Question

Let x, y be the coordinates in the physical domain and ξ, η  be the coordinates in the computational domain. Which of these is correct for adaptive grids?

(a) \(\frac{\partial\xi}{\partial x}≠1 \)

(b) \(\frac{\partial\xi}{\partial x}≠0 \)

(c) \(\frac{\partial\xi}{\partial t}≠0 \)

(d) \(\frac{\partial\xi}{\partial t}≠1 \)

This question was posed to me in an online interview.

This intriguing question comes from Discretization Aspects topic in section Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

Correct choice is (c) \(\frac{\partial\xi}{\partial t}≠0 \)

To explain I would say: Adaptive grids change with varying time. So, the time rate of change of coordinates will never be equal to zero. This is given by\(\frac{\partial\xi}{\partial x}≠0 \). They may or may not vary from the physical coordinates.