An iterative finite-volume method on an unstructured moving Grid (3rd report, unstructured adaptive mesh refinement method for unsteady problems)

A new adaptive mesh refinement method for unsteady compressible flow is presented in this paper. For unsteady flow problem, the solution-adapted grid is also dynamically changing its shape at every time step according to the flow change since the flow is non-stationary. For the present solution-adapted grid method, two grid cells are merged into one grid cell and one grid cell is divided into two grid cells according to a criterion of grid adaption in a time-dependent way in unstructured grid system. In this case, it is important to assure geometric conservation low as well as physical conservation low on such the grid system. Therefore, we adopt a finite volume method in which a control volume on the space-time unified domain for estimating numerical flux. The method is described and applied for two-dimensional unsteady compressible flows.