Quasi-gas-dynamic modeling of complex supersonic flows

A mathematical model for viscous gas flows modeling is considered taking into account the time scales limitation by the characteristic time between molecular collisions. This approach leads to a variant of the quasi-gas-dynamic equations system (QGD), based on the relationship between the kinetic and macroscopic descriptions of a continuous medium motion. Based on the presented model, a numerical algorithm is constructed for modeling viscous compressible gas flows. QGD equations are discretized by the finite volume method. Numerical investigation of the supersonic tip vortex interaction with the finite span wing has been carried out. The incoming flow has a Mach number M=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M = 3$$\end{document}, and a unit Reynolds number Re=107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Re}=10^{7}$$\end{document}. A hexagonal unstructured grid containing 4.1 * 107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{7}$$\end{document} cells was used for the simulation. Simulations were performed on the multiprocessor computer system K-60 at the Keldysh Institute of Applied Mathematics RAS. The deformation of the tip vortex was revealed. Numerical data obtained from QGD system were compared with those from the averaged Navier–Stokes equations.