Error control and adaptivity for low-Mach-number compressible flows

An error estimation and grid adaptation strategy is presented for low-Mach-number, compressible, isentropic flows in two dimensions. There is very little literature investigating error control and grid refinement strategies combined with low-Mach-number compressible flows simultaneously, although these two concepts have been treated separately. The error control and the refinement procedure is based on the adjoint formulation in which the adjoint function is connected to local residual error, as well as linear variation of the functional with respect to a coarse grid solution. The benefit of the presented local grid refinement strategy based on some prechosen relevant engineering quantity is that it quantifies the specific locations in the domain that most affect the approximation of this quantity while maintaining the computational efficiency. Moreover, this approach is broader in the sense of not requiring a priori knowledge of the flow compared to standard gradient-based or global refinement approaches. Finally, the predictive capability of the error estimation strategy is demonstrated quantitatively by comparing to experimental and theoretical results for flows past slender bumps and a National Aerospace Laboratory NLR7301 multi-element airfoil for Mach numbers from 0.001 to 0.185.