Far field boundary condition for convection diffusion equation at zero viscosity limit

Liu, Jian-Guo; Xu, Wen-Qing

doi:10.1090/qam/2032571

Authors: Jian-Guo Liu and Wen-Qing Xu
Journal: Quart. Appl. Math. 62 (2004), 27-52
MSC: Primary 35K57; Secondary 35B25, 76D99, 76R99
DOI: https://doi.org/10.1090/qam/2032571
MathSciNet review: MR2032571
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Abstract: In this paper, we give a systematic study of the boundary layer behavior for linear convection-diffusion equation in the zero viscosity limit. We analyze the boundary layer structures in the viscous solution and derive the boundary condition satisfied by the viscosity limit as a solution of the inviscid equation. The results confirm that the Neumann type of far-field boundary condition is preferred in the outlet and characteristic boundary condition. Under some appropriate regularity and compatibility conditions on the initial and boundary data, we obtain optimal error estimates between the full viscous solution and the inviscid solution with suitable boundary layer corrections. These results hold in arbitrary space dimensions and similar statements also hold for the strip problem.

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