SFB 1313 Publication "Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains"

New SFB 1313 publication, published in "NoDEA. Nonlinear Differential Equations and Applications". The work has been developed in the context of SFB 1313 research project B03. 

Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains

Authors

• Taras Mel'nyk (University of Stuttgart, SFB 1313  Internal Research Project I-08)
• Christian Rohde (University of Stuttgart, SFB 1313 research projects B03 and C02)

Abstract

The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection–diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Robin-type boundary condition involving convective and diffusive fluxes is imposed on the lateral surface. The limit problem for vanishing diffusion and the cylinder shrinking to an interval is a nonlinear first-order conservation law. For a time span that allows for a classical solution of this limit problem corresponding uniform pointwise and energy estimates are proven. They provide precise model error estimates with respect to the small parameter that controls the double viscosity-geometric limit. In addition, other problems with more higher Péclet numbers are also considered.