Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering

First Advisor

R. H. Pletcher


The Navier-Stokes equations are solved numerically for two-and three-dimensional viscous laminar flows. The domain is discretized using triangular control volumes in two dimensions and tetrahedra in three dimensions, using existing grid generators. The flow solvers are implemented on a variety of computers, including distributed memory parallel computers;A finite-volume approach is used to discretize the governing flow equations in conservation law form using conserved variables. A cell centered approach is used where the unknowns are computed at the center of each control volume. Both explicit and implicit solution strategies are pursued. In the two-dimensional version of the algorithm an explicit upwind scheme as well as a central-difference scheme with added artificial dissipation is used. The upwind scheme implemented in two dimensions is the advection upstream splitting method. Time-derivative preconditioning using primitive and conserved variables is applied to the two-dimensional flow solver. Time-derivative preconditioning is used to enhance the low Mach number rate of convergence. A multistage Runge-Kutta scheme is used to advance the solution in time;In the three-dimensional version of the algorithm, an implicit upwind scheme is used. For the implicit scheme, an approximate flux Jacobian is used on the left hand side to reduce the computational effort and a Roe flux difference splitting is used on the right hand side. The gradients in the control volume need to be computed so the upwind scheme is second order accurate;The gradients in each cell are computed based on the values of the flow variables at the vertices of the grid. The values at the vertices of the grid are obtained by inverse distance weighting all the cell-centered values of the control volumes surrounding each vertex. For the implicit scheme, a block Gauss-Seidel solver is used to solve the resulting sparse matrix. The correctness of the solution strategies is determined by comparing the calculated solutions to data available in the literature;The schemes are implemented on parallel distributed memory computers. The parallelism exploited is coarse grained. The discretized solution domain is partitioned such that each processing unit is allocated a part of the domain. The processing units perform the solution of the Navier-Stokes equations independently from each other on different parts of the grid and with different data. Communication between processors is needed to properly model the domain;Numerical results for two-dimensional flows are obtained for a developing channel flow, a sudden expansion flow, a driven cavity flow with and without heat transfer and the flow over on obstruction in a channel. Three-dimensional flows computed are a developing straight channel flow of constant cross section, a driven cavity flow, and a developing curved channel flow. Good agreement of the computed results with data available in the literature is found.



Digital Repository @ Iowa State University,

Copyright Owner

Thomas Hans Ramin



Proquest ID


File Format


File Size

127 pages