Question

Which of these schemes guarantee boundedness?

(a) Central difference schemes.

(b) Forward difference schemes

(c) High-resolution schemes

(d) First order schemes

This question was posed to me in semester exam.

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

Answer 1

Right option is (d) First order schemes

The explanation is: Irrespective of coarse or fine grids first order schemes always guarantee boundedness without any overshoots or undershoots. So, while choosing a coarse grid, it is better to use the first order schemes to get rid of errors.