# Solver library

Basic solver provides interfaces to the simulation system and to units.

Currently in Dyssol, you can develop your own agglomeration solver and add it to the solver library. Please refer to Solver development for detailed information.

The solver can also be added to a unit as a parameter.

## Agglomeration solvers

Solvers are applied to calculate the birth and death rate of agglomerates according to different mathematical models. In Dyssol, 3 types of solver are available:

> - Cell average

> - Fast Fourier transformation (FFT)

> - Fixed pivot

The applied equations in all solvers are listed as follows.

\frac{\partial n(v,t)}{\partial t} = B_{agg}(n,v,t) - D_{agg}(n,v,t)

B_{agg}(n,v,t) = \frac{1}{2}\,\beta_0\,\textstyle \int\limits_{0}^{v} \beta(u,v - u)\,n(u,t)\,n(v-u,t)\,du

D_{agg}(n,v,t) = \beta_0\,n(v,t)\, \textstyle \int\limits_{0}^{\infty}\,\beta(v,u)\,n(u,t)\,du

Note

Notations:

v,u – volumes of agglomerating particles

n(v,t) – number density function

B_{agg}(n,v,t), D_{agg}(n,v,t) – birth and death rates of particles with volume v caused due to agglomeration

\beta_0 – agglomeration rate constant, dependent on operating conditions but independent from particle sizes

\beta(v,u) – the agglomeration kernel, see section Kernels.

t – time

- Cell average
- FFT
- Fixed pivot