Computational Fluid Dynamics Multiple Choice Questions on “Numerical Methods – Discretization Approaches”.
1. The diagram represents a one-dimensional mesh.
The conservation equations are applied to which of these points while discretizing the equation using the Finite Difference Method?
a) 5, 7
b) 2, 3
c) 5, 6, 7
d) 1, 2, 3, 4
Answer: d
Clarification: The Finite Difference Method applies conservation equation to the nodes of each cell. The vertices of the cells form the nodes. So, points 1, 2, 3 and 4 are used for discretizing.
2. Which of these is the oldest method for numerical solution of partial differential equations?
a) Finite Element Method
b) Finite Difference Method
c) Finite Volume method
d) Spectral Element Method
Answer: b
Clarification: The Finite Difference Method is the oldest method for solving partial differential equations numerically. It is believed that this method is developed by Euler in the 18th century. This is the easiest method too.
3. Which of these properties is not ensured in Finite Difference Methods?
a) Stability
b) Convergence
c) Conservativeness
d) Accuracy
Answer: c
Clarification: Though the Finite Difference method is the easiest, it is suitable only for simple problems involving structured grids. Another main disadvantage is that conservation is not enforced unless special care is taken.
4. To obtain the derivatives of the variables with respect to the coordinates, which of these approximations are used in the Finite Difference Method?
a) Taylor series and polynomial fitting
b) Fourier series and polynomial fitting
c) Taylor series and Fourier series
d) Taylor series and interpolation
Answer: a
Clarification: The conservation equation of the partial differential form is used by the Finite Difference Method. To approximate the derivatives in this equation, Taylor series and polynomial fitting are used.
5. Which of these is an advantage of the Finite Difference Method over the Finite Volume Method?
a) Conservativeness
b) Higher-order
c) Stability
d) Complex problems
Answer: b
Clarification: The Finite Volume Method cannot be applied to higher orders. The disadvantage of the Finite Volume Method, when compared to the Finite Difference Method, is that for orders higher than second order are more difficult to develop in 3-D.
6. The diagram represents a one-dimensional mesh.
The conservation equations are applied to which of these points while discretizing the equation using the Finite Volume Method?
a) 5, 7
b) 2, 3
c) 5, 6, 7
d) 1, 2, 3, 4
Answer: c
Clarification: Governing equations are applied to each control volume at its centre in the Finite Volume Method. In the diagram, points 5, 6 and 7 represent cell centres. To get the nodal values, these answers are interpolated.
7. Conservation of Finite Volume Method depends on ___________
a) surface integrals
b) volume integrals
c) convection
d) diffusion
Answer: a
Clarification: The Finite Volume Methods are conservative as long as the surface integrals which represent the convective and diffusive fluxes are the same for two control volumes sharing the same boundary.
8. A hybrid method of which of these methods exists?
a) Finite Difference Method and Finite Element Method
b) Finite Volume Method and Finite Difference Method
c) Finite Volume Method and Finite Element Method
d) Finite Volume Method and Spectral Element Method