Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs
For researchers in computational science and engineering dealing with parametrized advection-dominated problems under uncertainty, this work offers a more efficient reduced-order modeling approach.
The paper proposes stabilized weighted reduced basis methods for parametrized advection-dominated problems with random inputs, combining weighted RB with SUPG stabilization and introducing selective online stabilization to reduce computational costs while maintaining accuracy. Numerical tests on steady and unsteady heat transfer problems demonstrate the effectiveness.
In this work, we propose viable and efficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of wRB (weighted reduced basis) method for stochastic parametrized problems with stabilized reduced basis method, which is the integration of classical stabilization methods (SUPG, in our case) in the Offline--Online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.