Question

Which of these statements is correct regarding the Adams-Moulton scheme used on the non-uniform grids?

(a) The current central coefficient for the finite difference and the finite volume schemes are the same

(b) The current central coefficient for the uniform and the non-uniform grid is the same

(c) The variation in time-steps does not result in any change

(d) There is no variation in the values when the grid is uniform

The question was posed to me in quiz.

I'd like to ask this question from Approaches for Non-uniform Time Steps in chapter Transient Flows of Computational Fluid Dynamics

Answer 1

The correct option is (a) The current central coefficient for the finite difference and the finite volume schemes are the same

For explanation I would say: For the finite difference approach,

\(a_c=(\frac{1}{\Delta t}+\frac{1}{\Delta t+\Delta t^o})\rho_C V_C\)

For the finite volume approach, the central coefficient is

FluxC=\((\frac{1}{\Delta t}+\frac{1}{\Delta t+\Delta t^o})\rho_C V_C\)

These two are the same irrespective of the approach.