Question

Which of these values is used to find the normalized residual?

(a) The minimum of all the residuals

(b) The maximum of all the residuals

(c) The sum of all the residuals

(d) The product of all the residuals

The question was asked at a job interview.

Question is taken from Relaxation topic in division Discretization of the Source Term & Relaxation of Computational Fluid Dynamics

Answer 1

In Computational Fluid Dynamics (CFD), the normalized residual is used to assess the convergence of a numerical solution. The normalized residual is typically calculated using the maximum of all the residuals within the solution domain, as it provides a measure of the largest remaining error. This helps determine how close the solution is to satisfying the governing equations across the entire domain.

Let’s analyze the options:

• (a) The minimum of all the residuals: The minimum residual does not represent the convergence status of the solution effectively, as it might be small even if other residuals are large.

• (b) The maximum of all the residuals: This is correct. The maximum residual is often used to normalize the residuals, giving a clear indication of the largest remaining error.

• (c) The sum of all the residuals: Summing the residuals can provide a cumulative measure but does not effectively indicate where the largest error lies.

• (d) The product of all the residuals: The product is not typically used, as it can be disproportionately affected by any zero residuals.

Correct Answer: (b) The maximum of all the residuals