Zonal-local solution method for the turbulent Navier-Stokes equations

Abstract

AZONAL-LOCAL solution method is developed for the solution of the compressible Navier-Stokes equations. The main feature of the method is coupling of the NavierStokes equations with the Euler equations and the local mesh solution procedure. Mesh sequencing (multilevel) technique is also used for the improvement of the efficiency of the algorithm. The methodology is applied to turbulent flowfields past an airfoil. A flux vector splitting method with an upwind scheme up to fourth-order accuracy is used for the discretization of the inviscid fluxes. The system of the equations is solved by an unfactored implicit method using Gauss-Seidel relaxation. Contents Techological improvements in supercomputer speed and memory size provided the means to solve the full compressible Navier-Stokes equations for turbulent flowfields and complex geometries. However, large amounts of computer time are required for the solution of the equations especially for problems in design practice. To reduce the computational time, a zonal-local solution method is presented for the solution of the two-dimensional Navier-Stokes equations in high Reynolds number flows. The equations are solved in time-dependent form and for a curvilinear body-fitted coordinate system JUt ^ + (Gvis)r] (1) where /is the Jacobian of the transformation of the Cartesian coordinates (x, z) to curvilinear coordinates (£, f), the subscripts inv, vis indicate the inviscid and viscous fluxes, respectively, and U is the conservative variables matrix. The equations are solved by a finite volume Navier-Stokes code1 which uses a modified 1 Steger-Warming flux vector splitting (FVS) method for the discretization of the inviscid fluxes. The FVS method split the fluxes into two parts, positive and negative, in accordance with the sign of the eigenvalues (2)