A new Crank-Nicolson-like ALE finite volume scheme verifying the discrete geometric conservation law for 3D flow computations on moving unstructured meshes

This paper describes a finite volume solver for the computation of unsteady Euler flows on moving unstructured grids. The Arbitrary Lagrangian Eulerian formulation takes the grid velocity into account. A Cranck-Nicolson time integration scheme and a quadratric spatial reconstruction technique are applied and yield a second order time and space truncation errors. A new way of satisfying the Discrete Geometric Conservation Law adapted to this scheme is proposed. This new method is computational efficient as it leaves the number of fluxes evaluations equal to their fixed grid counterpart. Results highlighting the robustness and accuracy of the proposed approach are presented.