250+ TOP MCQs on Convection-Diffusion Problems – QUICK Scheme and Answers

Computational Fluid Dynamics Multiple Choice Questions on “Convection-Diffusion Problems – QUICK Scheme”.

1. 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
Answer: a
Clarification: 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. 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
Answer: b
Clarification: 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. 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) (phi=phi_U+frac{(x-x_D)(x-x_C)}{(x_D-x_U)(x_D-x_C)}(phi_D-phi_U)+frac{(x-x_U)(x-x_D)}{(x_C-x_U)(x_C-x_D )}(phi_C-phi_U) )
b) (phi=phi_U+frac{(x-x_D)(x-x_C)}{(x_D-x_U)(x_D-x_C)}(phi_D-phi_U)+frac{(x-x_C)(x-x_D)}{(x_C-x_U)(x_C-x_D )}(phi_C-phi_U))
c) (phi=phi_U+frac{(x-x_U)(x-x_C)}{(x_D-x_U)(x_D-x_C)}(phi_D-phi_U)+frac{(x-x_C)(x-x_D)}{(x_C-x_U )(x_C-x_D)}(phi_C-phi_U))
d) (phi=phi_U+frac{(x-x_U )(x-x_C )}{(x_D-x_U)(x_D-x_C)}(phi_D-phi_U)+frac{(x-x_U)(x-x_D)}{(x_C-x_U)(x_C-x_D)}(phi_C-phi_U))
Answer: d
Clarification: The scheme should reduce to
(phi=begin{cases}
phi_U & if , x=x_U \
phi_C & if ,x=x_C \
phi_D & if ,x=x_D
end{cases} )
Incorporating these into a formula, the formula for quick scheme is
(phi=phi_U+frac{(x-x_U )(x-x_C )}{(x_D-x_U)(x_D-x_C)}(phi_D-phi_U)+frac{(x-x_U)(x-x_D)}{(x_C-x_U)(x_C-x_D)}(phi_C-phi_U)) .

4. Consider the stencil.

Assume a uniform grid. What is φ_e according to the QUICK scheme?
a) (phi_e=frac{phi_P-phi_E}{2}-frac{phi_E+2phi_P+phi_W}{8})
b) (phi_e=frac{phi_P+phi_E}{2}-frac{phi_E+2phi_P+phi_W}{8})
c) (phi_e=frac{phi_P+phi_E}{2}-frac{phi_E-2phi_P+phi_W}{8})
d) (phi_e=frac{phi_P-phi_E}{2}-frac{phi_E-2phi_P+phi_W}{8})
Answer: c
Clarification: According to the QUICK scheme,
(phi_e=phi_W+frac{(x_e-x_W)(x_e-x_P)}{(x_E-x_W)(x_E-x_P)}(phi_D-phi_W) + frac{(x_e-x_W)(x_e-x_E)}{(x_P-x_W)(x_P-x_E)}(phi_P-phi_W) )
For a uniform grid,
x_e-x_W=3(x_e-x_P); x_E-x_W = 4(x_e-x_P); x_E-x_P=2(x_e-x_P);
x_E-x_E = -(x_e-x_P);x_P-x_W=2(x_e-x_P);
Applying all these,
(phi_e=frac{phi_P+phi_E}{2}-frac{phi_E-2phi_P+phi_W}{8})

5. What is the order of accuracy of the QUICK scheme?
a) second-order
b) first-order
c) fourth-order
d) third-order
Answer: a
Clarification: 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. 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
Answer: b
Clarification: 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
a_P Φ_P+a_E Φ_E+a_W Φ_W+a_EE Φ_EE+a_WW Φ_WW=0
It contains 5 terms.