A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics (Q1062561)

Results of Harten and Tadmor [e.g.: \textit{A. Harten}, J. Comput. Phys. 49, 151-164 (1983; Zbl 0503.76088)] are generalized to the compressible Navier-Stokes equations including heat conducting effects. A symmetric form of the equations is derived in terms of entropy variables. It is shown that finite element methods based upon this form automatically satisfy the second law of thermodynamics and that stability of the discrete solution is thereby guaranteed ab initio.