Engineering Questions with Answers - Multiple Choice Questions

# Computational Fluid Dynamics – Convection-Diffusion Problems – Upwind and Downwind Schemes

1 - Question

The upwind scheme is suitable for _____________
a) convection term
b) diffusion term
c) both convection and diffusion terms
d) either convection or diffusion term
Explanation: The upwind scheme is not suitable for non-directional phenomena. The diffusion scheme is a non-directional phenomenon. The convection scheme is a directional phenomenon. So, the scheme is suitable for the convection term.

2 - Question

The upwind scheme is dependent on the _____________
a) Convection term
b) Peclet number
c) Flow direction
Explanation: The upwind scheme reflects the physics of advection. The cell-face value is dependent on the upwind nodal value. So, we can say it is dependent on the flow direction and it is suitable for directional flows.

3 - Question

Consider the stencil. Give the advection flux at face e (me˙ϕE) using the upwind scheme.
(Note: m˙ and Φ are the mass flow rate and the flow variable respectively).
a) me˙ϕE=max(me˙,0)ϕCmax(me˙,0)ϕE
b) me˙ϕE=min(me˙,0)ϕCmax(me˙,0)ϕE
c) me˙ϕE=max(me˙,0)ϕCmin(me˙,0)ϕE
d) me˙ϕE=min(me˙,0)ϕCmin(me˙,0)ϕE

Explanation: According to the upwind scheme,
ϕE={ϕCϕEifme˙>0ifme˙<0
Where, me˙>0 means that the flow is from C to e and me˙<0 means that the flow direction is opposite. Therefore,
me˙ϕE=max(me˙,0)ϕCmax(me˙,0)ϕE.

4 - Question

The neighbour coefficients yielded by the upwind scheme for convection is _____________
a) zero
b) cannot predict
c) negative
d) positive
Explanation: The upwind scheme leads to negative neighbouring coefficients. If continuity is ensured, the diagonal coefficients (coefficients of the central nodes) are the addition of the neighbouring coefficients.

5 - Question

Consider the following stencil. Give the relationship between ϕCϕWϕEϕW and Peclet number (Pe) for the upwind scheme while used for the convection term.
(Note: Φ is the flow variable).
a) ϕCϕWϕEϕW=2max(Pe,0)4+∣∣Pe∣∣
b) ϕCϕWϕEϕW=2max(Pe,0)4+∣∣Pe∣∣
c) ϕCϕWϕEϕW=2+max(Pe,0)4+∣∣Pe∣∣
d) ϕCϕWϕEϕW=2+max(Pe,0)4+∣∣Pe∣∣

Explanation: For the upwind scheme,
ΦCW = 2+max⁡(-Pe,0) and ΦEC = 2+max⁡(Pe,0)
Therefore,
ϕCϕWϕEϕC+ϕCϕW=2+max(Pe,0)2+max(Pe,0)+2+max(Pe,0)
ϕCϕWϕEϕW=2+max(Pe,0)4+∣∣Pe∣∣.

6 - Question

The order of accuracy of the upwind scheme is _____________
a) first-order
b) second-order
c) third-order
d) fourth-order
Explanation: The upwind scheme is first-order accurate. This is why, even though the fashion of the upwind scheme matches with that of the exact solution, it varies much. The downwind scheme is also first-accurate.

7 - Question

Consider the stencil. Give the advection flux at face w (mw˙ϕW) using the downwind scheme.
(Note: m˙ and Φ are the mass flow rate and the flow variable respectively).
a) mw˙ϕW=max(mw˙,0)ϕC+max(mw˙,0)ϕW
b) mw˙ϕW=max(mw˙,0)ϕC+max(mw˙,0)ϕW
c) mw˙ϕW=max(mw˙,0)ϕC+max(mw˙,0)ϕW
d) mw˙ϕW=max(mw˙,0)ϕC+max(mw˙,0)ϕW

Explanation: According to the downwind scheme,
ϕE={ϕCϕEifme˙>0ifme˙<0
Where, me˙>0 means that the flow is from C to e and me˙<0 means that the flow direction is opposite. Therefore,
mw˙ϕW=max(mw˙,0)ϕC+max(mw˙,0)ϕW.

8 - Question

The advantage of the upwind scheme is over the central-difference scheme is _____________
a) accuracy
b) stability
c) high convergence rate
d) consistency
Explanation: The upwind scheme is less accurate than the central difference schemes. But the central difference schemes are oscillatory. They do not give answers which are physically correct. This is the advantage of the upwind scheme over the central-difference scheme.

9 - Question

The upwind scheme is _____________
a) conservative but wiggles
b) bounded and conservative
c) bounded but not conservative
d) neither conservative nor bounded
Explanation: The upwind scheme does not produce results which wiggle. So, it is bounded. It uses consistent expressions to calculate fluxes through cells. Therefore, it is sure that the formulation is conservative.

10 - Question

When the flow is not aligned with the grid lines, the diffusion produced by the upwind scheme is ____________