Study on Numerical Methods for Flows with Moving Boundaries

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As governing equations for numerical methods of flows with moving boundaries, usually used are the conservative form in general coordinate system in the case of compressible fluid, and the ALE (Arbitrary Lagrangian-Eulerian) form in the case of incompressible fluid, but these methods have the difficulty to re-generate grids at each time step when the boundaries are moving. On the other hand, the moving-coordinate method that the head investigator proposed is to resolve the difficulty. The purposes of this research project covers two intent : one is to give the unified derivation to the governing equations for numerical methods of flows with moving boundaries, which have existed individually, and give the scientific prospect to the field ; the other is to extend the ALE method and the moving-coordinate method for general use, apply them to physical and engineering problems, and enable to solve problems which cannot be solved because of the difficulty above statedIn the fiscal year of 20 … More 00, it was shown that the governing equations for numerical methods including moving boundaries, i.e., the conservative form in general coordinate system, the ALE (Arbitrary Lagrangian-Eulerian) form, and the moving-coordinate form, are derived unifiedly in this order, and simultaneously the meaning of the geometric conservation laws which metrics should satisfy was analytically 〓〓rified. Furthermore the moving-coordinate method was extended for general use, and applied to two cases with each way and flows : a 〓〓lti-domain problem for unsteady flows about a flying projectile launched in a ballistic range and a single-domain problem with cut-cell method for branch flows in opening process of a high-voltage gas circuit breaker. As results, it has been confirmed that the moving-coordinate method works effectively.In the fiscal year of 2001, the ALE form was extended to the general coordinate system, and applied to gun-tunnel flows. In the numerical computation there are two courses : to simulate complicated flows closer to real phenomena and obtain detail, and to model (simplify) and obtain practical information with less computing time. As an example of the latter course, the quasi-one-dimensional Euler equations including the change of cross area with not only space but also time were derived, the ALE method was correctly applied with modelling of the piston motion and the pressure loss. Through comparison with experiments, it has been confirmed that the extended ALE method works well.In the fiscal year 2002, the results obtained till then were published in international Journals with evaluation and consideration added. As preparatory stage to future developments, unstructured-grid solvers for arbitrary configuration and high-accurate schemes including source terms have been developed Less