一种用于求解牛顿可压缩流的时空LATIN-PGD策略
A space-time LATIN-PGD strategy for solving Newtonian compressible flows
AI总结：
本文提出了一种用于求解牛顿可压缩流的时空LATIN-PGD策略，通过压力-速度解耦算法和PGD分解方法，实现了对复杂流体问题的高效模拟。
摘要：
模拟流体问题是许多工程应用的核心，但往往需要高计算成本，尤其是在处理复杂模型时。本文提出了一种使用LATIN-PGD求解器解决流体问题的新方法。在本研究中，我们聚焦于牛顿可压缩和层流的具体且相对简单的案例，这使得能够专注于那些状态方程能直接建立压力与密度之间关系的流体。因此，可以使用LATIN求解器来设置压力-速度解耦算法。此外，适当广义分解（PGD）原生地包含在求解器中，为速度和压力场分别提供两个独立的时空分解。作为第一步，求解器在具有解析解的问题上进行了验证。然后应用于稍微复杂一些的问题。结果与文献中的结果有良好的一致，我们预计该求解器未来可用于计算更复杂的材料定律。
英文摘要：
Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the LATIN-PGD solver. In this contribution, we place ourselves within the framework of Newtonian compressible and laminar flows. This specific and relatively simple case enables focusing on flows for which a state equation provides a direct relation between pressure and density. It is then possible to use the LATIN solver to set up a pressure-velocity decoupling algorithm. Moreover, Proper Generalised Decomposition (PGD) is natively included in the solver and yields two independent space-time decompositions for the velocity and the pressure fields. As a first step, the solver is validated on a problem for which an analytical solution is available. It is then applied to slightly more complex problems. The results show good agreement with the literature, and we expect that the solver could be used to compute more complicated material laws in the future.
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