Question

The range of the relaxation factor in the pressure correction equation is ____________

(a) 0 ≤ factor < 1

(b) 0 < factor < 1

(c) 0 < factor ≤ 1

(d) 0 ≤ factor ≤ 1

The question was posed to me in my homework.

My question comes from Incompressible Flows in chapter Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

The correct answer is:

(b) 0 < factor < 1

Explanation:

In the context of solving the pressure correction equation in incompressible flows, especially when using algorithms like SIMPLE or PISO, a relaxation factor is introduced to improve the convergence of the solution.

The relaxation factor α is a parameter that controls the extent to which the pressure correction is applied during each iteration. Its value lies within the range 0 < α < 1, meaning:

• 0 < α < 1: The relaxation factor is typically chosen to be less than 1, which helps in stabilizing the solution and preventing overcorrection. A smaller factor slows down the correction, ensuring that the solution gradually converges.

• α = 1: This would imply full correction at each iteration, which can sometimes lead to instability or oscillations in the solution, especially in more complex or transient flow problems.

Thus, the relaxation factor must be greater than 0 and less than 1 to maintain a stable iterative procedure.