This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Discretization Aspects – Conservativeness”.
1. Conservation of the flow properties should be ensured in __________
a) both the global and local domains
b) the global domain only
c) the local domain only
d) the global domain and optionally in the local domain
Explanation: We know that the conservation laws govern the flows and the properties like energy and mass are conserved in the global domain. This must be applicable to the local domain also after discretization. Otherwise, the solution will be unrealistic.
2. The flux of one element must have _________ to the flux of the neighbouring element.
a) different magnitude and equal sign
b) different magnitude and opposite sign
c) equal magnitude and equal sign
d) equal magnitude and opposite sign
Explanation: Flux leaving the face of one element should be the flux entering the neighbouring element. So, the fluxes of two near-by elements should have equal magnitude and opposite sign. This ensures the conservativeness of the system.
3. Conservation of the system leaves a limitation to the __________
b) solution error
Explanation: If the conservation of mass, momentum and energy are ensured, the error can only interchange the values at different nodes. The overall system will not be erroneous. So, the solution error is a way decreased by the conservativeness of a system.
4. Non-conservative schemes can be consistent and stable if ____________
a) grid is fine
b) grid is coarse
c) solution converges
d) solution is bounded
Explanation: For fine rids, non-conservative schemes can also give a consistent and stable solution. The errors due to non-conservation are negligible. These errors become appreciable only if the grid is coarse and the grid size is more.
5. Which of these methods is usually conservative?
a) Finite Difference Method
b) Finite Element Method
c) Finite Volume Method
d) Iterative Method
Explanation: Conservativeness is defined for the discretization schemes only. Finite volume methods often guarantee conservation. They integrate the flow variables over each elemental domain. They ensure that flux leaving one domain is equal to that entering the neighbouring domain.
6. For a system with a source or sink to be conservative, which of these is correct?
a) The total source or sink in the domain is divided equally between the elements
b) The total source or sink in the domain is equal to the net flux through the boundaries
c) The total source or sink in the domain is not considered for checking conservativeness
d) Flux leaving the face of one element is equal to the flux entering the neighbouring element
Explanation: The general condition of equal and opposite fluxes cannot be applied to a system with sources or sinks. For this case, the total source or sink in the domain should be equal to the net flux through the boundaries of the whole domain.
7. Non-conservative schemes produce ___________
a) artificial radiation
b) artificial diffusion
c) artificial convection
d) artificial source or sink
Explanation: Non-conservative schemes do not have the net fluxes conserved. In the global domain, the fluxes entering the domain and that leaving the domain are not the same. This will create artificial sources and sinks which do not actually exist in the physical problem.
8. Which of these schemes ensure conservativeness?
a) Central differencing
b) Upwind differencing
c) TVD scheme
d) Quadratic schemes
Explanation: Conservation of flow property is ensured for the central differencing scheme over the entire domain. Here, the flux interpolation formula is consistent. So, only the two boundary fluxes remain when the global domain is considered.
9. Which of these higher-order schemes is conservative?
d) Power law scheme
Explanation: QUICK scheme is one of the higher-order schemes involving quadratic interpolation. While the other quadratic interpolation schemes give rise to conservation problems, the QUICK scheme ensures the conservation of the quantities. But, it has boundedness problems.
10. Quadratic interpolation results in conservation problems. Why?
a) Their physical problem is non-conservative
b) They involve quadratic equations
c) They are higher order schemes
d) Interpolation curves vary at the face
Explanation: Quadratic interpolation models the physical problems using quadratic equations. At the intersection faces, we get two different quadratic equations and their values do not cancel out there. This gives a problem to conservation in the Quadratic interpolation schemes.
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