A model for two coupled turbulent fluids Part III: Numerical approximation by finite elements |
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| Authors: | C?Bernardi Email author" target="_blank">T Chacón?RebolloEmail author M Gómez?Mármol R?Lewandowski F?Murat |
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| Institution: | (1) Laboratoire Jacques-Louis Lions, C.N.R.S. & Université, Pierre et Marie Curie B. C. 187, 75252 Paris Cedex 05, France;(2) Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevillai C/ Tarfia, s/ni 41080 Sevilla, Spain;(3) IRMAR, Campus de Beaulieu, Université Rennes 1, CS 74205, 35042 Rennes Cedex, France |
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| Abstract: | Summary. This paper introduces a scheme for the numerical solution of a model for two turbulent flows with coupling at an interface. We consider a variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 2D flows by piecewise affine triangular elements. Our main contribution is to prove that the standard Galerkin - finite element approximation of the Laplace equation approximates in L2 norm its solution by transposition, for data with low smoothness. We include some numerical tests for simple geometries that exhibit the behaviour predicted by our analysis.Mathematics Subject Classification (2000): 65 N30, 76M10Revised version received March 24, 2003This research was partially supported by Spanish Government REN2000-1162-C02-01 and REN2000-1168-C02-01 grants |
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