Adaptive Remeshing for the k-Epsilon Model of Turbulence

An adaptive ® nite element method for solving incompressible turbulentows using the k± ≤model of turbulence is presented. Solutions are obtained in primitive variables using a highly accurate quadratic ® nite element on unstructured grids. Turbulence is modeled using the k± ≤ model of turbulence. Two error estimators are presented that take into account in a rigorous way the relative importance of the errors in velocity, pressure, turbulence variables, and eddy viscosity. The ef® ciency and convergence rate of the methodology are evaluated by solving problemswith known analytical solutions. Themethod isthen applied to turbulent free shearowsand predictions are compared to measurements. Nomenclature Cl , C1, C2 = k±≤ model constants e = error f = body force h = element size K = element in the mesh k = turbulent kinetic energy n = outward unit vector P(u) = production of turbulence p = pressure u = velocity vector

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