Numerical solution of the Navier-Stokes equations with a generalized state eqution

Title: Numerical solution of the Navier-Stokes equations with a generalized state eqution Author: Martina Ullrichová Department: Department of numerical Mathematics Supervisor: doc. RNDr. Vít Dolejší, Ph.D., DSc. Supervisor's e-mail address: dolejsi@karlin.mff.cuni.cz Abstract: In the present work we study the simulation of viscous compressible flow. We consider a generalized model of gas described by a generalized state equation. We firstly summarize construction of this generalized equation and its consequences for the existence and uniquenes of the solution of the compressible flow problem. We suggest particular ways how define this generalized relations. Afterwards, we solve the Navier-Stokes problem by the discontinous Galerkin method. Considering the properties of the generalized model we choose explicit time discretization. Finally, we compare new generalized model with the standard model (ideal gas) for different flow regimes around the NACA0012 profil. Keywords: viscous compressible flow, Navier-Stokes equations, discontinous Ga- lerkin method, generalized state equatio