A study on convergence criteria for a simple-based finite-volume algorithm

Two commonly used quantities for deciding numerical iteration convergence of elliptic and parabolic flow fields are assessed. Three 2-D test case problems, which are representative of many problems of momentum and/or heat transport, are used. The numerical model employed is the pressure-based finite-volume algorithm SIMPLE to solve the steady, incompressible-flow Navier-Stokes equations in full elliptic form. Considerable insight is gained by comparing the variation of the two quantities with the true mean relative error for the velocity components, the local mass imbalance, and the temperature. It is concluded that, except when using low underrelaxation factors, use of the maximum local value of the relative change, over two consecutive iterations, of the dependent variable is somewhat more appealing than the nondimensionalized sum of the local residual magnitudes.