## Electronic Theses and Dissertations

1998

Dissertation

Ph.D.

#### Department

Mathematics and Statistics

Barron, R.

Mathematics.

CC BY-NC-ND 4.0

#### Abstract

By formulating the governing equations of fluid motion in streamline-aligned coordinates one can avoid difficulties associated with grid generation and can solve problems of inverse design or problems with free boundaries. In this dissertation, previous approaches utilizing streamline-aligned coordinates have been extended for both steady and unsteady flow motions. The governing equations for steady inviscid two-dimensional gas motion have been formulated in an orthogonal system of independent coordinates consisting of the streamfunction and its orthogonal complimentary function. The resulting system of differential conservation laws expresses conservation of mass, momentum and energy. The conservative finite volume approximation of these equations can be used to calculate flows with strong shocks. For the case of potential velocity vector field, two different simplified formulations of the governing equations are derived. In order to compute purely supersonic flows, a conservative hybrid grid-characteristic scheme has been developed. To calculate transonic potential flows, two iterative algorithms have been implemented. For the case of compressible unsteady flow, the streamline-aligned coordinates are introduced through a consideration of metric coefficients of the coordinate transformation. It is demonstrated that, if one family of coordinate lines is aligned along the velocity vector field at any time and certain compatibility conditions for this coordinate transformation are satisfied, it is possible to use the remaining degrees of freedom to ensure that the resulting coordinate system is orthogonal, or to specify the local value of the jacobian of the transformation. A central-difference Lax-Wendroff numerical scheme with additional explicitly added dissipation is used to solve the resulting system of transformed equations. The developed approaches and numerical algorithms are tested on calculations of subsonic, transonic and supersonic internal flows.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1997 .L38. Source: Dissertation Abstracts International, Volume: 61-09, Section: B, page: 4763. Adviser: Ronald Barron. Thesis (Ph.D.)--University of Windsor (Canada), 1998.

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