Computational Fluid Dynamics test on “Numerical Methods – Mesh Topology”.
1. Which of these is related to the flux terms?
a) Element connectivity
b) Node connectivity
c) Face connectivity
d) Vertex connectivity
Answer: c
Clarification: For faces, information about elements sharing the face is stored for computational uses. Since the flux terms completely depend upon the faces, face connectivity should be in a way that it represents flux.
2. The direction of the normal vector to a face in mesh ____________
a) is from the owner element to the neighbour element
b) is from the neighbour element to the owner element
c) is in the direction of the flux
d) is in the direction opposite to the flux
Answer: a
Clarification: The orientation of the faces is such that the normal vector to the face points from the owner element to the neighbour element. Depending on this the sign of flux term changes. Orientation does not depend on fluxes.
3. In the boundary faces, the normal vector points _____________
a) to the owner element
b) outside the domain
c) in the direction of the flux
d) in the direction opposite to the flux
Answer: b
Clarification: The boundary faces bound only one element and they do not have any neighbouring elements. So, the owner elements in the boundaries have their faces with the normal vectors pointing outside the domain.
4. Which of these points is shared by the maximum number of elements?
a) Grid point
b) Cell centre
c) Face centre
d) Vertex
Answer: d
Clarification: A vertex is shared by the most number of elements. In structured grids, a vertex point is shared by eight elements. Gridpoint can be either the cell centre or the vertex depending upon the type of discretization.
5. Vertex connectivity is important while __________
a) solving the discretized equation
b) discretizing
c) post-processing
d) pre-processing
Answer: c
Clarification: Vertex connectivity is important for post-processing especially while computing gradients. Vertex connectivity generally contains information like the elements and faces sharing that vertex.
6. Which of these establish a one-to-one relationship between two elements?
a) Face
b) Node
c) Vertex
d) Element
Answer: a
Clarification: A one-to-one relationship is given by the faces of a mesh. One face is shared by two elements. It usually contains information about the fluxes flowing between those elements.
7. Element connectivity is responsible for ___________
a) consistency of the fluxes of different elements
b) consistency of the equations formed for different elements
c) flow field variables
d) gradient of the flow field variables
Answer: b
Clarification: Element connectivity relates the local matrix to the global matrix. This ensures that the equations formed for one element are consistent with those formed for the other elements in the computational domain.
8. In a two-dimensional flow, the algebraic equation of an element relates the element with ___________
a) its face centres
b) its vertices
c) its faces
d) its neighbours
Answer: d
Clarification: Each element in a mesh has its own algebraic equation. This algebraic equation has the coefficients of the neighbouring elements too. This way, the elements are connected to their neighbours by these algebraic equations.
9. The aspect ratio of each element should be ___________
a) less than one
b) equal to one
c) around one
d) greater than one
Answer: c
Clarification: Ideally, the aspect ratio of each element should be equal to 1. But, this cannot be practically ensured. So, in real, the elements have their aspect ratio around 1. If it is large, it will lead to errors.
10. The variation of the size of a cell from an optimal cell size is its __________
a) centroid
b) structure
c) orthogonality
d) skewness
Answer: d
Clarification: The skewness of a cell is its variation from the optimal cell size. This is an apt indicator of the quality and suitability of a mesh. Large skewness leads to less accuracy.
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