High-order Lagrangian cell-centered conservative scheme on unstructured meshes

A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is introduced. With the high-order piecewise pressure of the cell, the high-order spatial discretization fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.