Analysis of a singular limit of boundary conditions for convection–diffusion equations

Article type: Research Article

Authors: Chacón Rebollo, Tomás | Gómez Mármol, Macarena | Sánchez Muñoz, Isabel

Affiliations: Departamento de Ecuaciones Diferenciales y Análisis Numérico de la Universidad de Sevilla, Sevilla, Spain | Departamento de Matemática Aplicada I de la Universidad de Sevilla, Sevilla, Spain

Abstract: In this work we justify the way to set the boundary conditions by certain numerical methods to solve convection–diffusion problems, in particular convection–diffusion problems that appear in turbulence models. To do it, we analyze the limit of convection–diffusion equations when the total flux is imposed in the inflow boundary, and Newmann boundary conditions are imposed in the remaining of the boundary. We prove that the solution converges in L2 to the solution of the pure convection problem, with Dirichlet boundary conditions in the inflow boundary, in both the steady and evolution problems. In addition, the convective derivatives also converge in L2, and the convective traces in the inflow and outflow boundaries converge in spaces of L2 kind.

Keywords: singular limit, convection–diffusion equations, total-flux boundary conditions

DOI: 10.3233/ASY-2010-1008

Journal: Asymptotic Analysis, vol. 70, no. 3-4, pp. 141-154, 2010