This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Numerical Methods – Components”.

1. Which is the first step in the numerical solution of a fluid flow problem?

a) Discretization

b) Physical model of the flow

c) Mathematical model of the flow

d) Iteration

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Explanation: The first step of any numerical solution of a fluid problem is converting the physical flow into a mathematical model. Physical model of the flow is what we have to solve. After generating the mathematical model only steps like discretization and iterative solution follows.

2. What does the mathematical model of a fluid flow contain?

a) Partial differential equations

b) Discretized partial differential equations

c) Partial differential equations and boundary conditions

d) Discretized partial differential equations and boundary conditions

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Explanation: After generating the mathematical model of the physical flow in a problem, we will have a set of partial differential equations along with its boundary conditions. The mathematical model is not complete without the boundary conditions which make the problem unique.

3. Choosing a particular type of discretization method is ineffective when ___________

a) mathematical model is complex

b) mathematical model is simple

c) grid is coarse

d) grid is very fine

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Explanation: When the grid size is very small, whatever the type of discretization method is, the results will be the same. As very fine grids are not practically acceptable, we choose a particular type of discretization method which will be the best fit for the problem.

4. The mathematical model is based on ____________

a) physical principles and assumptions

b) physical principles

c) flow model

d) flow model and assumptions

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Explanation: For generating the mathematical model, first of all, the physical principles which are applicable to the given flow should be taken. Along with these some assumptions also must be made to make the model suit the mathematical solution. These assumptions result in modelling errors.

5. Express the 2-dimensional continuity equation in cylindrical coordinates.

a) \(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\frac{\rho v_r}{r}=0\)

b) \(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\rho \frac{v_r}{r}+\frac{\partial\rho}{\partial t}=0 \)

c) \(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\frac{\partial\rho}{\partial t}=0\)

d) \(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\rho \frac{v_r}{r}+\frac{\partial\rho}{\partial t}=0\)

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Explanation: In Cartesian coordinates, radial and angular velocities replace the x and y velocity components. Similarly, (r, θ) is the coordinate system used here. The continuity equation in this system can be given by \(\frac{\partial(\rho v_r)}{\partial r}+\frac{1}{r}\frac{\partial(\rho v_\theta)}{\partial\theta}+\rho \frac{v_r}{r}+\frac{\partial\rho}{\partial t}=0 \).

6. Each node has 4 nearest neighbours. This statement is correct for which of these grid types?

a) Structured 2-D grids

b) Unstructured 2-D grids

c) Structured 3-D grids

d) Unstructured 3-D grids

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Explanation: Structured grids have 2 nearest neighbours in 1-D, 4 in 2-D and 6 in 3-D. There is no standard number of nearest neighbours in the unstructured grid type except 1-D case where there is no option for the grids to have more than two neighbours.

7. Which of these features of structured grids is a disadvantage?

a) Easy to solve

b) Suitable for simple geometries

c) Efficient in memory requirements

d) Less time requirement

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Explanation: One of the major disadvantages of structured grids is that they are not suitable for complex geometries. Those can be modelled using unstructured grids only. The other disadvantage of structured grids is distribution.

8. Which of these grids are called Chimera grids?

a) Structured grids with overlapping blocks

b) Block-structured grids

c) Block-structured grids with overlapping blocks

d) Structured grids

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Explanation: Block-structured grids with overlapping blocks are called composite or chimera grids. The disadvantage of these grids is that conservation is not ensured in boundaries. This is helpful to follow moving bodies.

9. While using a Finite Element Method, one has to approximate ____________

a) boundary conditions

b) integrals at grid faces

c) derivatives at grid points

d) shape functions and weighting functions

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Explanation: While using the Finite Element Method for solving a problem, shape functions and weighting functions are approximated. Integrals at grid faces are approximated for Finite Volume Methods. Derivatives at grid points are approximated for Finite Difference Methods.

10. Which of these coordinates are not used in CFD?

a) Orthogonal coordinates

b) Cartesian coordinates

c) Spherical coordinates

d) Number line

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Explanation: The type of coordinate system can be opted between Cartesian, Cylindrical, Spherical, Curvilinear orthogonal and non-orthogonal. A Number line cannot be used as a coordinate system in CFD.

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