This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Source Term Discretization”.

1. Which of these transport phenomena do not involve any source term?

a) Heat conduction

b) Heat radiation

c) Turbulence models

d) Chemical reactions

View Answer

Explanation: Many of the physical phenomena include the source and sinks. The equations of turbulence models, chemical reactions, radiation heat transfer and multiphase flows contain source terms. Pure heat conduction problem does not include any source term.

2. Which of these physical properties of the flow problems is affected by the source term?

a) Order of accuracy

b) Reduction of error

c) Stability

d) Accuracy

View Answer

Explanation: The physics of the problem is greatly affected by the source term. Moreover, talking from the analysis side, the stability condition of the problem differs for the problems with sources and the problems without sources.

3. Which of these methods is recommended for the source term treatment in general?

a) Treat sinks explicitly and sources implicitly

b) Treat sinks implicitly and sources explicitly

c) Treat the source term explicitly

d) Treat the source term implicitly

View Answer

Explanation: If the source term is properly treated, the robustness of the problem will increase. In general, it is better to treat the sinks (negative values) implicitly and the sources (positive values) explicitly.

4. The source term is ____________

a) equal to the square of the source term

b) equal to the source term

c) a function of the flow variable

d) a function of the product of flow variable and the sink term

View Answer

Explanation: The source term Q

_{C}is a function of the dependent variable which is the flow variable. Giving this mathematically,

Q

_{C}=Q(Φ

_{C}).

5. When the source term does not vary much, the source term is ___________

a) implicitly calculated

b) calculated from the previous iteration’s values

c) solved simultaneously

d) calculated form the current values

View Answer

Explanation: As the source term is a function of the flow variable, it can be calculated using the available Φ values. In an iterative process, the available values are the previous iteration’s flow variable values.

6. When the source term varies highly, which of these properties is affected?

a) Consistency

b) Boundedness

c) Stability

d) Rate of convergence

View Answer

Explanation: When the source term is a constant or small, the analysis is not affected by it. But, when the variation of the source term is large, the rate of convergence of the numerical process is greatly affected.

7. For linearizing the source term, which of these methods is used?

a) Weighted average

b) Series expansion

c) Normalization

d) Central differencing

View Answer

Explanation: To reduce the effects of the highly varying source term on the process, the term should be linearized. For this linearization, a series expansion like the Taylor series expansion is used.

8. The general form of the equation for the source term is

[a_{C}-FluxC_{C} ] Φ_{C}+∑_{F~NB(C)}a_{F} Φ_{F} =FluxV_{C}.

What constraint does the term FluxC_{C} have?

a) FluxC_{C} must be greater than one

b) FluxC_{C} must be less than one

c) FluxC_{C} must be less than zero

d) FluxC_{C} must be greater than zero

View Answer

Explanation: The diagonal terms are those which are the coefficients of Φ

_{C}. In the above equation, the diagonal coefficients are given by a

_{C}-FluxC

_{C}. For this value to be high, FluxC

_{C}should be less than one.

9. The general form of the equation for the source term is

[a_{C}-FluxC_{C} ] Φ_{C}+∑_{F~NB(C)}a_{F} Φ_{F} =FluxV_{C}.

The constraint on the term FluxC_{C} is imposed by ______________

a) Scarborough criterion

b) Richardson extrapolation

c) Stability criterion

d) Gauss-Siedel criterion

View Answer

Explanation: The constraint on the term FluxC

_{C}for diagonal dominance. Diagonal dominance is needed by the Scarborough criterion. The Scarborough criterion is used to ensure the convergence of the linear system of equations.

10. The general form of the equation for the source term is

[a_{C}-FluxC_{C} ] Φ_{C}+∑_{F~NB(C)}a_{F} Φ_{F} =FluxV_{C}.

When the variable Φ is positive-definite, the FluxV_{C} should be ______________

a) FluxV_{C} must be greater than one

b) FluxV_{C} must be less than one

c) FluxV_{C} must be less than zero

d) FluxV_{C} must be greater than zero

View Answer

Explanation: In some of the cases, the value of the flow variable Φ

_{C}will always be a positive non-zero value. In these cases, the value of FluxV

_{C}must be greater than zero to ensure that the value of Φ will also be greater than zero.

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