2.2.5. Species Advection Solver (ADVECT module)

2.2.5.1. Governing equations

Tdyn solves the transient Species Advection Equations in a given fluid domain \(\Omega_F\) for a number of different species, and time interval \((0, t)\):

(2.379)\[\begin{aligned} & \frac{\partial φ}{\partial t} + \left( \boldsymbol{u} \cdot \nabla \right) φ + \left( c \cdot φ \cdot g \cdot \nabla \right) φ - \nabla \cdot \left( \kappa_P \nabla φ \right) = q_F & \text{in } \Omega_F \times (0,t) \end{aligned}\]

where \(φ = φ (x, t)\) denotes the concentration of species field, \(c\) the decantation coefficient, \(k_P\) the total diffusion coefficient (including turbulent effects) and \(q_F\) a volumetric source. The above equations need to be combined with the standard boundary conditions.

As in the previous examples, the spatial discretization of the Species Advection equations has been done by means of the finite element method, while for the time discretization implicit first and second order schemes have been implemented. Problems with dominating convection are stabilized by the Finite Calculus (FIC) method, presented above.