The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes of 1981, which approximates the set of five Navier-Stokes equations completed by the turbulence model of Baldwin and Lomax. The analysis procedure implements the check-up of the necessary von Neumann stability criterion. It is shown with the aid of the proposed symbolic-numeric strategy that the physical viscosity terms in the Navier-Stokes equations have a dominant effect on the sizes of the stability region in comparison with the heat conduction terms. It turns out that the consideration of turbulence with the aid of eddy viscosity model of Baldwin and Lomax has an insignificant effect on the size of the necessary stability region.
|Title of host publication||International Symposium on Symbolic and Algebraic Computation '94|
|Place of Publication||Oxford, United Kingdom|
|Publisher||Association for Computing Machinery (ACM)|
|Publication status||Published - 20 Dec 1994|
Ganzha, V. G., Vorozhtsov, E. V., Boers, J., van Hulzen, J. A., & van Hulzen, J. A. (1994). Symbolic-numeric stability investigations of Jameson's scheme for this-layer Navier-Stokes equations. In International Symposium on Symbolic and Algebraic Computation '94 (pp. 234-241). Oxford, United Kingdom: Association for Computing Machinery (ACM). https://doi.org/10.1145/190347.190422