Assignment No. - 01

Title: Computational fluid dynamics

 

Date of submission:

 

Cross those boxes corresponding to questions that you have not  attempted

 

 

1.What is CFD ? How does a CFD code work ?

 

2.There are two methods of prediction of heat transfer and fluid flow : experimental investigation and theoretical calculation. State the advantages and disadvantages of both the methods. Which among the two prediction methods you would choose.

 

3.Consider the governing partial differential equation for the dependent variable Φ(x, y), given as

∂Φ           ∂Φ               ∂²Φ

 -----   + A -----    =   B  -----

∂x             ∂y               ∂y²

where A and B are constants. Determine the nature of this equation.

 

4.Burger’s equation, which arises frequently in fluid dynamics, is

∂u             ∂u                ∂²u

-----    + u -----  =     v  -----

∂t              ∂x               ∂x²

 

where u is the velocity, t is the time, x is the coordinate distance, and v the kinematic viscosity of the fluid. Classify this equation.

 

5.All of CFD, in one form or another, is based on the fundamental governing equations of fluid dynamics-the continuity, momentum and energy equations. Write  and explain these equations.

 

6.Determine the nature of the given equation:

∂w            ∂w

---- +  [A]  ----  = 0

∂x             ∂y

where,

w = [u v]

and [A] = [0  -1,1  0]

 

7.Show that the first order wave equation:

  ∂u          ∂u

----  + c ---- = 0

  ∂t           ∂x

is a hyperbolic equation.

 

8.Consider Laplace’s equation, given by:

 

 ∂²Φ        ∂²Φ

          -----   +   -----  =  0

 ∂²x         ∂²y

show that this is an elliptic equation.

 

9.Show that all three conservation equations- continuity, momentum, and energy – can be put in a single generic integral form.

 

10. There are two approaches for the modeling of flow: finite control volume and infinitesimal fluid element approach, differentiate between them ?