Entropy stable finite volume fluxes and formulas for compressible Euler and Navier-Stokes. Code based off of formulas in Chandrashekar 2012 and Winters et al. 2019. Formulas for entropy variables are from Hughes, Mallet, Franca 1986 and from Parsani, Carpenter, Nielsen 2015

The package consists mainly of three sub-modules Fluxes1D, Fluxes2D, Fluxes3D. Each module exports entropy conservative fluxes, as well as helper routines.

For example, Fluxes2D exports

• euler_fluxes, which evaluates entropy conservative fluxes
• u_vfun, v_ufun to convert between conservative and entropy variables
• conservative_to_primitive_beta to convert between conservative and "primitive" variables (involving inverse temperature β) used to evaluate fluxes.

using EntropyStableEuler.Fluxes2D

# construct solution at two states
rhoL,rhouL,rhovL,EL = map(x->x.*ones(4),(1,.1,.2,2))
rhoR,rhouR,rhovR,ER = map(x->x.+.1*randn(4),(rhoL,rhouL,rhovL,EL)) # small perturbation

# convert to "primitive" variables for efficient flux evaluation
rhoL,uL,vL,betaL = conservative_to_primitive_beta(rhoL,rhouL,rhovL,EL)
rhoR,uR,vR,betaR = conservative_to_primitive_beta(rhoR,rhouR,rhovR,ER)

# evaluate fluxes
Fx,Fy = euler_fluxes(rhoL,uL,vL,betaL,rhoR,uR,vR,betaR)

# can also pass in precomputed log values for efficiency
#      euler_fluxes(rhoL,uL,vL,betaL,rhologL,betalogL,
#                   rhoR,uR,vR,betaR,rhologR,betalogR)

• add Lax-Friedrichs penalty and matrix dissipation from Winters et al. 2017
• add Jacobians for transforms between conservative and entropy variables