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upwind_2_limiter.m
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upwind_2_limiter.m
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%Spatial 2nd order upwind numerical scheme using flux limiter
%Note: for each ion the same lines of code are used. This is somewhat ugly
%as a full loop around one set can do the same. This, in a struct, is
%however very slow (10 times). Therefore it is now done by hand. Any P.better
%solution for a more compact code?
%Generate r-values for all ions, for the full column length at a single time step.
for m=1:P.nsw
if m == 1 || m ==P.nsw
P.r.Na(m,n) = 0;
P.r.K(m,n) = 0;
P.r.Ca(m,n) = 0;
P.r.Mg(m,n) = 0;
P.r.Ba(m,n) = 0;
P.r.Sr(m,n) = 0;
P.r.Cl(m,n) = 0;
P.r.S(m,n) = 0;
P.r.B(m,n) = 0;
P.r.Al(m,n) = 0;
P.r.Si(m,n) = 0;
P.r.Li(m,n) = 0;
P.r.H(m,n) = 0;
P.r.C4(m,n) = 0;
P.r.HCO3(m,n) = 0;
else
P.r.Na(m,n) = (C.Na(m+1,n) - C.Na(m,n))/(C.Na(m,n) - C.Na(m-1,n));
P.r.K(m,n) = (C.K(m+1,n) - C.K(m,n))/(C.K(m,n) - C.K(m-1,n));
P.r.Ca(m,n) = (C.Ca(m+1,n) - C.Ca(m,n))/(C.Ca(m,n) - C.Ca(m-1,n));
P.r.Mg(m,n) = (C.Mg(m+1,n) - C.Mg(m,n))/(C.Mg(m,n) - C.Mg(m-1,n));
P.r.Ba(m,n) = (C.Ba(m+1,n) - C.Ba(m,n))/(C.Ba(m,n) - C.Ba(m-1,n));
P.r.Sr(m,n) = (C.Sr(m+1,n) - C.Sr(m,n))/(C.Sr(m,n) - C.Sr(m-1,n));
P.r.Cl(m,n) = (C.Cl(m+1,n) - C.Cl(m,n))/(C.Cl(m,n) - C.Cl(m-1,n));
P.r.S(m,n) = (C.S(m+1,n) - C.S(m,n))/(C.S(m,n) - C.S(m-1,n));
P.r.B(m,n) = (C.B(m+1,n) - C.B(m,n))/(C.B(m,n) - C.B(m-1,n));
P.r.Al(m,n) = (C.Al(m+1,n) - C.Al(m,n))/(C.Al(m,n) - C.Al(m-1,n));
P.r.Si(m,n) = (C.Si(m+1,n) - C.Si(m,n))/(C.Si(m,n) - C.Si(m-1,n));
P.r.Li(m,n) = (C.Li(m+1,n) - C.Li(m,n))/(C.Li(m,n) - C.Li(m-1,n));
P.r.H(m,n) = (C.H(m+1,n) - C.H(m,n))/(C.H(m,n) - C.H(m-1,n));
P.r.C4(m,n) = (C.C4(m+1,n) - C.C4(m,n))/(C.C4(m,n) - C.C4(m-1,n));
P.r.HCO3(m,n) = (C.HCO3(m+1,n) - C.HCO3(m,n))/(C.HCO3(m,n) - C.HCO3(m-1,n));
if isnan(P.r.Na(m,n)) && C.Na(m+1,n) - C.Na(m,n) == 0; P.r.Na(m,n) = 0; elseif isnan(P.r.Na(m,n)); P.r.Na(m,n) = inf; end;
if isnan(P.r.K(m,n)) && C.K(m+1,n) - C.K(m,n) == 0; P.r.K(m,n) = 0; elseif isnan(P.r.K(m,n)); P.r.K(m,n) = inf; end;
if isnan(P.r.Ca(m,n)) && C.Ca(m+1,n) - C.Ca(m,n) == 0; P.r.Ca(m,n) = 0; elseif isnan(P.r.Ca(m,n)); P.r.Ca(m,n) = inf; end;
if isnan(P.r.Mg(m,n)) && C.Mg(m+1,n) - C.Mg(m,n) == 0; P.r.Mg(m,n) = 0; elseif isnan(P.r.Mg(m,n)); P.r.Mg(m,n) = inf; end;
if isnan(P.r.Ba(m,n)) && C.Ba(m+1,n) - C.Ba(m,n) == 0; P.r.Ba(m,n) = 0; elseif isnan(P.r.Ba(m,n)); P.r.Ba(m,n) = inf; end;
if isnan(P.r.Sr(m,n)) && C.Sr(m+1,n) - C.Sr(m,n) == 0; P.r.Sr(m,n) = 0; elseif isnan(P.r.Sr(m,n)); P.r.Sr(m,n) = inf; end;
