A combined entropy and output-based adjoint approach for mesh refinement and error estimation

This paper presents a strategy for mesh refinement driven by an indicator that combines two previously-investigated indicators: one based on a user-specified engineering output, and the other based on entropy variables. Using the entropy-variable indicator to adapt a mesh is computationally advantageous since it does not require the solution of an auxiliary adjoint equation. However, the entropy-variable indicator targets any region of the domain where spurious entropy is generated, regardless of whether or not this region affects an engineering output of interest. On the other hand, an indicator computed from an engineering output generally targets only those regions important for the chosen output, though it is more computationally taxing because of the required adjoint solution. Approximations in the adjoint calculation reduce this cost, at the expense of indicator accuracy. In combining these indicators, our objective is to maintain the low cost of approximate adjoint solutions while achieving improved indicator accuracy from the entropy adjoint. We demonstrate the potential for this method through several simulations governed by the compressible Navier-Stokes equations.