Engineering Questions with Answers - Multiple Choice Questions
Computational Fluid Dynamics – Numerical Methods – Discretization Approaches
1 - Question
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
View Answer
Explanation: 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 - Question
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
View Answer
Explanation: 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 - Question
Which of these properties is not ensured in Finite Difference Methods?
a) Stability
b) Convergence
c) Conservativeness
d) Accuracy
View Answer
Explanation: 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 - Question
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
View Answer
Explanation: 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 - Question
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
View Answer
Explanation: 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 - Question
The diagram represents a one-dimensional mesh.
View Answer
Explanation: 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 - Question
Conservation of Finite Volume Method depends on ___________
a) surface integrals
b) volume integrals
c) convection
d) diffusion
View Answer
Explanation: 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 - Question
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
View Answer
Explanation: A hybrid method integrating Finite Volume Method and Finite Element Method called the Control Volume based Finite Element Method (CV-FEM) is also used for solving PDEs. In this, shape functions are used to describe the variation of the variables over an element.
9 - Question
In which of these methods, the calculation for interior nodes is done at the post-processing stage?
a) Spectral element method
b) Boundary element method
c) Finite Element method
d) Finite Volume Method
View Answer
Explanation: In Boundary element method, the given boundary conditions are used to fit the boundary values into the integral equations. After this, using the boundary solutions, the solution for the interior nodes is carried out at the post-processing stage.
10 - Question
Which of these statements are wrong considering Control Volume based Finite Element Method?
a) Control volumes are formed
b) Integral form of the conservation equation is used
c) The centroid of the elements is used
d) Conservation equations are applied to the centroids
View Answer
Explanation: In CV-FEM, control volumes are formed by joining the centroids of the elements. The conservation equation in the integral form is applied to these control volumes as in the Finite Volume Method.