论文标题
riemannian barycentric插值：参数不稳定的Navier-Stokes降低订单模型
A Riemannian Barycentric Interpolation : Derivation of the Parametric Unsteady Navier-Stokes Reduced Order Model
论文作者
论文摘要
提出了一个新的应用程序插值的新应用，以构建非线性参数降低订单模型（PROM）。这种方法基于由dimension q的正交组q形成的歧管的riemannian几何形状。通过使用一组未经训练的参数化正交分解（POD）Q的子空间，可以将新的未经训练参数的子空间作为广义的Karcher Barycenter获得，通过解决简单的固定点问题，可以寻求解决方案。与现有的舞会方法相反，拟议的barycentric舞会是通过施工更易于实施的，并且在变化参数值方面更加灵活。为了评估barycentric舞会的潜力，当雷诺数的值变化时，在圆柱体上的参数流进行数值实验和盖子驱动腔中的流动。证明拟议的barycentric Prom方法以大大降低的计算成本实现了竞争结果。
A new application of subspaces interpolation for the construction of nonlinear Parametric Reduced Order Models (PROMs) is proposed. This approach is based upon the Riemannian geometry of the manifold formed by the quotient of the set of full-rank N-by-q matrices by the orthogonal group of dimension q. By using a set of untrained parametrized Proper Orthogonal Decomposition (POD) subspaces of dimension q, the subspace for a new untrained parameter is obtained as the generalized Karcher barycenter which solution is sought after by solving a simple fixed point problem. Contrary to existing PROM approaches, the proposed barycentric PROM is by construction easier to implement and more flexible with respect to change in parameter values. To assess the potential of the barycentric PROM, numerical experiments are conducted on the parametric flow past a circular cylinder and the flow in a lid driven cavity when the value of Reynolds number varies. It is demonstrated that the proposed barycentric PROM approach achieves competitive results with considerably reduced computational cost.
