Species transport equations

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::species_properties
	Type declaration of physical properties of species. More...

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

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.

Function Documentation

solve_species_transport()

subroutine solve_species_transport

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