if isnan(P.r.Cl(m,n)) && C.Cl(m+1,n) - C.Cl(m,n) == 0; P.r.Cl(m,n) = 0; elseif isnan(P.r.Cl(m,n)); P.r.Cl(m,n) = inf; end;
if isnan(P.r.S(m,n)) && C.S(m+1,n) - C.S(m,n) == 0; P.r.S(m,n) = 0; elseif isnan(P.r.S(m,n)); P.r.S(m,n) = inf; end;
if isnan(P.r.B(m,n)) && C.B(m+1,n) - C.B(m,n) == 0; P.r.B(m,n) = 0; elseif isnan(P.r.B(m,n)); P.r.B(m,n) = inf; end;
if isnan(P.r.Al(m,n)) && C.Al(m+1,n) - C.Al(m,n) == 0; P.r.Al(m,n) = 0; elseif isnan(P.r.Al(m,n)); P.r.Al(m,n) = inf; end;
if isnan(P.r.Si(m,n)) && C.Si(m+1,n) - C.Si(m,n) == 0; P.r.Si(m,n) = 0; elseif isnan(P.r.Si(m,n)); P.r.Si(m,n) = inf; end;
if isnan(P.r.Li(m,n)) && C.Li(m+1,n) - C.Li(m,n) == 0; P.r.Li(m,n) = 0; elseif isnan(P.r.Li(m,n)); P.r.Li(m,n) = inf; end;
if isnan(P.r.H(m,n)) && C.H(m+1,n) - C.H(m,n) == 0; P.r.H(m,n) = 0; elseif isnan(P.r.H(m,n)); P.r.H(m,n) = inf; end;
if isnan(P.r.C4(m,n)) && C.C4(m+1,n) - C.C4(m,n) == 0; P.r.C4(m,n) = 0; elseif isnan(P.r.C4(m,n)); P.r.C4(m,n) = inf; end;
if isnan(P.r.HCO3(m,n)) && C.HCO3(m+1,n) - C.HCO3(m,n) == 0; P.r.HCO3(m,n) = 0; elseif isnan(P.r.HCO3(m,n)); P.r.HCO3(m,n) = inf; end;
end
end
for i=1:P.nsw
switch P.Limiter
case 'sweby'
P.psi.Na(i,n) = max([0 min([P.bet*P.r.Na(i,n) 1]) min([P.r.Na(i,n) P.bet])]); %sweby
P.psi.K(i,n) = max([0 min([P.bet*P.r.K(i,n) 1]) min([P.r.K(i,n) P.bet])]); %sweby
P.psi.Ca(i,n) = max([0 min([P.bet*P.r.Ca(i,n) 1]) min([P.r.Ca(i,n) P.bet])]); %sweby
P.psi.Mg(i,n) = max([0 min([P.bet*P.r.Mg(i,n) 1]) min([P.r.Mg(i,n) P.bet])]); %sweby
P.psi.Ba(i,n) = max([0 min([P.bet*P.r.Ba(i,n) 1]) min([P.r.Ba(i,n) P.bet])]); %sweby
P.psi.Sr(i,n) = max([0 min([P.bet*P.r.Sr(i,n) 1]) min([P.r.Sr(i,n) P.bet])]); %sweby
P.psi.Cl(i,n) = max([0 min([P.bet*P.r.Cl(i,n) 1]) min([P.r.Cl(i,n) P.bet])]); %sweby
P.psi.S(i,n) = max([0 min([P.bet*P.r.S(i,n) 1]) min([P.r.S(i,n) P.bet])]); %sweby
P.psi.B(i,n) = max([0 min([P.bet*P.r.B(i,n) 1]) min([P.r.B(i,n) P.bet])]); %sweby
P.psi.Al(i,n) = max([0 min([P.bet*P.r.Al(i,n) 1]) min([P.r.Al(i,n) P.bet])]); %sweby
P.psi.Si(i,n) = max([0 min([P.bet*P.r.Si(i,n) 1]) min([P.r.Si(i,n) P.bet])]); %sweby
P.psi.Li(i,n) = max([0 min([P.bet*P.r.Li(i,n) 1]) min([P.r.Li(i,n) P.bet])]); %sweby
P.psi.H(i,n) = max([0 min([P.bet*P.r.H(i,n) 1]) min([P.r.H(i,n) P.bet])]); %sweby
P.psi.C4(i,n) = max([0 min([P.bet*P.r.C4(i,n) 1]) min([P.r.C4(i,n) P.bet])]); %sweby
P.psi.HCO3(i,n) = max([0 min([P.bet*P.r.HCO3(i,n) 1]) min([P.r.HCO3(i,n) P.bet])]); %sweby
case 'superbee'
P.psi.Na(i,n) = max([0 min([2*P.r.Na(i,n) 1]) min([P.r.Na(i,n) 2])]); %Superbee
P.psi.K(i,n) = max([0 min([2*P.r.K(i,n) 1]) min([P.r.K(i,n) 2])]); %Superbee
P.psi.Ca(i,n) = max([0 min([2*P.r.Ca(i,n) 1]) min([P.r.Ca(i,n) 2])]); %Superbee
