A New Boundary Condition for Rate-Type Non-Newtonian Diffusive Models and the Stable MAC Scheme (Journal of Computational Mathematics, 2018)
We present a new Dirichlet boundary condition for the rate-type non-Newtonian diffusiveconstitutive models. The newly proposed boundary condition is compared withtwo such well-known and popularly used boundary conditions as the pure Neumann condition[1] and the Dirichlet condition by Sureshkumar and Beris [2]. Our condition is demonstratedto be more stable and robust in a number of numerical test cases. A new Dirichletboundary condition is implemented in the framework of the finite difference Marker andCell (MAC) method. In this paper, we also present an energy-stable finite difference MACscheme that preserves the positivity for the conformation tensor and show how the additionof the diffusion helps the energy-stability in a finite difference MAC scheme-setting.
Keywords: Boundary conditions; Diffusive complex fluids models; Positivity preserving schemes; Stability of the MAC schemes.