CH12: Method of Characteristics

Question 1

The method of characteristics is associated with what type of differential equation?

Answer 1

A hyperbolic differential equation .

GD, Roshko, Pg. 284

Question 2

True or False
An equation is hyperbolic if a certain relation is satisfied by the coefficients of its highest order derivatives.

Answer 2

True.

GD, Roshko, Pg. 285

Question 3

The distinguishing property of a hyperbolic equation is the existence of certain_________ in the XY plane, usually called________.

Answer 3

Characteristic directions
Characteristics

GD, Roshko, Pg. 285

Question 4

on a characteristic, the normal derivative of the dependent variables may be _________.

Answer 4

Discontinuous

GD, Roshko, Pg. 285

Question 5

For non-linear two-dimensional, irrotational flow, the characteristics are the ________.

Answer 5

Mach lines.

GD, Roshko, Pg. 285

Question 6

True or False
Because the normal velocity derivatives on mock lines may be discontinuous, it is possible to patch different flows together at these lines so long as the velocity itself is continuous.

Answer 6

True.

GD, Roshko, Pg. 285

Question 7

True or False
The Mach line Network is not known a priori as a result of the nonlinearity of the governing equation of motions.

Answer 7

True.

GD, Roshko, Pg. 285

Question 8

On the characteristics or Mach lines, the dependent variables satisfy a relation known as the ____________.

Answer 8

Compatability relation.

GD, Roshko, Pg. 285

Question 9

Mach lines are inclined at the angle ________ to the streamlines.

Answer 9

mu
Where mu = arcsin(1/M)

GD, Roshko, Pg. 286