A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions - Mathematics > Analysis of PDEsReportar como inadecuado




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Abstract: Stents are medical devices designed to modify blood flow in aneurysm sacs, inorder to prevent their rupture. Some of them can be considered as a locallyperiodic rough boundary. In order to approximate blood flow in arteries andvessels of the cardio-vascular system containing stents, we use multi-scaletechniques to construct boundary layers and wall laws. Simplifying the flow weturn to consider a 2-dimensional Poisson problem that conserves essentialfeatures related to the rough boundary. Then, we investigate convergence ofboundary layer approximations and the corresponding wall laws in the case ofNeumann type boundary conditions at the inlet and outlet parts of the domain.The difficulty comes from the fact that correctors, for the boundary layersnear the rough surface, may introduce error terms on the other portions of theboundary. In order to correct these spurious oscillations, we introduce avertical boundary layer. Trough a careful study of its behavior, we proverigorously decay estimates. We then construct complete boundary layers thatrespect the macroscopic boundary conditions. We also derive error estimates interms of the roughness size epsilon either for the full boundary layerapproximation and for the corresponding averaged wall law.



Autor: Eric Bonnetier LMC - Imag, Didier Bresch LMC - Imag, Vuk Milisic LMC - Imag, Icp

Fuente: https://arxiv.org/







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