Question

If the discretization error is the ratio of grid spacing to time step, then for the system to be consistent, which of these is correct?

(a) the ratio should be equal to one

(b) the ratio should be equal to zero

(c) the ratio should tend to zero

(d) the ratio should be equal to negative one

I have been asked this question during an online interview.

This interesting question is from Discretization Aspects in chapter Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

Right answer is (c) the ratio should tend to zero

To explain I would say: We know that consistency is satisfied if discretization error is zero. When discretization error is the ratio of grid spacing to time step, then actually the ratio should be zero. But, this is not practically possible as the grid spacing cannot be zero. So, grid spacing and time step must be reduced in a way that the ratio tends to zero.