Computational Fluid Dynamics Practice Test 8

1. The value of DWF_f for the central difference scheme is __________

\(\frac{1}{4}\)

\(\frac{1}{2}\)

\(\frac{1}{3}\)

2. DWF_f for the FROMM scheme is ___________

\(\frac{1}{2(1-\tilde{\phi_c})}\)

\(\frac{1}{2}\)

\(\frac{1}{4(1-\tilde{\phi_c})}\)

\(\frac{1}{4}\)

3. Plotting the QUICK scheme in the (\(\tilde{\phi_c},\tilde{\phi_f}\)) plane, the profile will be ____
(Note: \(\tilde{\phi_c} \,and\, \tilde{\phi_f}\) are the normalized flow variable at the upwind node and at the face respectively).

a parabola

quadratic line

straight line

curved line

4. The value of the Downwind Weighing Factor (DWF) lies between ___________

DWF≤1

0≤DWF≤1

0≤DWF≤∞

DWF≥0

5. Boundedness is ensured in the steady-state diffusion problem _______________

only when the source term is non-zero

only when the source term is non-negative

only when the source term is zero

only when the source term is negative

6. Which of these methods is used to treat the non-orthogonal diffusion term?

Trial and error method

Deferred correction

Green-gauss

Predictor–corrector

7. While using the Cartesian grids, the coefficient matrix becomes ____________

an upper triangular matrix

a lower triangular matrix

a diagonal matrix

a square matrix

8. The numerical convection schemes should be _________

considering both upwind and downwind equally

upwind or downwind depending on the problem

upwind biased

downwind biased

9. The SMART scheme is constructed using the ____________

MINMOD scheme

STOIC scheme

QUICK scheme

SUPERBEE scheme

10. Consider the discretized form of an equation given by \(\frac{\partial(\rho u\phi)}{\partial x}=-a(\phi_c-\phi_u)+b(\phi_d-\phi_c).\) For this numerical scheme to be TVD, what is the condition?
(Note: Φ_u, Φ_c and Φ_d are the flow variables at the far upwind, upwind and downwind schemes).

a≥0;b≤0;0≤a+b≤1

a≥0;b≥0;0≤a-b≤1

a≥0;≤0;0≤a-b≤1

a≥0;b≥0;0≤a+b≤1