Accession Number:

ADA164038

Title:

Adaptive-Grid Optimization for Minimizing Steady-State, Truncation Error

Descriptive Note:

Master's thesis,

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING

Personal Author(s):

Report Date:

1985-12-01

Pagination or Media Count:

153.0

Abstract:

This thesis develops an adaptive grid method which minimizes the truncation error in the finite difference solution. The study solves compressible, steady state, boundary layer equations assuming perfect gas flow over an isothermal wall. The Dorodnitsyn, compressibility transformation changes the boundary layer equations, as expressed in two dimensional, cartesian coordinates, into an incompressible form. The equations are then transformed into variables of a computational plane. Implicit Successive Over Relaxation SOR solves the finite differenced, computational, boundary layer equations. Comparison of the computed solution for incompressible flow over a flat plate to Blasius, exact solution shows the boundary layer code is accurate. The adaptive grid method uses Powells method to optimize the solution grid by minimizing the sum of the third derivative in the computational plane of the tangential velocity component. This study tests the sum of the squares of the first, second, and third derivative of the tangential velocity as minimized functions. The accuracy of the optimized, adaptive grid solution is greater than the original, fixed grid solution. The study then applies the optimization to supersonic and hypersonic problems. The computed, adaptive grid solutions show good correlation with theoretical models for supersonic and hypersonic flow developed by Van Driest and Eckert.

Subject Categories:

  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE