On entropy-stable discretizations and the entropy adjoint
For symmetrizable conservation laws, the entropy variables are adjoints for a functional that balances entropy flux into the domain with sources of entropy inside the domain. In this paper, it was shown that entropy-stable summation by parts (SBP) discretizations mimic an additional property of the continuous equations: the entropy adjoint. The entropy variables satisfy the discrete adjoint equation for a discretized entropy-balance functional if they are evaluated from the discrete solution. They are identical to the discrete adjoint variables up to machine accuracy. The theoretical results are verified for steady inviscid (Euler equation) and viscous flows (Navier-Stokes equation) over an airfoil.
scientific article; zbMATH DE number 7352181
scientific article