On existence and uniqueness of solutions to Boussinesq systems with nonlinear and mixed boundary conditions

CERETANI, ANDREA N.

Congreso; IFIP TC7: Conference on System Modeling and Optimization; 2021

We address Boussinesq systems in a bounded domain with an outlet boundary portion where fluid can leave or re-enter naturally. On this boundary part, we consider either a do-nothing or a directional do-nothing condition for the fluid flow, and a new artificial condition for the heat transfer that couples nonlinearly the fluid velocity and temperature. The latter can be further adjusted if convective or conductive phenomena are dominant. We prove the existence and, in some cases, the uniqueness of weak solutions to stationary and evolutionary problems. A variety of numerical tests shows the improved performance of the new artificial condition concerning other standard choices in the literature. Joint work with Carlos N. Rautenberg and Rafael Arndt, George Mason University, USA.