53 + Interview Questions in Diffusion Problem in Computational Fluid Dynamics Page 2 InterviewSolution

51.	The face-centred stencil is second-order _________(a) always(b) only when the centroid of the face and the line connecting the two cells meet(c) only when the centroid of the face and the line connecting the two cells do not meet(d) neverThis question was posed to me in an online interview.My question is based upon Diffusion Problem in chapter Diffusion Problem of Computational Fluid Dynamics
Answer» RIGHT option is (B) only when the centroid of the face and the line connecting the TWO CELLS meet Explanation: The face-centred stencil is second-order accurate when the centroid of the face is the same as the point of intersection of the face and the line connecting the two cells. This happens when the centroid and the line connecting the two cells meet.

52.	In the vertex-based stencil, the flow variable at the face centroid is computed as ___________(a) the mean of the values at the vertices defining the surface(b) the mean of the values at the cell centres(c) the mean of the values at the vertices of the cells(d) the mean of the values at the centroids of the neighbouring facesThe question was asked in an online quiz.My doubt is from Diffusion Problem in division Diffusion Problem of Computational Fluid Dynamics
Answer» Correct option is (a) the mean of the values at the VERTICES defining the surface Explanation: In the ENLARGED STENCIL, the value Φf is CALCULATED as the mean of the values at the vertices defining the surface. Mathematically representing it, Φf=\(\frac{\phi_{N1}+\phi_{n2}}{2}\).

53.	The area in the western face of a 2-D steady-state diffusion stencil (uniform) is _______________(a) grid size in the x-direction(b) grid size in the y-direction(c) product of the grid sizes in the x and y-directions(d) ratio of the grid sizes in the x and y-directionsThis question was addressed to me in an online interview.Question is taken from FVM for Multi-dimensional Steady State Diffusion in portion Diffusion Problem of Computational Fluid Dynamics
Answer» RIGHT choice is (b) grid SIZE in the y-DIRECTION To elaborate: In the one-dimensional CASE, the area is taken to be unity. In the two-dimensional case, the area is the grid size in the PERPENDICULAR direction multiplied by unity. So, for area Ae=Aw=Δy and An=As=Δx.

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