A numerical method to solve the steady-state Navier-Stokes equations for natural convection in enclosures
Abstract
A numerical method is presented for thermally driven laminar flow in two-dimensional enclosures. The procedure solves the Navier-Stokes equations in terms of the stream function by using the finite-difference method of Hermitian type. For the solution of the complex system of finite-difference equations a direct solver is developed based on the LU decomposition of the matrix. In order to linearize the nonlinear stream function equation, two methods, Biharmonic Driver and Newtonian-Raphson, are considered. Results with respect to accuracy and rate of convergence demonstrate the reliability of the procedure for low Rayleigh number flows.
- Publication:
-
Recent Contributions to Fluid Mechanics
- Pub Date:
- 1982
- Bibcode:
- 1982rcfm.book..222S
- Keywords:
-
- Computational Fluid Dynamics;
- Enclosures;
- Free Convection;
- Laminar Flow;
- Navier-Stokes Equation;
- Steady Flow;
- Differential Equations;
- Finite Difference Theory;
- Isotherms;
- Low Reynolds Number;
- Stream Functions (Fluids);
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer