entropy

The capabilities of summation-by-parts and structure-preserving operators for compressible computational fluid dynamics and reaction-diffusion models

With the algorithm’s suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. In this dissertation, …

Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows

Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Svärd (Phys A Stat Mech Appl 506:350–375, 2018). The spatial discretization is based on entropy stable …

Entropy Stable No-Slip Wall Boundary Conditions for the Eulerian Model for Viscous and Heat Conducting Compressible Flows

Nonlinear (entropy) stability analysis is used to derive entropy–stable no–slip wall boundary conditions at the continuous and semi–discrete levels for the Eulerian model proposed by Svärd in 2018 (Physica A: Statistical Mechanics and its …

Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations

The framework of inner product norm preserving relaxation Runge--Kutta methods [D. I. Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex quantities. Conservation, dissipation, or other solution properties with …

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

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 …