A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we present a new vertex-centered arbitrary Lagrangian-Eulerian (ALE) finite volume scheme for two-dimensional compressible flow. In ourscheme, the momentum equation is discretized on the vertex control volume, whilethe mass equation and the energy equation are discretized on the sub-cells which areincluded in the vertex control volume. We attain the average of the fluid velocityon the vertex control volume directly by solving the conservation equations. Thenwe can obtain the fluid velocity at vertex with the reconstructed polynomial of thevelocity. This fluid velocity is chosen as the mesh velocity, which makes the meshmove in a Lagrangian manner. Two WENO (Weighted Essentially Non-Oscillatory)reconstructions for the density (the total energy) and the velocity are used to makeour scheme achieve the anticipated accuracy. Compared with the general vertex-centered schemes, our scheme with the new approach for the space discretizationcan simulate some multi-material flows which do not involve large deformations.In addition, our scheme has good robustness, and some numerical examples arepresented to demonstrate the anticipated accuracy and the good properties of ourscheme.