1. NAE C_S2001 FINAL PROJECT PRESENTATION LASIC ISMAR 04/12/01 INSTRUCTOR: PROF. GUTIERREZ

2. PROBLEM STATEMENT l Numerical l Numerical solution for 2-Dimensional, steady-state, temperature distributions in a flat plate with 3 edges at a fixed temperature and one edge in Convection. l Base l Base Line - Exact solution of simpler case found analytically. l Modeling l Modeling and validating the numerical solution (Fortran).

3. MODELING A SYSTEM l Partial Differential Equations used to model the system. l Finding the temperature values at a finite number of points characterized by mesh.

4. FINITE DIFFERENCE APPROACH l Heat flows vertically and horizontally into node of interest.

5. ITERATIVE SOLUTION (Gauss-Seidel) l Gauss-Seidel l Gauss-Seidel (near-neighbor) sweeps to convergence. l Interior l Interior n-by-n points updated in each sweep according to the formula: l Updates done in-place in grid, and residual value computed. l Check if error has converged (to within a tolerance parameter). l If so, exit solver; if not, do another sweep.

6. IN CLOSING

7. QUESTIONS ??? LASICIS@IFC.UTC.COM