This article provides more information on the use of relaxation parameters available in the Flow Solver. |
What are the Relaxation Parameters in the Flow Solver Settings Used for?
The flow solver has many properties that can be changed to influence how the solver will calculate a solution. This article will describe the relaxation parameters under the flow solver properties and how to use them as a possible tool for solving networks that don't converge. These relaxation parameters can be found under the "Relaxation Parameters" section in the flow solver properties, as seen in Figure 1. If you are not able to see them, you may need to select "All" for the level of detail shown under the flow solver properties.
What are Relaxation Parameters?
To understand how relaxation parameters are used, we will briefly look at how Flownex's solver works. During the solving process, Flownex's solver uses the user's inputs as initial variables and tries to solve momentum and energy equations. If the solutions do not converge, the variables are adjusted with correction factors to obtain new variables used to solve the equations again until convergence is achieved or for the number of iterations specified. Relaxation parameters are used to calculate the new subsequent variable value for the next iteration during the solving process. The relaxation parameters are a measure of how much of the correction factor or newly solved variable value will be used to calculate the subsequent variable value. For example, the new pressure value is equal to the pressure from the previous iteration summed with the relaxation parameter times the newly calculated pressure correction, as seen in Figure 2. The same formula is applied to the mass flow rate.
Another example is how the fluid density and enthalpy are calculated. These variables are calculated as the difference between one and the relaxation parameter times the variable of the previous iteration summed with the newly calculated variable times the relaxation parameter, as seen in Figure 3.
Thus by reducing the relaxation parameters, the solver uses smaller variable increments during iterations to obtain a converged solution. Thus, smaller relaxation parameters will result in slower converging and more stable solutions. Small relaxation parameters should be used with care, and generally, values less than 0.1 should be avoided.
A detailed description of the relaxation parameters can be found in the Flownex SE User Manual under section 3.3.2.2 Solver Settings. The user manual also describes how the different relaxation parameters can be used to stabilise the solution for specific scenarios.