Enthalpy damping for the steady Euler equations

Abstract

For inviscid steady flow problems where the enthalpy is constant at steady state, it has been proposed by Jameson, Schmidt, and Turkel to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed here, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which can move all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping can be effective in accelerating convergence to steady state.