移动网格下求解多相反应流的间断有限元方法

Discontinuous finite element method for multiphase reaction flow equations based on mesh-moving technology

针对传统的数值方法很难有效解决实际应用中的激波以及界面问题,给出了一种基于网格移动技术求解质量、动量、能量守恒的一维多相反应流方程的间断有限元方法。使用高阶精度的间断Galerkin方法进行空间离散以及龙格—库塔方法进行时间离散求解控制方程组。通过数值算例比较了两种数值通量的高阶精度的误差,以及不同权重的Roe平均处理单元节点速度的效果,发现使用一阶格式时HLLC的精度更好,另外权重对误差影响不大。

Considering that traditional numerical methods are difficult to effectively solve shock waves and interface problems in practical applications,a discontinuous finite element method is proposed to solve the mass,momentum,and energy conservation of the one-dimensional multiphase reaction flow equation based on the mesh-moving technology.High-order discontinuous Galerkin method is used for spatial discretization,and Runge Kutta method is used for time discretization to solve the control equations.An example is given to compare the error of high order precision of the two numerical fluxes and the effect of Roe average processing unit node velocity with different weights.It is found that the accuracy of HLLC is better when using the first-order scheme,and the weight has little effect on the error.