Combined Entropy and Output-Based Adjoint Approach for Mesh Refinement and Error Estimation

摘要

This paper presents a strategy for mesh refinement driven by a new indicator that combines two previously investigated indicators: one based on a user-specified engineering output, such as drag or lift coefficient, and the other based on entropy variables. Using the entropy-variable indicator to adapt a mesh is computationally advantageous because it does not require the solution of an auxiliary adjoint equation, which for unsteady problems is particularly costly. 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 variables. This paper demonstrates the potential for this method through several simulations governed by the compressible Navier-Stokes equations using both hanging-node refinement and mesh optimization via error sampling and synthesis. In general, mesh optimization via error sampling and synthesis will provide more optimal meshes, but often it is not a viable option. This demonstrates the need to show that the combined approach benefits are not dependent on the mesh adaptation strategy.