  A high-order quasi-conservative discontinuous Galerkin (DG) method is
proposed for the numerical simulation of compressible multi-component flows. A
distinct feature of the method is a predictor-corrector strategy to define the
grid velocity. A Lagrangian mesh is first computed based on the flow velocity
and then used as an initial mesh in a moving mesh method (the moving mesh
partial differential equation or MMPDE method ) to improve its quality. The
fluid dynamic equations are discretized in the direct arbitrary
Lagrangian-Eulerian framework using DG elements and the non-oscillatory kinetic
flux while the species equation is discretized using a quasi-conservative DG
scheme to avoid numerical oscillations near material interfaces. A selection of
one- and two-dimensional examples are presented to verify the convergence order
and the constant-pressure-velocity preservation property of the method. They
also demonstrate that the incorporation of the Lagrangian meshing with the
MMPDE moving mesh method works well to concentrate mesh points in regions of
shocks and material interfaces.
