This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Types of FVM Elements”.

1. What is the minimum number of vertices that a 3-D element can have?

a) 6 vertices

b) 5 vertices

c) 3 vertices

d) 4 vertices

View Answer

Explanation: At least four points are needed to make an element. A tetrahedron is a shape which has the least number of vertices and the least number of faces. It has 4 faces and 4 vertices. A 2-D element can be formed using three vertices.

2. What is the shape of a tetrahedral element’s face?

a) Cuboid

b) Cube

c) Triangle

d) Quadrilateral

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Explanation: A tetrahedron has four triangular faces. Each face is formed by connecting three vertices of the tetrahedron. This is one of the most common shapes of element used in unstructured grids.

3. The general shape of a 3-D element is __________

a) Quadrilateral

b) Tetrahedral

c) Polyhedron

d) Polygon

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Explanation: The number of sides in an element is not restricted. The general shape of a two-dimensional element can be named polygon which can have any number of sides. The same way, the general shape of a three-dimensional element can be named polygon which can have any number of faces.

4. Which of these three-dimensional elements has faces as a mixture of two shapes?

a) Tetrahedron

b) Prism

c) Hexahedron

d) Octahedron

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Explanation: A prism is made up of two triangular faces and three rectangular faces. This is a regular shape which has faces of mixed shapes. It has six vertices. It can be used to make a structured grid.

5. Each face of a hexahedron is __________

a) Cuboid

b) Cube

c) Triangle

d) Quadrilateral

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Explanation: A hexahedron is made up of six faces. Each of its faces may have the same dimensions or may not. In general, all hexahedrons will have faces in quadrilateral (four edges) shape.

6. To find the volume and centroid of a polyhedral, it is divided into ____________

a) Quadrilaterals

b) Pyramids

c) Polygons

d) Hexahedrons

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Explanation: The first step of calculating the volume and centroid of any three-dimensional element is to pyramids. The summation of the volumes of these pyramids is the volume of the whole polyhedron.

7. The apex of the sub-element while calculating the volume of a polyhedron is ____________

a) its centre of mass

b) its centre of gravity

c) its centroid

d) its geometric centre

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Explanation: First, the geometric centre of the polyhedron is located. This is the apex of the pyramid. The distance of this apex from the face of the element gives the height of the pyramid. From the base and height of the pyramid, its volume is calculated.

8. The centroid of the polyhedron is ___________

a) the summation of the centroids of the pyramids

b) the arithmetic mean of the centroids of the pyramids

c) the weighted average of centroids of the pyramids

d) the Pythagorean mean of centroids of the pyramids

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Explanation: The centroid of each of the sub-pyramids is calculated. Their volumes are also calculated. The weighted average of these centroids is calculated by using the volumes as the weights. This gives the centroid of the element.

9. Which of these formulae is used to calculate the centroid of a polyhedron?

a) \(\sum_{n=1}^{No. \, of \,pyramids}Centroid_n×Volume_n\)

b) \(\frac{\sum_{n=1}^{No. \,of \,pyramids}Centroid_n×Volume_n}{\sum_{n=1}^{No. \, of \,pyramids}Volume_n}\)

c) \(\frac{\sum_{n=1}^{No. \,of\, pyramids}Centroid_n×Volume_n}{Volume_n} \)

d) \(\frac{\sum_{n=1}^{No. \,of \,pyramids}Centroid_n×Volume_n}{Centroid_n} \)

View Answer

Explanation: The centroid of a polyhedron is the volume-weighted average of the centroid of its sub-elements. Giving mathematically,

\(\frac{\sum_{n=1}^{No. \,of \,pyramids}Centroid_n×Volume_n}{\sum_{n=1}^{No. of pyramids}Volume_n}\).

10. In case of a two-dimensional element, which of these will serve as the face area?

a) Distance of the connecting line

b) Area of the element

c) Unit area

d) Volume of the element

View Answer

Explanation: For a two-dimensional element, the area of the element is equivalent to its volume. Similarly, the length of the connecting line is equivalent to the face area. However, the direction of flux is given by a normal vector.

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