Computational Fluid Dynamics Multiple Choice Questions 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: c
Clarification: The source term QC is a function of the dependent variable which is the flow variable. Giving this mathematically,
QC=Q(ΦC).
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
Answer: b
Clarification: 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
Answer: d
Clarification: 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
Answer: b
Clarification: 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
[aC-FluxCC ] ΦC+∑F~NB(C)aF ΦF =FluxVC.
What constraint does the term FluxCC have?
a) FluxCC must be greater than one
b) FluxCC must be less than one
c) FluxCC must be less than zero
d) FluxCC must be greater than zero