ME 523

Numerical Solutions Applied To Heat Transfer And Fluid Mechanics Problems

# Use of Numerical Methods

During your education you've been taught a large number of clever tricks to solve various mathmatical equations (algebraic, ODE, PDE).  However, as you look carefully at the mathmatical models for problems of serious interest, you find that they are too complex for any of these tricks to get you far in obtaining a solution to the problem.  In the end you find that you need to construct approximations to the mathmatical model and solve these approximations on a computer.  This class with provide the basics for constructing and evaluating such approximations.  In the process it will hopefully help you refine your skills in breaking a complex problem into a series of relatively simple steps.

## What is the basic approach?

1. Physical phenomena are defined by a mathematical model.
2. The mathematical model is approximated by algebraic expressions at discreet points or volumes in the physical domain.
3. The set of algebraic equations are solved simultaneously using the digital computer.

## Solution Options

1. Use commercial program.
2. Use public domain ("freeware") program

## Major Concerns

1. Has adequate detail been included in the mathematical model?
2. If the set of algebraic equations are solved simultaneously using an iterative method, have you obtained a converged system?  Is the measure of convergence adequate?
3. Is the solution independent of the number of discreet points used?

## Other Lectures / Home

Created by  Frank Schmidt
Maintained by John Mahaffy : jhm@psu.edu