P.psi.Mg(i,n) = max([0 min([2*P.r.Mg(i,n) 1]) min([P.r.Mg(i,n) 2])]); %Superbee
P.psi.Ba(i,n) = max([0 min([2*P.r.Ba(i,n) 1]) min([P.r.Ba(i,n) 2])]); %Superbee
P.psi.Sr(i,n) = max([0 min([2*P.r.Sr(i,n) 1]) min([P.r.Sr(i,n) 2])]); %Superbee
P.psi.Cl(i,n) = max([0 min([2*P.r.Cl(i,n) 1]) min([P.r.Cl(i,n) 2])]); %Superbee
P.psi.S(i,n) = max([0 min([2*P.r.S(i,n) 1]) min([P.r.S(i,n) 2])]); %Superbee
P.psi.B(i,n) = max([0 min([2*P.r.B(i,n) 1]) min([P.r.B(i,n) 2])]); %Superbee
P.psi.Al(i,n) = max([0 min([2*P.r.Al(i,n) 1]) min([P.r.Al(i,n) 2])]); %Superbee
P.psi.Si(i,n) = max([0 min([2*P.r.Si(i,n) 1]) min([P.r.Si(i,n) 2])]); %Superbee
P.psi.Li(i,n) = max([0 min([2*P.r.Li(i,n) 1]) min([P.r.Li(i,n) 2])]); %Superbee
P.psi.H(i,n) = max([0 min([2*P.r.H(i,n) 1]) min([P.r.H(i,n) 2])]); %Superbee
P.psi.C4(i,n) = max([0 min([2*P.r.C4(i,n) 1]) min([P.r.C4(i,n) 2])]); %Superbee
P.psi.HCO3(i,n) = max([0 min([2*P.r.HCO3(i,n) 1]) min([P.r.HCO3(i,n) 2])]); %Superbee
case 'minmod'
P.psi.Na(i,n) = max([0 min([1 P.r.Na(i,n)])]); %minmod
P.psi.K(i,n) = max([0 min([1 P.r.K(i,n)])]); %minmod
P.psi.Ca(i,n) = max([0 min([1 P.r.Ca(i,n)])]); %minmod
P.psi.Mg(i,n) = max([0 min([1 P.r.Mg(i,n)])]); %minmod
P.psi.Ba(i,n) = max([0 min([1 P.r.Ba(i,n)])]); %minmod
P.psi.Sr(i,n) = max([0 min([1 P.r.Sr(i,n)])]); %minmod
P.psi.Cl(i,n) = max([0 min([1 P.r.Cl(i,n)])]); %minmod
P.psi.S(i,n) = max([0 min([1 P.r.S(i,n)])]); %minmod
P.psi.B(i,n) = max([0 min([1 P.r.B(i,n)])]); %minmod
P.psi.Al(i,n) = max([0 min([1 P.r.Al(i,n)])]); %minmod
P.psi.Si(i,n) = max([0 min([1 P.r.Si(i,n)])]); %minmod
P.psi.Li(i,n) = max([0 min([1 P.r.Li(i,n)])]); %minmod
P.psi.H(i,n) = max([0 min([1 P.r.H(i,n)])]); %minmod
P.psi.C4(i,n) = max([0 min([1 P.r.C4(i,n)])]); %minmod
P.psi.HCO3(i,n) = max([0 min([1 P.r.HCO3(i,n)])]); %minmod
otherwise
error('No limiter defined. Check spelling.');
end
end
for i=1:P.nsw
%Second order
if i==1
%C.Na(i,n+1) = (1./F.Sw(i,n+1)) .* (F.Sw(i,n).*C.Na(i,n) - ((P.ut * P.dt) / (P.porosity * P.dx))*(1+.5*P.psi.Na(i,n)) * (C.Na(i,n)*F.fw(i,n)-C_bc.Na(1,n)*1));
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Na(i,n)-C_bc.Na(1,n));
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.K(i,n)-C_bc.K(1,n));
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Ca(i,n)-C_bc.Ca(1,n));
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Mg(i,n)-C_bc.Mg(1,n));
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Ba(i,n)-C_bc.Ba(1,n));
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Sr(i,n)-C_bc.Sr(1,n));
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Cl(i,n)-C_bc.Cl(1,n));
