A Spectral Element Reduced Basis Method for Navier-Stokes Equations with Geometric Variations
For engineers and scientists simulating fluid flows in varying geometries, this method offers a more efficient alternative to full-order simulations, though it is an incremental improvement combining existing techniques.
The paper develops a reduced basis method for Navier-Stokes equations with geometric variations, achieving accurate steady-state solutions for different geometries while reducing computational time in parametric many-query scenarios.
We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions define a reduced order space through a standard POD procedure. The reduced order space allows to accurately and efficiently evaluate the steady-state solutions for different geometries. In particular, we detail different aspects of implementing the reduced order model in combination with a spectral element discretization. It is shown that an expansion in element-wise local degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.