TracerConservationEquation

function [UserVar,c1,lambda]=TracerConservationEquation(UserVar,CtrlVar,MUA,dt,c0,u0,v0,a0,u1,v1,a1,kappa,BCsTracer)

Solves the linear tracer conservation equation for the tracer c on the form:

$\frac{\partial c}{\partial t} + \nabla (c \mathbf{v} )- \nabla \cdot (\kappa \nabla c) = a$

The natural boundary condition is

$\nabla c \cdot \hat{n} = 0$

This equation is an advection-diffusion equation

It gives c1 at the end of the time step, i.e. time=time+dt

c is solved implicitly using the theta method ie:

$\Delta c / \Delta t = \Theta d c_1/dt + (1-\Theta) d c_0/dt$

with theta=CtrlVar.theta; and SUPG with tauSUPG=CalcSUPGtau(CtrlVar,MUA,u0,v0,dt);

Boundary conditions: The BCs are entered as h conditions. So define the relevant BCs as you were defining BCs for h and these will be used for c.

[UserVar,kv,rh]=TracerConservationEquationAssembly(UserVar,CtrlVar,MUA,dt,c0,u0,v0,a0,u1,v1,a1,kappa);

% Now apply BCs.
% Note: When defining tracer boundary conditions, use the thickness fields (h) in the BCs structure
% for that purpose.
%
MLC=BCs2MLC(CtrlVar,MUA,BCsTracer);
L=MLC.hL ; Lrhs=MLC.hRhs ; lambda=Lrhs*0;



[c1,lambda]=solveKApe(kv,L,rh,Lrhs,c0,lambda,CtrlVar);
c1=full(c1);

end