Computational Fluid Dynamics Multiple Choice Questions on “The Geometry of FVM Elements”.
1. How are the faces of a 3-D element divided to find the area?
a) Squares
b) Quadrilaterals
c) Rectangles
d) Triangles
Answer: d
Clarification: The faces of a 3-D element are 2-D polygons. With the intention of finding the area of these faces, they are divided into triangles of different type and sizes. Triangles give the advantage of having any length in all three of its sides.
2. Which of these points form the apex of the sub-elements of the faces?
a) Centre of mass of the face
b) Vertex of the face
c) Geometric centre of the face
d) Apex of the face
Answer: c
Clarification: The sub-elements are all triangular in shape. The apex of these triangles are all the same point. The geometric centre of the face is chosen as the apex of the triangles. The geometric centre is not the centroid of the polygon.
3. Which formula is suitable for finding the geometric centre of a polygonal face?
a) (frac{1}{No.of points}sum_{i=1}^{No.of points}) Point defining the polygoni
b) (sum_{i=1}^{No.of, points}) Point defining the polygoni
c) (frac{1}{Point, defining, the, polygon}sum_{i=1}^{No.of, points}) Point defining the polygoni
d) (frac{1}{No.of, points}sum_{i=1}^{No.of, points})Centroidi
Answer: a
Clarification: The average of all the points that define the polygon is the geometric centre of the polygon. Therefore,
Geometric centre=(frac{1}{No.of points}sum_{i=1}^{No.of points}) Point defining the polygoni
4. Which of these formulae is used to find the area of the sub-elements in CFD?
a) Vector product of two sides
b) Half of the vector product of two sides
c) Half of the base times height
d) Half of the vector product of all three sides
Answer: b
Clarification: Sub-elements are in triangular shape. Half of the base times height is the formula generally used to find the area of a triangle. But, CFD uses the vector-based formula to make it algorithmically easier, which is given by half of the vector product of two sides.
5. The centroid of the faces of a 3-D element is obtained by _________
a) Area-weighted average of the sub-elements
b) Average of the sub-elements
c) Area-weighted average of the centroid of the sub-elements
d) Volume-weighted average of the centroid of the sub-elements
Answer: c
Clarification: The centroid of each of the sub-elements are first located. The weighted average of these centroids is the centroid of the whole face. Areas of the triangles are used as the weight for this average.
6. The surface area of the face of a 3-D element is a _____________
a) 3-D tensor
b) 2-D tensor
c) Scalar
d) Vector
Answer: d
Clarification: The surface area of the face of a 3-D element is a vector with the area as its magnitude and pointing in a direction. This direction decides if the face points outwards or inwards. Moreover, the area is the result of the cross product of two vectors which will again be a vector.
7. How is it identified whether a vector is pointing outwards or inwards?
a) Sign of the vector joining the element’s centroid with the face’s centroid is used
b) Sign of the surface vector is used
c) Cross product of the surface vector and the vector joining the element’s centroid with the face’s centroid
d) Dot product of the surface vector and the vector joining the element’s centroid with the face’s centroid