器来确保在不连续性附近无振荡，并分别保留体积分数的物理界限。数值测试表明，该方法可以达到平滑解决方案的高阶，并保持不连续性。此外，速度和压力在界面处不含振荡，体积分数可以保持在间隔中[0,1]。
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 WENO 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].
