A 3-dimensional h-adaptive algorithm for species transport prediction

David Bradley Carrington, University of Nevada, Las Vegas


Development of 3-dimensional self-adaptive algorithms for unstructured finite element grids is recent to the solution of partial differential equations. An h-adaptive grid embedding method is employed to help solve the Navier-Stokes equations for fluid flow and scalar transport; This h-adaptive algorithm, in combination with the finite element solver, has been designed to solve simple to moderately complex 3-dimensional problems on high-end PC's with at least 16 megabytes of ram, and more complex geometries on workstations and mainframes. The finite element solver is a one point Gauss-Legendre integration scheme which employs mass lumping, Cholesky skyline L-U decomposition, and Petrov-Galerkin upwinding; This thesis introduces and explains the Galerkin weighted residual finite element solution process with the use of the Laplace heat conduction equation. Development of the weak statements for the non-dimensional primitive variable Navier-Stokes equations is presented with a Poisson formulation for pressure. The explicit solution process of this Poisson formulation is described in detail. Various adaptive methods are presented with emphasis on grid embedDing Single element division or grid embedding allows for the use of the one point quadrature integration scheme used in the solution process. 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 equations.