Entropy Stability of Finite Difference Schemes for the Compressible Navier-Stokes Equations

Abstract

In this thesis, we study the entropy stability of the compressible Navier-Stokes model along with a modification of the model. We use the discretization of the inviscid terms with the Ismail-Roe entropy conservative flux. Then, we study entropy stability of the augmentation of viscous, heat and mass diffusion finite difference approximations to the entropy conservative flux. Additionally, we look at different choices of the diffusion coefficient that arise from combining the viscous, heat and mass diffusion terms. Lastly, we present numerical results of the discretizations comparing the effects of the viscous terms on the oscillations near the shock and show that they preserve entropy stability.

Mohammed Sayyari

Postdoc & Adjunct

Mohammed is a systems thinker. His Mathematical interests are in Numerical Analysis, HPC, entropy-stable high-order methods, and boundary conditions. His Scientific interests are in the development of robust and efficient numerical methods for fluid flow models relevant to our changing climate.