Engineering Questions with Answers - Multiple Choice Questions
Computational Fluid Dynamics – High Resolution Schemes – Downwind and Normalized Weighing Factor
. The Downwind Weighing Factor in the normalized form is given by __________
Explanation: The Downwind Weighing Factor is given by
Normalizing this, we get
But, the value of ϕd~ is 1. So,
The value of the Downwind Weighing Factor (DWF) lies between ___________
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.
The value of DWF for the downwind scheme is __________
Explanation: The relation between the DWF formulation and the TVD formulation is given by
The ψ(rf) value for downwind scheme is 2. Therefore, the DWFf value is 1.
DWFf for the FROMM scheme is ___________
Explanation: For FROMM scheme,
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(Φc+Φd).
The value of DWFf for the central difference scheme is __________
Explanation: For the central difference scheme,
So, the value of DWFf for this scheme is ½.
The deferred correction source term of the NWF method using he normalized interpolation profile ϕf~=lϕc~+k is _________
Explanation: We have the equation
This can be expanded as
The term (1-l-k)Φu in this equation is the deferred correction source term.
The high-resolution schemes formulated using the NWF method with the equation ϕf~=lϕc~+k are stable without any alteration when __________<br/>
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.
What is DWFf for the second-order upwind scheme?
Explanation: For the second order upwind scheme,
Along the downwind line of the NVD, the values of _____________ are changed to make the system stable.
Explanation: Along the downwind line of NVD, the values of (l,k)=(0,1), a value of zero is obtained for the diagonal coefficient and the system becomes unstable. To overcome this problem, the values of (l,k) are set equal to (L,1-LΦf). The value of L can be chosen which is usually set to l in the previous interval.