The use of spectral element methods in computational fluid dynamics allows highly accurate computations by using high-order spectral element ansatz functions. Typically, an exponential error decay can be observed under p-refinement. We consider the incompressible Navier-Stokes equations for a jet flow and a cavity, which exhibit bifurcations with changing parameter values, such as Reynolds number and Grashof number. Applications of interest are contraction-expansion channels, found in many biological systems, such as the human heart for instance, or cavities used in semiconductor crystal growth. Applying the reduced basis model reduction to flow problems allows to reconstruct the field solution over a parameter range of interest from a few high-order solves. In particular, we use the method to reconstruct bifurcation branches with efficient reduced order models, which are localized to the respective branch.

Co-authors: Gianluigi Rozza, Max Gunzburger, Annalisa Quaini, Alessandro Alla