Following the article "On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes" of Zhang and Shu, JCP 2010.
They claim that:
"It can be easily verified that p is a concave function of w=(rho,rho u,rho E) if rho ≥ 0."
This is true according to Jensen's inequality, where W is the conservative variables vector and rho is the density.
"Define the set of admissible states by G = {w|rho>0 and
p =(gamma − 1)(E − (1/2)(m2/r))>0},
then G is a convex set."
How is it possible to conclude that G is a convex set based on the first sentence?
Asghar Bohluly
Hi, If you use the finite volume methods, it is enough to use some simple controls on fluxes for positivity preserving.
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