Finite-volume solution of two-dimensional compressible flows over dynamic adaptive grids

A novel Finite Volume (FV) technique for solving the compressible unsteady Euler equations is presented for two-dimensional adaptive grids over time dependent geometries. The interpretation of the grid modifications as continuous deformations of the underlying discrete finite volumes allows to determine the solution over the new grid by direct integration of the governing equations within the Arbitrary Lagrangian–Eulerian (ALE) framework, without any explicit interpolation step. The grid adaptation is performed using a suitable mix of grid deformation, edge-swapping, node insertion and node removal techniques in order to comply with the displacement of the boundaries of the computational domain and to preserve the quality of the grid elements. Both steady and unsteady simulations over adaptive grids are presented that demonstrate the validity of the proposed approach. The adaptive ALE scheme is used to perform high-resolution computations of the steady flow past a translating airfoil and of the unsteady flow of a pitching airfoil in both the airfoil and the laboratory reference, with airfoil displacement as large as 200 airfoil chords. Grid adaptation is found to be of paramount importance to preserve the grid quality in the considered problems.