ABSTRACT We consider the Navier–Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced-order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced-order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e. symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

中文翻译：

---

具有不同曲率壁的域中 Navier-Stokes 方程的简化基础模型降阶

摘要 我们考虑具有变窄和不同曲率壁的通道中的 Navier-Stokes 方程。通过应用经验插值方法来生成仿射参数依赖性，离线-在线过程可用于计算参数变化的降阶解。降阶空间是通过标准 POD 程序从稳态快照解计算出来的。该模型使用高阶光谱元素 ansatz 函数进行离散化，从而产生 4752 个自由度。所提出的降阶模型可为各种几何形状和运动粘度值生成稳态解的精确近似值。推动本研究的应用是通过反流二尖瓣的血流不对称（即对称破坏分叉）的开始，取决于雷诺数和阀门形状。通过我们的计算研究，我们发现对称破坏的临界雷诺数随着壁曲率的增加而增加。