AcuSolve Convergence Criteria

The convergence of the solution provides insight into the accuracy of solving the discretized equation set for the specific application. It reflects the imbalance of terms in the governing equations at each iteration.

As a general rule, lower residuals indicate a smaller error resulting from imbalances in the equation terms.

At each time step, AcuSolve determines convergence by comparing the residual ratio and the solution ratio to the convergence tolerance. This convergence check is performed for each equation in the problem, using the residual and solution increment ratios. These ratios are computed individually for solution fields such as pressure, velocity and temperature.

The residual ratio serves as a global measure of how well the solution aligns with the equations being solved. It calculates the relative imbalance between the left and right-hand sides of the equation. On the other hand, the solution ratio provides a global measure of the magnitude of changes in the solution at each node as the solution progresses from one step to the next. Both the residual ratio and solution ratio are normalized using appropriate values. The normalization factor is computed separately for each stagger and is recalculated at each time step.

By default, with a convergence tolerance of 0.001, the residual ratio must be below 0.001 for pressure, velocity, temperature, species, and radiation, and below 0.01 for eddy-viscosity or other turbulent quantities. The solution ratio must be below 0.01 for pressure, velocity, temperature, species, and radiation, and below 0.1 for eddy-viscosity or other turbulent quantities. If these criteria are met during the first pass through the equation set for the time step, the run is considered converged. The convergence tolerance can be adjusted by modifying the CONVERGENCE_CHECK_PARAMETERS in the input deck, which determines the relationship between the convergence check and the specified convergence tolerance. The Standard setting means the value must be below the specified convergence tolerance, Looser By 10 allows the value to be up to 10 times larger than the convergence tolerance, and Tighter By 10 requires the value to be less than one-tenth of the convergence tolerance.

While the default convergence criteria are suitable for many applications, it is important to monitor the impact of convergence on the solution for the specific application of interest. For steady-state simulations, this involves monitoring the desired solution quantity as the simulation approaches further convergence. For transient applications, it is necessary to evaluate convergence at each time step to understand its overall impact on the transient behavior.