Question

Which of these methods is employed to find solution using method of characteristics?

(a) Taylor series

(b) Fourier series

(c) McLaurin series

(d) Laurent series

I have been asked this question during an online exam.

The doubt is from Philosophy of Method of Characteristics in chapter Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer 1

The correct option is (a) Taylor series

Explanation: The flow field properties such as the pressure, density at the discrete points in a grid (xy coordinate plane) are found out by expanding these properties in using Taylor series. If we know the pressure at some point (i,j), then the pressure at the point (i + 1,j) point can be computed using this series as follows:

ui + 1,j = ui,j + \(\frac {∂P}{∂x_{i,j}}\) ∆x + \(\frac {∂^2 P}{∂x^{2}_{i,j}} \frac {∆x^{2}}{2} + \frac {∂^3 P}{∂x^{3}_{i,j}} \frac {∆x^{3}}{3}\) + ⋯.