version 0.6.0
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Species transport equations

It prepares and solves the species transport (or advection/diffusion) equations. More...


module  fields_species_transport
 Contains the field arrays associated to the species transport equation.
module  variables_species_transport
 Declaration of scalar variables associated to species transport equations.


type  type_species_properties::t_species_properties
 Type declaration of physical properties of species. More...


subroutine solve_species_transport ()
 This routine solves the species Transport (advection/diffusion) equations.

Detailed Description

A system of species transport equation can be solved. For \( 1<i<n_{species} \), it writes:

\[ \omega_i \left( \frac {\alpha \mathbf{C_i}^{n+1} + \beta \mathbf{C_i}^n + \gamma \mathbf{C_i}^{n-1}} {\Delta t} + \mathbf{u^{n+1}} \cdot \nabla \tilde{C_i} \right) = \nabla \cdot \left( \lambda \nabla C_i^{n+1} \right) \]

where values of \( \alpha, \beta, \gamma \) helps to switch from Euler time discretization scheme of order 1 to the 2nd order backward differential one:

\( \alpha = 1, \beta = -1, \gamma = 0 \) for the Euler scheme

\( \alpha = \frac {3} {2}, \beta = -2, \gamma = \frac {1} {2} \) for 2nd order BDF

As regards the advection term, velocity at time \( t^{n+1} \) is know since the Navier-Stokes equations are solved before. This term can be treated explicitly ( \( \tilde{C_i}=C_i^{n} \)) or implicitly ( \( \tilde{C_i}=C_i^{n+1} \))

Description of the directory

Function Documentation

◆ solve_species_transport()

subroutine solve_species_transport

The generic advection/diffusion equation is used to solve this equation.