Question

For a system to be bounded, the coefficients of the nodes should ___________

(a) have the same sign

(b) be the same

(c) be different everywhere

(d) have different signs everywhere

This question was posed to me in homework.

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

Answer 1

Correct option is (a) have the same sign

For explanation: All the coefficients of the discretized form of the governing equations should have the same sign for the system to be bounded. In most of the cases, the signs should be all positive. This means that an increase in the flow variable at one node increases the variables at the neighbouring nodes too.