(untitled) (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 our scheme, the momentum equation is discretized on the vertex control volume, while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control volume. We attain the average of the fluid velocity on the vertex control volume directly by solving the conservation equations. Then we can obtain the fluid velocity at vertex with the reconstructed polynomial of the velocity. This fluid velocity is chosen as the mesh velocity, which makes the mesh move in a Lagrangian manner. Two WENO (Weighted Essentially Non-Oscillatory) reconstructions for the density (the total energy) and the velocity are used to make our scheme achieve the anticipated accuracy. Compared with the general vertex-centered schemes, our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large deformations. In addition, our scheme has good robustness, and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.