## 8.14. Convergence Control for Particle Transport

Within the particle transport model, the total flow of the particle phase is modeled by tracking individual particles from their injection point until they escape the domain or some integration limit criterion is met. The fluid affects the particle and conversely, there is a counteracting influence of the particle on the fluid flow. This effect is termed coupling between the phases. Particle source terms are generated for each particle as they are tracked through the flow. The sources are applied in the control volume that the particle is in during the time step.

Depending on the flow being solved, particles may introduce very large source terms to the hydrodynamic equations. In reacting flows, large source terms may be generated in the mass, component mass fraction, and energy equations. In heavily laden flows, viscous drag may introduce large source terms in the momentum equations. In some cases, these source terms may have a destabilizing influence on the convergence of the hydrodynamic equations, resulting in oscillations, or in severe cases, divergence.

A possibility to minimize the oscillations is to under-relax the particle source terms more strongly (that is, to decrease the values of the following CCL parameters from their defaults of 1.0 to a smaller value):

Source Term | CCL Parameter
--- | ---
Momentum | `Velocity Under-Relaxation Factor`
Energy | `Energy Under-Relaxation Factor`
Mass | `Mass Under-Relaxation Factor`

The effects of the sources on the continuous phase are often linearizable, because drag depends upon the fluid velocity, and so on. The linear coefficient is calculated as the derivative of the source with respect to the relevant fluid variable (for example, dS/dVelF for momentum). Sometimes, it is useful for convergence to multiply this linear coefficient by a factor (<10) using the expert parameter: `pt linear src coef multiplier`.

In a rapidly changing fluids solution, you may want to increase the iteration interval from its default value of 5, updating tracks and sources less often, so that the flow has a chance to relax between successive calls to the particle solver.

The particle source terms acting on the fluid phase are proportional to the `Particle Number Rate` (that is, the number of physical particles that a computational particle represents). The convergence of a simulation can be improved if a sufficiently large number of particles are tracked.

In addition to the already mentioned steps, it can be helpful to start a particle transport simulation with less than the full particle mass flow rate, and gradually increase the mass flow rate using a ramping function.

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