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Artificial viscosity proper orthogonal decomposition. (English) Zbl 1211.76077

Summary: We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standard models created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a small diffusion parameter. We present a thorough numerical analysis for the time discretization of the new models. We then test these models in two problems displaying shock-like phenomena. Of course, since the Burgers equation does not model turbulence, we next need to test our new models in realistic turbulent flow settings. This is the subject of a forthcoming report.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76F65 Direct numerical and large eddy simulation of turbulence
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