High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes

We have validated our new unstructured Lagrangian LTS approach over a wide sample of test cases solving the Euler equations of compressible gas dynamics in two space dimensions, including shock tube problems, cylindrical explosion problems, as well as specific tests typically adopted in Lagrangian calculations, such as the Kidder, the Saltzman and the Sedov problem. When compared to the traditional global time stepping (GTS) method, the newly proposed LTS algorithm allows to reduce the number of element updates in a given simulation by a factor that may depend on the complexity of the dynamics, but which can be as large as ∼4.7. Finally, we have also shown the improvement in terms of computational efficiency in a representative test for the special relativistic magnetohydrodynamics (RMHD) equations.