A numerical approach based on preconditioning and dual-time stepping (DTS) is proposed to simulate cavitating flows at low Mach numbers. The methodology is based on a fully-compressible homogeneous mixture model and finite rate mass transfer as discussed in Gnanaskandan and Mahesh (2015). The method has shown promising results for capturing the large-scale cavitation in developed cavitation regimes (e.g. Bhatt and Mahesh, 2020; Gnanaskandan and Mahesh, 2016a). Small-scale vapor regions in the incipient cavitation, cavitation inception and wetted conditions are sensitive to free-stream nuclei content (e.g. Hsiao and Chahine, 2005; Bhatt and Mahesh, 2019, 2020). In these regimes, lower values of free-stream nuclei are necessary than what is typically prescribed in homogeneous mixture models that use a fully-compressible formulation. While important for the physical modeling, lower values of free-stream nuclei lead to acoustic stiffness. The goal of the present work is to present a numerical approach to enable such low free-stream nuclei calculations in an accurate manner and in a reasonable amount of time. The key aspects of the numerical approach are: (i) preconditioning applied to the cavitating flow equations in a fully-compressible (density-based) solver, (ii) modifications based on the all-speed Roe-type scheme to the characteristic-based filtering, and (iii) implementation in parallel and on unstructured grids that allow the simulation of complex problems. The numerical formulation of the time-derivative preconditioning matrix, the DTS framework, and modification to the shock-capturing are discussed. A proper conditioning of the preconditioned system of equations is obtained. The methodology is demonstrated for the unsteady flow over a cylinder under wetted and cavitation inception conditions, and LES of flow over a propeller under wetted conditions. Overall, a significant saving in total run-time as compared to the original solver is obtained, without compromising accuracy.

基于预处理和双时间步长（DTS）的数值方法）被提出来模拟低马赫数的空化流。该方法基于完全可压缩的均质混合物模型和有限速率传质，如Gnanaskandan和Mahesh（2015）所述。该方法已显示出在发达的空化体系中捕获大规模空化的有希望的结果（例如Bhatt和Mahesh，2020； Gnanaskandan和Mahesh，2016a）。初期空化，空化开始和湿润条件下的小规模蒸汽区域对自由流核含量敏感（例如Hsiao和Chahine，2005； Bhatt和Mahesh，2019，2020）。在这些情况下，与使用完全可压缩配方的均质混合物模型中通常规定的值相比，自由流核的值较低是必需的。虽然对物理建模很重要，较低的自由流核值会导致声学刚度。本工作的目的是提出一种数值方法，以精确的方式和合理的时间实现这种低自由流核的计算。数值方法的关键方面是：（i）在完全可压缩（基于密度）求解器中对空化流方程进行预处理，（ii）基于全速Roe型方案对基于特性的修改过滤，以及（iii）在并行的非结构化网格上实现，从而可以模拟复杂的问题。时间导数预处理矩阵的数值公式，本工作的目的是提出一种数值方法，以精确的方式和合理的时间实现这种低自由流核的计算。数值方法的关键方面是：（i）在完全可压缩（基于密度）求解器中对空化流方程进行预处理，（ii）基于全速Roe型方案对基于特性的修改过滤，以及（iii）在并行的非结构化网格上实现，从而可以模拟复杂的问题。时间导数预处理矩阵的数值公式，本工作的目的是提出一种数值方法，以精确的方式和合理的时间实现这种低自由流核的计算。数值方法的关键方面是：（i）在完全可压缩（基于密度）求解器中对空化流方程进行预处理，（ii）基于全速Roe型方案对基于特性的修改过滤，以及（iii）在并行的非结构化网格上实现，从而可以模拟复杂的问题。时间导数预处理矩阵的数值公式，（ii）基于全速Roe型方案对基于特征的滤波进行修改，以及（iii）并行执行并基于允许模拟复杂问题的非结构化网格实施。时间导数预处理矩阵的数值公式，（ii）基于全速Roe型方案对基于特征的滤波进行修改，以及（iii）并行执行并基于允许模拟复杂问题的非结构化网格实施。时间导数预处理矩阵的数值公式，讨论了DTS框架以及对震荡捕捉的修改。获得了方程组的预处理系统的适当条件。该方法论证明了在湿润和空化开始条件下在圆柱体上的不稳定流动，以及在湿润条件下在螺旋桨上的不稳定流动。总体而言，与原始求解器相比，可以节省大量的总运行时间，而不会影响精度。