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An polyhedral mesh method with hundreds or thousands faces has been proposed as a kind of unstructured mesh method. In particular, at computation for compressible flows, contrast of mesh element size is very high. Thus, it is useful from the viewpoint of computational efficiency as there is large possibility of reducing unnecessary grid points. In this paper, the polyhedral mesh method was improved for moving boundary problems which requires high computational cost. Specifically, the polyhedral mesh method was combined with the unstructured moving grid finite volume method. Then, the moving polyhedral mesh method which satisfies both physical and geometric conservation laws was proposed. The method allows moving grid computation with high accuracy. In this paper, the new method was formulated. Then, the reliability of its scheme was shown by confirming the geometric conservation law to apply the moving grid problem in a uniform flow. Furthermore, to confirm its code for compressible flows, it was applied to a shock tube problem. Then, the complete matching with exact solution was shown. At last, the method was applied to piston problem for compressible flow. By comparing with exact solution of the shock wave position, effectiveness and promising future of the method were shown.

Computational fluid dynamics, Moving mesh, Polyhedral mesh, Compressible flows