We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the parameter space, which includes either time only or time and Reynolds number, are computed with a Finite Volume method and used to generate a reduced basis via Proper Orthogonal Decomposition (POD). Galerkin projection of the Navier-Stokes equations onto the reduced space is used to compute the ROM solution. To ensure computational efficiency, the number of POD modes is truncated and ROM solution accuracy is recovered through two stabilization methods: i) adding a global constant artificial viscosity to the reduced dimensional model, and ii) adding a different value of artificial viscosity for the different POD modes. We test the stabilized ROMs for fluid flow in an idealized medical device consisting of a conical convergent, a narrow throat, and a sudden expansion. Both stabilization methods significantly improve the ROM solution accuracy over a standard (non-stabilized) POD-Galerkin model.

翻译：本文针对对流主导不可压缩流动（雷诺数达数千量级）的模拟，对两种稳定化降阶模型（ROM）进行了比较计算研究。参数空间中的代表性解（仅含时间变量或同时包含时间变量与雷诺数）通过有限体积法计算获得，并采用本征正交分解（POD）生成约化基。通过将纳维-斯托克斯方程在约化空间上进行伽辽金投影，计算降阶模型解。为确保计算效率，对POD模态数量进行截断处理，并采用两种稳定化方法恢复降阶模型解的精度：i）在降维模型中添加全局常数人工黏性；ii）对不同POD模态施加不同量级的人工黏性。我们以一个由锥形收缩段、窄喉管和突扩段组成的理想化医疗装置中的流体流动为测试案例。结果表明，两种稳定化方法相较于标准（非稳定化）POD-伽辽金模型，均能显著提升降阶模型解的精度。