An Explicit Modal Discontinuous Galerkin Approach to Compressible Multicomponent Flows

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 strong 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. The 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 heavy bubbles are explained based on flow field visualization and vorticity production in detail.