A simple and stable scale-similarity model for large eddy simulation: Energy balance and existence of weak solutions. (English) Zbl 1039.76027

Summary: In averaging the Navier-Stokes equations, the problem of closure arises. Scale-similarity models address closure by (roughly speaking) extrapolation from the (known) resolved scales to the (unknown) unresolved scales. In a posteriori tests, scale-similarity models are often the most accurate but can prove to be unstable when used in a numerical simulation. In this report, we consider the scale-similarity model given by \(\nabla \cdot w=0 \text{ and } w_t+\nabla \cdot (\overline{ww})-\nu\Delta w+\nabla p=f.\) We prove that it is stable (the solution satisfies an energy inequality), and deduce from that the existence of weak solutions of the model.


76F65 Direct numerical and large eddy simulation of turbulence
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
Full Text: DOI


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