An explicit modal discontinuous Galerkin approach to compressible multicomponent flows: application to shock-bubble interaction

Abstract

An explicit modal discontinuous Galerkin method is developed for solving compressible multicomponent flows. The multicomponent flows are governed by the two-dimensional compressible Euler equations for a gas mixture. For spatial discretization, scaled Legendre polynomials with third-order accuracy are utilized, while an explicit third-order accurate Strongly Stability Preserving Runge-Kutta scheme is adopted to march the solution in time. Numerical experiments are carried out for the shock-bubble interaction problem to validate the present numerical method. Results of the present numerical method are compared with the available experimental results. A close agreement is observed between the numerical and experimental results, indicating that the present method has the capability to capture sharp discontinuities. Finally, certain numerical results of the shock-bubble interaction problem with both light and bubbles are explained based on flow fields visualization and vorticity production in detail.