Math @ Duke

Publications [#246955] of JianGuo Liu
Papers Published
 Liu, JG; Xu, WQ, Far field boundary condition for convection diffusion equation at zero viscosity limit,
Quarterly of Applied Mathematics, vol. 62 no. 1
(January, 2004),
pp. 2752, American Mathematical Society (AMS) [doi]
(last updated on 2019/06/19)
Abstract: In this paper, we give a systematic study of the boundary layer behavior for linear convectiondiffusion 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 farfield boundary condition is preferred in the outlet and characteristic boundary dondition. 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 This model well describes the behavior at the farfield for many physical and engineering systems such as fluid dynamical equation and electromagnetic equation. The results obtained here should provide some theoretical guidance for designing effective farfield boundary conditions.


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