Low speed preconditioning applied to the compressible Navier-Stokes equations

The concept of low-speed time-derivative preconditioning is extended for use in production CFD analysis codes. A number of techniques are developed which allow preconditioning to be retrofitted into existing CFD analysis codes. A two-dimensional finite-volume Navier-Stokes code is developed as a test-bed for developing specific implementation techniques and testing the behavior of state-of-the-art CFD techniques with preconditioning. The standard equations and three preconditioners are implemented in the test code using both central-difference and a Roe's flux-difference splitting upwind techniques. The test code also includes four solver techniques, two non-dimensionalizations, and three flux limiters.; Techniques are developed to maintain the conservative formulation necessary for proper shock wave modeling and to improve robustness during the early transient phase of solution convergence. Results of numerous tests indicate that properly implemented low-speed preconditioning produces Mach number independent convergence. For an inviscid bump-in-a-channel test case, identical convergence rates are obtained for a series of Mach numbers ranging from 0.2 to 0.0000001.; Test cases indicate that solution accuracy is degraded significantly as the Mach number is reduced without preconditioning. It is shown analytically that the truncation error of the original equations is significantly higher than that of the preconditioned equations at very low Mach numbers. A numerical study is performed which supports the analytical result and establishes the link between the truncation error and the low Mach number solution accuracy problem.; The techniques developed are validated by the implementation of low-speed preconditioning into an existing unstructured hybrid Cartesian-prismatic grid CFD solver. The three-dimensional implementation is validated by computing the solutions of a low-speed lifting body and a subsonic jet-in-crossflow. The analysis of a complex V/STOL aircraft configuration in low-speed hover is demonstrated using the three-dimensional code.