  We present a high-order accurate reconstructed discontinuous Galerkin (rDG)
method in arbitrary Lagrangian-Eulerian (ALE) formulation, for solving
two-dimensional compressible flows on moving and deforming domains with
unstructured curved meshes. The Taylor basis functions in use are defined on
the time-dependent domain, on which also the integration and computations are
performed. A third order ESDIRK3 scheme is employed for the temporal
integration. The Geometric Conservation Law (GCL) is satisfied by modifying the
grid velocity terms on the right-hand side of the discretized equations at
Gauss quadrature points. To avoid excessive distortion and invalid elements
near the moving boundary, we use the radial basis function (RBF) interpolation
method for propagating the mesh motion of the boundary nodes to the interior of
the mesh. Several numerical examples are performed to verify the designed
spatial and temporal orders of accuracy, and to demonstrate the ability of
handling moving boundary problems of the rDG-ALE method.
