Systematic Approach to Nondimensionalization

This series is focused on how to derive a dimensionless equation for any given differential equation in 6 steps using linear algebra. Part I contains the general introduction to the problem. Part II gives an example on how to solve the problem Bateman–Burgers equation.

Numerical solution of the Burgers equation.[1]

Nondimensionalization

Nondimensionalization is a systematic technique to make a given equation dimensionless. We apply this technique in scientific computing to make our lives easier. By applying the systematic approach to nondimensionality we:

1. Make the equation recognizable

2. Make it easier to solve the equation numerically

3. Compare orders of magnitude of each parameter (i.e. what influence does each parameter have on the equation?)

Bateman-Burgers Equation

The Bateman-Burgers equation is a fundamental differential equation occurring in various areas of scientific computing concerned with dynamics. The equation can be found in areas of fluid dynamics, fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow.