CFD - Governing Equations

Question 1

True or False
The physical aspects of the boundary equations are fundamentally independent of the forms of the governing equations.

Answer 1

True.

Anderson CFD, Pg. 40

Question 2

The fluid flow equations that we directly obtain by applying the fundamental physical principles to a finite control volume are in ______ form.

Answer 2

Integral

Anderson CFD, Pg. 42

Question 3

Explain the conservation vs. non-conservation form of the governing equations.

Answer 3

> Conservation forms are derived from a fixed CV or
differential element.

> Non-conservation forms are derived from a moving
CV or differential element.

Anderson CFD, Pg. 42

Question 4

What are the two parts of the substantial derivative?

Answer 4

1. The local derivative (∂/∂t)
2. The convective derivative (V ∙ ∇)

Df/dt = ∂f/∂t + V ∙ ∇

Anderson CFD, Pg. 45

Question 5

Explain the physical meaning of the local derivative as shown in the definition of the substantial derivative.

Answer 5

The local derivative ∂/∂t, is physically the time rate of change of a given fluid property at a fixed point.

Anderson CFD, Pg. 45

Question 6

Explain the physical meaning of the convective derivative term of the substantial derivative.

Answer 6

The time rate of change due to the movement of the fluid element from one location to another in the flow field where the flow properties are spatially different.

Anderson CFD, Pg. 45

Question 7

True or False
The substantial derivative is the same as that of a total derivative (from calculus) with respect to time.

Answer 7

True.

Anderson CFD, Pg. 46

Question 8

What is the physical meaning of the divergence of velocity (∇ ∙ V)?

Answer 8

(∇ ∙ V) is physically the time rate of change of the volume of a moving fluid element per unit volume.

∇ ∙ V = (1/(δV)) * (D(δV)/Dt)

Anderson CFD, Pg. 48

Question 9

The _____ forms of the governing equations provide a numerical and computer programing convenience in that the continuity, momentum, and energy equations in conservation form can all be expressed by the same generic equation.

Answer 9

conservation

Anderson CFD, Pg. 83

Question 10

What are the flux variables?

Answer 10

ρ
ρu
ρv
ρw
ρ(e + V^2/2)

Anderson CFD, Pg. 85

Question 11

What are the primitive variables?

Answer 11

u, v, w, and e

Anderson CFD, Pg. 85

Question 12

The conservation forms of the governing equations can be written in a generic form __________.

Answer 12

∂U/∂t + ∂F/∂x + ∂G/∂y + ∂H/∂z = J
Where,
U = the solution vector
F, G, H = Flux vectors
J = source vector

Anderson CFD, Pgs 83,84