engleski

Rigorous justification of the asymptotic model describing a curved-pipe flow in a time- dependent domain

This paper is devoted to the mathematical justification of an asymptotic model of a viscousflow in a curved tube with moving walls by proving error estimates. To this aim, we first construct the space correctors near the pipe’s inlet and outlet due to the boundary layer phenomenon. In order to guarantee the adequate properties for these correctors we study what we called modified Leray’s problem defined in a semi-infinite strip. We ensure the existence and uniqueness of an exponential decaying solution when the axial variable tends to infinity. Then, by deriving a Poincar´e’s type inequality and other estimates for the boundary value problems taking into account the condition on the pipe’s lateral boundary, we evaluate the difference between the asymptotic approximation and the exact solution of the problem.

curved pipe ; time-dependent domain ; Navier-Stokes equations ; asymptotic analysis ; error estimates

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