version 0.6.0
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Species transport equations

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

## Namespaces

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.

## Classes

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

## Functions

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

• variables.f90 defines scalar variables associated to the resolution of this equation (time step, schemes, etc.)
• fields.f90 defines field arrays of this equation (species concentration, diffusion coefficient, etc.)
• solve.f90 does the discretization of the equation and call the linear system solver to compute the solution. It is called in the time loop.

## ◆ solve_species_transport()

 subroutine solve_species_transport

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