Question

Which of these is correct for extra viscous terms in cylindrical coordinates?

(a) The implicit and explicit treatments do not depend on the sign of the coefficients

(b) It is treated implicitly when its contribution to the coefficient of the central node is negative

(c) It is treated implicitly when its contribution to the coefficient of the central node is positive

(d) It is treated explicitly when its contribution to the coefficient of the central node is positive

I got this question by my school principal while I was bunking the class.

The question is from Incompressible Flows topic in division Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

The correct answer is:

(b) It is treated implicitly when its contribution to the coefficient of the central node is negative

Explanation:

In the context of solving the Navier-Stokes equations for incompressible flows using finite difference methods in cylindrical coordinates, viscous terms need to be handled carefully, especially when they appear in the discretization. The treatment of these terms depends on the sign of the coefficients associated with the central node.

• Implicit treatment is used when the contribution of the viscous term to the central node coefficient is negative. This approach is more stable, especially for flows with high viscosity or in cases where the solution requires more numerical stability.

• Explicit treatment is generally used when the coefficient is positive, as it leads to a faster, though sometimes less stable, solution.