保持球对称的相容流体算法的构造

重点研究如何在二维柱坐标系中保持流体运动的球对称问题．该问题需要对整个流体算法做细致的分析与设计，从而获得不同的方法．基于Caramana介绍的修正压强梯度算子构造了保持球对称的相容流体算法，该算法还包括了边人工粘性方法、子网格压力的计算方法，以及预估步与校正步相结合的策略．并且，考虑了总能量的守恒性，讨论了网格节点质量保持不变的必要性，以及基于相容格式证明了边人工粘性的耗散性．数值模拟结果与已知数据的比对验证了程序的正确性、稳定性.

Construction of Compatible Hydrodynamics Algorithms With the Preservation of Spherical Symmetry

The problem of preserving the spherical symmetry of fluid flow in two dimensional cylindrical geometry was detailed studied. This problem called for cautious analysis and design of the entire hydrodynamics algorithms, which led to various methods. A programs was created, which based on the following schemes: utilizing the staggered Lagrangian algorithms; evolving the momentum by using the modified pressure gradient operators introduced by Caramana; advancing the internal energy compatibly; utilizing the edge-centered artificial viscosity; including the effects of the subzonal pressure forces; and ensuring the second order time accuracy by combining the predictor and corrector steps. The conservation of total energy was also investigated, the necessity of maintaining constant nodal masses was discussed, and the dissipativity of edge-centered artificial viscosity based on the compatible hydrodynamics algorithms was proved. In the end, the comparisons between numerical results and the known solutions demonstrated the correctness and robustness of the programs.