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A manufactured solution for verifying CFD boundary conditions: part II

Knupp, Patrick K.; Ober, Curtis C.

Order-of-accuracy verification is necessary to ensure that software correctly solves a given set of equations. One method to verify the order of accuracy of a code is the method of manufactured solutions. In this study, a manufactured solution has been derived and implemented that allows verification of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes (RANS) equation sets, but also some of their associated boundary conditions (BC's): slip, no-slip (adiabatic and isothermal), and outflow (subsonic, supersonic, and mixed). Order-of-accuracy verification has been performed for the Euler and Navier-Stokes equations and these BC's in a compressible computational fluid dynamics code. All of the results shown are on skewed, non-uniform meshes. RANS results will be presented in a future paper. The observed order of accuracy was lower than the expected order of accuracy in two cases. One of these cases resulted in the identification and correction of a coding mistake in the CHAD gradient correction that was reducing the observed order of accuracy. This mistake would have been undetectable on a Cartesian mesh. During the search for the CHAD gradient correction problem, an unrelated coding mistake was found and corrected. The other case in which the observed order of accuracy was less than expected was a test of the slip BC; although no specific coding or formulation mistakes have yet been identified. After the correction of the identified coding mistakes, all of the aforementioned equation sets and BC's demonstrated the expected (or at least acceptable) order of accuracy except the slip condition.