Study on Numerical Methods for Flows with Moving Boundaries

动边界流动数值方法的控制方程，在可压缩流体情况下通常采用一般坐标系中的守恒型，在不可压缩流体情况下通常采用ALE(任意拉格朗日-欧拉)形式，但这些方法在边界移动时难以在每一时间步重新生成网格。另一方面，首席调查员提出的移动坐标方法就是为了解决这一困难。本研究项目的目的包括两个方面：一是对已有的具有运动边界的流动数值方法的控制方程进行统一推导，为该领域提供科学前景；二是推广通用的ALE方法和移动坐标方法，将它们应用于物理和工程问题，使之能够在20…财政年度内解决因上述困难而无法解决的问题在此基础上，统一推导了运动边界、任意拉格朗日-欧拉(ALE)形式和运动坐标形式等数值方法的控制方程，并对度量所满足的几何守恒律的意义进行了解析〓〓证明。在此基础上，将移动坐标方法推广到一般情况，并将其应用于两种情况：弹丸在弹道范围内发射的非定常流动的〓〓LTI域问题和高压气体断路器合闸过程中分支流动的割格法单域问题。2001财年，将ALE格式推广到一般坐标系，并应用于火炮身管流动。在数值计算中，有两个过程：一是更接近真实现象的复杂流动的模拟和细节的获取；二是以较少的计算时间模拟(简化)和获取实际信息。作为后一种情况的算例，推导了包含截面积随空间和时间变化的准一维欧拉方程，正确地应用了ALE方法，模拟了活塞运动和压力损失。通过与实验的对比，证实了扩展的ALE方法的有效性。2002财年，到目前为止所获得的结果在国际期刊上发表，并增加了评估和考虑。作为未来发展的准备阶段，用于任意构型和包括源项的高精度格式的非结构网格解算器开发得较少

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