Award Date


Degree Type


Degree Name

Doctor of Philosophy (PhD)

First Committee Member

Darrell W. Pepper

Number of Pages



Self-adaptive algorithms for 2 and 3-dimensional unstructured finite element grids are recent to the solution of partial differential equations, particularly those equations describing environmental transport. An h-adaptive grid embedding method is developed to solve the incompressible Navier-Stokes equations for fluid flow and scalar transport. An application to atmospheric mass transport is presented; This h-adaptive algorithm, in combination with the finite element method, has been designed to solve 2 and 3-dimensional problems on Pentium PC's, including problems involving complex geometry on high end PC's, workstations and mainframes. The Galerkin finite element solver is a 2 point Gauss-Legendre integration scheme which employs mass lumping, Cholesky skyline L-U decomposition, and Petrov-Galerkin upwinding; This dissertation introduces and explains the application of the Galerkin weighted residual finite element method. Development of the weak statements for the non-dimensional primitive variable Navier-Stokes equations is presented along with a Poisson formulation for resolving pressure. The semi-implicit solution process of this Poisson formulation is described in detail. Various adaptive methods are presented with emphasis on grid embedDing Finally the application of the adaptive process coupled with the finite element solver is applied to the solution of the Navier-Stokes equations along with the species transport equation; Adaptive methods are becoming common place in the solution of partial differential equations. In this thesis, an algorithm employing h-adaptation is developed for the solution of the non-linear Navier-Stokes equations for incompressible flow and its application to environmental fluid dynamics. Improvements in computational requirements are discussed including comparison with solutions on globally refined domains. Comparison of solutions is provided by using benchmark problems that provide a means for assuring the verification and validation of the computer code. Implementation of the algorithm for environmental species transport is an effective method to improve the accuracy of transport prediction.


Adaptation; Application; Element; Environmental; Environmental Flow; Finite Elements; Flow; Fluid Dynamics; Heat; Incompressible Flow; Mass; Momentum; Transport; H-adaptation

Controlled Subject

Mechanical engineering; Plasma astrophysics; Atmospheric physics

File Format


File Size

3.95 MB

Degree Grantor

University of Nevada, Las Vegas




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