Contributions to numerical solution of Navier-Stokes equations in two and three dimensional flows
Abstract
A method for solving Navier-Stokes continuity and energy equations with reduced computation time and memory allocation is presented. A three dimensional stream function formulation with four partial differential equations was given and reduced to a two dimensional form. Two particular cases were considered such as Benard problem and low Prandtl fluids. The Newton chord process was used for numerical solution of the two dimensional formulation. A partial linear differential equation system as a block three diagonal system and an eigenvalue problem in a Banach space were obtained. A local and global continuity method was used for discretization. Results obtained for free and Marangoni convection are presented, which show the importance of boundary condition choice.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1992
- Bibcode:
- 1992PhDT........56W
- Keywords:
-
- Banach Space;
- Computational Fluid Dynamics;
- Continuity Equation;
- Free Convection;
- Marangoni Convection;
- Navier-Stokes Equation;
- Stream Functions (Fluids);
- Biot Number;
- Branching (Mathematics);
- Computational Grids;
- Grashof Number;
- Heat Transfer;
- Newton Methods;
- Prandtl Number;
- Rayleigh Number;
- Fluid Mechanics and Heat Transfer