Secondary Conservative Finite Difference Schemes for Moving Grids

概要

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The secondary conservative finite difference for convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme has not been extended to a moving grid. In this study, the secondary conservative convection scheme for ALE type moving grid simulations is proposed. For the moving grid simulations, the geometric conservation law (GCL) is known as the mathematical constraint on metrics and is interpreted as the condition for capturing a uniform flow. A new role of the GCL is revealed for the commutability and conservation properties of convective forms. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. In order to check the commutability of the convection schemes, a numerical test is done on a wavy grid problem. Then the reliability of the schemes is demonstrated on the piston problem and the flow around an oscillating square cylinder.