3-4. Characteristics

Basic supersonic equations and integration method

Near sonic and supersonic flow

Method of characteristics
for solving sonic initial value problems (2D plane flow), compilation of the analytical basis

The coefficients K13, K23
The coefficient K is a function of the velocity variable (nue), via the local Mach number M. Averaging of K between gridpoints 1 and 3, and between 2 and 3 to K13 and K23, (which for the present applications are the same because nue(1) and nue(2) are equal), allows 2nd order accurate integration of the whole triangular domain to obtain a solution Phi, Psi(nue, theta). Synchroneous integration of the physical plane (x, y) result in a flow pattern with Mach waves ( = characteristics), and streamlines (Psi = const).

Characteristic equations in the near sonic domain

(In Lecture 3): Basic equations (2) in the domain M ~ 1 for the variables U, V, X, Y in a parameter plane (s, t),

for j = 0 (plane 2D flow), k= 1/3, and l = 1 (flow domain part where M > 1).

These equations are transformed to 'characteristic variables" in the half plane s > 0:


Lit.: Sobieczky, H., Qian, Y. J.: Extended Mapping and Characteristics Techniques. Proc. Third Int. Conf. on Inverse Design Concepts and Optimization in Engineering Sciences. Washington, D.C. pp 1 - 7 (1991)