论文标题
与相变的两个相流的显式无限域分裂
Explicit-Implicit Domain Splitting for Two Phase Flows with Phase Transition
论文作者
论文摘要
包括相变的两个相位流，尤其是相位创建，尖锐的界面仍然是数字的挑战性任务。我们考虑具有液体和蒸气相之间具有相变的等温EULER方程。相位界面被建模为尖锐的界面，并且跨相边界的质量转移由动力学关系建模。参考文献中证明了存在和唯一性结果。 \ cite {hantke2019a}。使用尖锐的界面来模拟成核和空化导致包含小细胞的网格，这些细胞比其余网格细胞小几个数量级。这迫使明确的时间步进方案在这些细胞上采取很小的时间步骤。作为一种补救措施，我们建议明确的隐式域分裂，其中大多数网格细胞被明确处理，并且只有小细胞的邻域被隐式处理。我们使用双重时间步进来求解所得的小隐式系统。我们的数值结果表明，与完全明确的治疗相比，新方案是强大的，并提供了显着的加速。
Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The phase interface is modeled as a sharp interface and the mass transfer across the phase boundary is modeled by a kinetic relation. Existence and uniqueness results were proven in Ref. \cite{Hantke2019a}. Using sharp interfaces for simulating nucleation and cavitation results in the grid containing tiny cells that are several orders of magnitude smaller than the remaining grid cells. This forces explicit time stepping schemes to take tiny time steps on these cells. As a remedy we suggest an explicit implicit domain splitting where the majority of the grid cells is treated explicitly and only the neighborhood of the tiny cells is treated implicitly. We use dual time stepping to solve the resulting small implicit systems. Our numerical results indicate that the new scheme is robust and provides significant speed-up compared to a fully explicit treatment.
