Engineering Questions with Answers - Multiple Choice Questions

# Computational Fluid Dynamics – High Resolution Schemes – Downwind and Normalized Weighing Factor

1 - Question

. The Downwind Weighing Factor in the normalized form is given by __________
a) ϕf~−ϕc~1−ϕc~
b) ϕc~−ϕf~1−ϕc~
c) ϕf~−ϕc~1−ϕf~
d) ϕc~−ϕf~1−ϕf~

Explanation: The Downwind Weighing Factor is given by
DWFf=ϕf−ϕcϕd−ϕc
Normalizing this, we get
DWFf=ϕf~−ϕc~ϕd~−ϕc~
But, the value of ϕd~ is 1. So,
DWFf=ϕf~−ϕc~1−ϕc~

2 - Question

The value of the Downwind Weighing Factor (DWF) lies between ___________
a) 0≤DWF≤∞
b) DWF≥0
c) 0≤DWF≤1
d) DWF≤1

Explanation: By using DWF, the high-resolution estimate of ϕf~orϕf is redistributed between the upwind and the downwind nodes. As the value of Φf computed using Φc and Φc. The value of DWF always lies between 0 and 1.

3 - Question

The value of DWF for the downwind scheme is __________
a) 0
b) 1
c) 2
d) 3

Explanation: The relation between the DWF formulation and the TVD formulation is given by
DWFf=12 ψ(rf)
The ψ(rf) value for downwind scheme is 2. Therefore, the DWFf value is 1.

4 - Question

DWFf for the FROMM scheme is ___________
a) 12(1ϕc~)
b) 14(1ϕc~)
c) 12
d) 14

Explanation: For FROMM scheme,
ϕf~=ϕc~+14
Therefore,
DWFf=(ϕc~+1/4)ϕc~1ϕc~
DWFf=14(1ϕc~).

5 - Question

For a scheme modelled using the DWF method, the diagonal coefficient becomes zero when ___________
a) DWFf > 0
b) DWFf > 1
c) DWFf > 0.5
d) DWFf > 2

Explanation: For values of DWFf larger than 0.5, results in a system with negative diagonal coefficients. So, the system becomes unsolvable by iterative methods. This happens whenever Φf > 0.5(Φcd).

6 - Question

The value of DWFf for the central difference scheme is __________
a) 1
b) 13
c) 14
d) 12
Explanation: For the central difference scheme,
ψ(rf)=1
So, the value of DWFf for this scheme is ½.

7 - Question

The deferred correction source term of the NWF method using he normalized interpolation profile ϕf~=lϕc~+k is _________
a) (1-l-k)Φu
b) (k)Φu
c) (-l)Φu
d) (l-k)Φu

Explanation: We have the equation
ϕf~=lϕc~+k
This can be expanded as
ϕfϕuϕdϕu=lϕcϕuϕdϕu+k
ϕfϕuϕdϕu=lϕcϕuϕdϕu+kϕdϕuϕdϕu
Φf=l(Φcu)+k(Φdu)+Φu
Φf=l(Φc))+k(Φd))+(1-l-k)Φu
The term (1-l-k)Φu in this equation is the deferred correction source term.

8 - Question

The high-resolution schemes formulated using the NWF method with the equation ϕf~=lϕc~+k are stable without any alteration when __________<br/>
a) k>2<br/>
b) l>2<br/>
c) k>l<br/>
d) l>k

Explanation: The NWF formulation of the high-resolution schemes, when the value of l is greater than the value of k, the diagonal coefficients are all positive and hence the solution is highly stable. This is the case everywhere except a narrow region in NVD.

9 - Question

What is DWFf for the second-order upwind scheme?
a) ϕc~2(1ϕc~)
b) 12(1ϕc~)
c) ϕc~4(1ϕc~)
d) 14(1ϕc~)

Explanation: For the second order upwind scheme,
ϕf~=32ϕc~
Therefore,
DWFf=32ϕc~ϕc~1ϕc~
DWFf=ϕc~2(1ϕc~).

10 - Question

Along the downwind line of the NVD, the values of _____________ are changed to make the system stable.
a) ac
b) (l,k)
c) Φc
d) Φf