Accession Number : ADA319013

Title :   A Method to Construct Godunov-Type Schemes and Implicit PPV Schemes and Newton Method to Solve CFD Problems of Viscous External Aerodynamics.

Descriptive Note : Final rept. 17-21 May 93,

Corporate Author : TSENTRAL'NYI AERO-GIDRODINAMICHE'SKII INST MOSCOW (RUSSIA)

Personal Author(s) : Babaev, Igor Yu. ; Dedesh, Valery

PDF Url : ADA319013

Report Date : MAY 1993

Pagination or Media Count : 3

Abstract : The efficiency of the Newton method 1 and high resolution PPV schemes 2 to solve steady Navier-Stokes equations is assessed. Linear systems on each Newton iteration step are solved using either iterative (GMRES 3 preconditioned by the incomplete LU decomposition by positions), or direct (nested dissection method 1) large sparse matrix inversion procedure. Linear system coefficients are computed using numerical differentiation. As test problems, two-D viscous transonic flows about circular cylinder and NACAOOl2 airfoil are considered. An influence of a PPV scheme option, the linear system solution accuracy, Newton method initial guess choice and - associated CPU time savings are analyzed. The Newton method convergence rate at different Mach and Reynolds numbers generally proves to be linear. A significantly influenced by local supersonic zones and shocks, the allowed accuracy of the linear system solution for the Newton method convergence is found to vary depending on the concrete problem. Used with care, iterative solvers are several times (5-10) faster and economic, than direct ones, which in their turn, do not show problem parameter-dependent performance. From the three possible variants of an initial guess to compute with a high resolution PPV scheme, namely free-stream flow, first-order solution or the second order solution at different Mach and/or Reynolds numbers, the most successful is the second variant. This is because otherwise the shock location is far from being exact, and at each Newton iteration step present in a PPV scheme a smooth nonlinear limiter function makes the quadratic convergence rate of the Newton method linear.

Descriptors :   *AERODYNAMICS, TEST AND EVALUATION, LINEAR SYSTEMS, FUNCTIONS, STEADY STATE, POSITION(LOCATION), COMPUTERS, RATES, ACCURACY, CONCRETE, HIGH RESOLUTION, TIME, VARIATIONS, SOLUTIONS(GENERAL), COEFFICIENTS, SHOCK, QUADRATIC EQUATIONS, CONVERGENCE, EXTERNAL, FLOW, NONLINEAR ANALYSIS, MACH NUMBER, SUPERSONIC CHARACTERISTICS, NAVIER STOKES EQUATIONS, FREE STREAM, VISCOSITY, DECOMPOSITION, SAVINGS, REYNOLDS NUMBER, LIMITERS.

Subject Categories : Aerodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE