#### Date of Award

1991

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical Engineering

#### First Advisor

Sumanta Acharya

#### Abstract

A solution-adaptive grid procedure based on an error equi-distribution scheme is developed and applied to a Parabolized Navier-Stokes solver. The adaptation scheme re-distributes grid points line-by-line, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional spring force at a point proportional to the error estimate. Where the error estimates are large, the tensional forces become high and drive grid points to cluster in these high error estimate regions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and orthogonality. A method of selecting error estimates or weighting functions is introduced which involves normalizing a combination of flow-field gradients and curvature of a number of dependent variables and then selecting the largest at each point. The resulting grid is therefore adapted based on each independent variable. A grid-fitting scheme is introduced for external flows in which the farfield extent of the computational grid is adjusted during the course of the calculation procedure in order to align the grid with flow-field structure and to minimize the number of grid points in the freestream. The adaptive grid method is tested on a variety of two-dimensional problems which include the hypersonic flow over a leading-edge compression ramp, the hypersonic flow through a cowl-type inlet configuration and the axi-symmetric flow over a cone-cylinder geometry. For each case, flow-field results computed using the solution-adaptive algorithm show significant improvements over results obtained using a fixed grid. Three-dimensional applications solved numerically include, (a) hypersonic flow over a right circular cone at various angles of freestream incidence, (b) flow over the NASA Ames allbody vehicle, (c) flow over the McDonnell Douglas generic option vehicle and (d) the chemically reacting flow over a blunt cone at incidence. Again, numerical results using the solution-adaptive grid scheme show significant improvements in flow-field resolution. Pilot-pressure predictions obtained using the solution-adaptive technique show improved agreement with experiment over those obtained using a conventional fixed grid.

#### Recommended Citation

Harvey, Albert Destrehan III, "Solution Adaptive Grid Procedures for High-Speed Parabolic Flows." (1991). *LSU Historical Dissertations and Theses*. 5240.

https://digitalcommons.lsu.edu/gradschool_disstheses/5240

#### Pages

204

#### DOI

10.31390/gradschool_disstheses.5240