Weak uniqueness of the navier-stokes equations and adaptive turbulence simulation

• We consider the problem of computational simulation of turbulence, where we study turbulent solutions to the incompressible Navier- Stokes equations. We construct approximate weak solutions using a stabilized Galerkin finite element method, here referred to as General Galerkin G2, for which we investigate uniqueness in output (or weak uniqueness ) by solving an associated dual problem computationally, with data coupling to the particular output we are interested in. For simulation of turbulent flow we refer to the adaptive version of G2 as Adaptive DNS/LES, with part of the flow being resolved in a Direct Numerical Simulation DNS, and part of the flow being left unresolved in a Large Eddy Simulation LES , with the stabilization in G2 acting as a dissipative subgrid model. We present computational results using Adaptive DNS/LES, where we find that for the problem of simulating the turbulent flow past various bluff bodies we are able to compute mean value output, such as drag, using  10-100 times less degrees of freedom than in typical LES computations using ad hoc mesh refinement. We further use Adaptive DNS/LES to simulate the turbulent flow past a cylinder rolling along ground.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

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