A Discontinuous Galerkin Method on Moving Mesh for Ejecta Mixing

Abstract In this work, a discontinuous Galerkin (DG) method on moving mesh is presented for solving ejecta mixing problems, which are described by the particle trajectory model. The DG method is used for spatial discretization of fluid dynamics equations in Arbitrary Lagrangian–Eulerian framework, which results in a semi-discrete system. This semi-discrete system and particle motion equations are then solved by using the Runge–Kutta (RK) method in time. To ensure consistency between the accuracy of the moving mesh discretization scheme and the DG method, the operator-compensation method is employed to discretize the Euler–Lagrange equations for moving mesh. As a result, the more accurate mesh vertex velocity can be obtained. Finally, some numerical experiments are conducted to verify the effectiveness of the proposed numerical method, demonstrating its high-order accuracy and robustness.