Engineering Questions with Answers - Multiple Choice Questions

# Computational Fluid Dynamics – Convection-Diffusion Problems – QUICK Scheme

1 - Question

What does QUICK stand for?
a) Quadratic Upstream Interpolation for Convective Kinetics
b) Quadratic Upstream Interval for Convective Kinetics
c) Quadratic Upwind Interval for Convective Kinetics
d) Quadratic Upwind Interpolation for Convective Kinetics
Explanation: QUICK is a higher-order differencing scheme introduced by Brian P. Leonard in his paper in the year 1979. It is the abbreviation of Quadratic Upstream Interpolation for Convective Kinetics.

2 - Question

Which is correct about the QUICK scheme?
a) A two-point upwind biased interpolation
b) A three-point upwind biased interpolation
c) A three-point downwind biased interpolation
d) A two-point downwind biased interpolation
Explanation: QUICK scheme uses a three-point upstream-weighted quadratic interpolation to approximate the cell face values. It uses two immediate neighbours of the face and an extra upstream node (totally, three points).

3 - Question

According to the QUICK scheme, the flow variable (φ) is given by ____
(Note: U, D and C represents the upwind, downwind and the central nodes respectively).
a) ϕ=ϕU+(xxD)(xxC)(xDxU)(xDxC)(ϕDϕU)+(xxU)(xxD)(xCxU)(xCxD)(ϕCϕU)
b) ϕ=ϕU+(xxD)(xxC)(xDxU)(xDxC)(ϕDϕU)+(xxC)(xxD)(xCxU)(xCxD)(ϕCϕU)
c) ϕ=ϕU+(xxU)(xxC)(xDxU)(xDxC)(ϕDϕU)+(xxC)(xxD)(xCxU)(xCxD)(ϕCϕU)
d) ϕ=ϕU+(xxU)(xxC)(xDxU)(xDxC)(ϕDϕU)+(xxU)(xxD)(xCxU)(xCxD)(ϕCϕU)

Explanation: The scheme should reduce to
ϕ=⎧⎩⎨ϕUϕCϕDifx=xUifx=xCifx=xD
Incorporating these into a formula, the formula for quick scheme is
ϕ=ϕU+(xxU)(xxC)(xDxU)(xDxC)(ϕDϕU)+(xxU)(xxD)(xCxU)(xCxD)(ϕCϕU) .

4 - Question

Consider the stencil. Assume a uniform grid. What is φe according to the QUICK scheme?
a) ϕe=ϕPϕE2ϕE+2ϕP+ϕW8
b) ϕe=ϕP+ϕE2ϕE+2ϕP+ϕW8
c) ϕe=ϕP+ϕE2ϕE2ϕP+ϕW8
d) ϕe=ϕPϕE2ϕE2ϕP+ϕW8

Explanation: According to the QUICK scheme,
ϕe=ϕW+(xexW)(xexP)(xExW)(xExP)(ϕDϕW)+(xexW)(xexE)(xPxW)(xPxE)(ϕPϕW)
For a uniform grid,
xe-xW=3(xe-xP); xE-xW = 4(xe-xP); xE-xP=2(xe-xP);
xE-xE = -(xe-xP);xP-xW=2(xe-xP);
Applying all these,
ϕe=ϕP+ϕE2ϕE2ϕP+ϕW8

5 - Question

What is the order of accuracy of the QUICK scheme?
a) second-order
b) first-order
c) fourth-order
d) third-order
Explanation: As the QUICK scheme is based on a quadratic function, its accuracy in terms of Taylor Series truncation error is third-order. This has a higher order of accuracy than the upwind and second-order upwind schemes.

6 - Question

How many terms does the discretized form of source-free 1-D convection problem modelled using the QUICK scheme has?
a) 3
b) 5
c) 2
d) 4

Explanation: The discretized form of a source-free 1-D convection problem modelled using the QUICK scheme involves the far upstream and the far downstream nodes too. Therefore, it contains extra terms than the upwind and the second-order upwind schemes. The stencil is The discretized equation is
aP ΦP+aE ΦE+aW ΦW+aEE ΦEE+aWW ΦWW=0
It contains 5 terms.

7 - Question

What is the first term of the truncation error of the QUICK scheme?
a) 116(Δx)2ϕC
b) 116(Δx)3ϕC
c) 116(Δx)3ϕivC
d) 116(Δx)2ϕivC

Explanation: The order of accuracy is 3. Therefore, (Δ x)3 should be there in the first term of the truncation error. The truncation error is obtained using the Taylor series. Therefore, this (Δ x)3 comes along with ΦCiv.

8 - Question

Which of these is correct about the QUICK scheme?
a) Stable and bounded
b) Stable and unbounded
c) Unstable and bounded
d) Unstable and unbounded
Explanation: The QUICK scheme is not bounded. It involves undershoots and overshoots. The main coefficients (immediate eastern and western coefficients) are not guaranteed to be positive. The coefficients aEE and aWW are negative. Therefore, the solution is not stable.

9 - Question

Consider the stencil. a) (34ϕP18ϕW+38ϕE)×max(mw˙,0)(34ϕW18ϕWW+38ϕC)×max(mw˙,0)
b) (34ϕP+18ϕW+38ϕE)×max(mw˙,0)(34ϕW+18ϕWW+38ϕC)×max(mw˙,0)
c) (34ϕP18ϕW38ϕE)×max(mw˙,0)(34ϕW18ϕWW38ϕC)×max(mw˙,0)
d) (34ϕP+18ϕW38ϕE)×max(mw˙,0)(34ϕW+18ϕWW38ϕC)×max(mw˙,0)

Explanation: Using QUICK scheme, for a flow in the positive x-direction,
ϕe=ϕP+ϕE2ϕE2ϕP+ϕW8=34ϕP+38ϕE18ϕW
In a similar manner, for a flow in the positive x-direction,
ϕw=34ϕP18ϕW+38ϕE
For a flow in the negative x-direction,
ϕw=34ϕW18ϕWW+38ϕC
Therefore,
mw˙ϕw=(34ϕP18ϕW+38ϕE)×max(mw˙,0)
(34ϕW18ϕWW+38ϕC)×max(mw˙,0)

10 - Question

Which of these is correct for a QUICK scheme?
a) False diffusion is zero
b) False diffusion is small
c) False diffusion is big
d) False diffusion is infinity