Question

Which of these statements is correct about a small relaxation factor?

(a) Computation is unstable but convergence is fast

(b) Computation is stable and convergence is fast

(c) Computation is stable but convergence is slow

(d) Computation is unstable and convergence is slow

The question was asked during an interview for a job.

Origin of the question is Incompressible Flows in division Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

Right answer is (c) Computation is stable but convergence is slow

To elaborate: When the under-relaxation factor is small, the speed of computation is very slow. Because, to get the solutions converged, a large number of iterations are needed. But, this small under-relaxation factor will lead to a stable computation.