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.S(i,n)-C_bc.S(1,n));
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.B(i,n)-C_bc.B(1,n));
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Al(i,n)-C_bc.Al(1,n));
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Si(i,n)-C_bc.Si(1,n));
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.Li(i,n)-C_bc.Li(1,n));
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.H(i,n)-C_bc.H(1,n));
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.C4(i,n)-C_bc.C4(1,n));
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (C.HCO3(i,n)-C_bc.HCO3(1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Na(i,n)+C.Na(i,n+1))/2-C_bc.Na(1,n));
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.K(i,n)+C.K(i,n+1))/2-C_bc.K(1,n));
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Ca(i,n)+C.Ca(i,n+1))/2-C_bc.Ca(1,n));
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Mg(i,n)+C.Mg(i,n+1))/2-C_bc.Mg(1,n));
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Ba(i,n)+C.Ba(i,n+1))/2-C_bc.Ba(1,n));
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Sr(i,n)+C.Sr(i,n+1))/2-C_bc.Sr(1,n));
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Cl(i,n)+C.Cl(i,n+1))/2-C_bc.Cl(1,n));
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.S(i,n)+C.S(i,n+1))/2-C_bc.S(1,n));
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.B(i,n)+C.B(i,n+1))/2-C_bc.B(1,n));
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Al(i,n)+C.Al(i,n+1))/2-C_bc.Al(1,n));
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Si(i,n)+C.Si(i,n+1))/2-C_bc.Si(1,n));
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.Li(i,n)+C.Li(i,n+1))/2-C_bc.Li(1,n));
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.H(i,n)+C.H(i,n+1))/2-C_bc.H(1,n));
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.C4(i,n)+C.C4(i,n+1))/2-C_bc.C4(1,n));
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * ((C.HCO3(i,n)+C.HCO3(i,n+1))/2-C_bc.HCO3(1,n));
end
else
%Na,K,Ca,Mg,Ba,Sr,Cl,S,B,Al,Si,Li,H,C4,HCO3
%Na
if abs(P.psi.Na(i-1,n)) == 0
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Na(i,n)-0.5 * 0 ) * (C.Na(i,n)-C.Na(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Na(i,n)-0.5 * 0 ) * (((C.Na(i,n)-C.Na(i-1,n))+(C.Na(i,n+1)-C.Na(i-1,n+1)))/2);
end
else
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Na(i,n)-0.5 * P.psi.Na(i-1,n) / P.r.Na(i-1,n) ) * (C.Na(i,n)-C.Na(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Na(i,n+1) = C.Na(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Na(i,n)-0.5 * P.psi.Na(i-1,n) / P.r.Na(i-1,n) ) * (((C.Na(i,n)-C.Na(i-1,n))+(C.Na(i,n+1)-C.Na(i-1,n+1)))/2);
end
end
%K
if abs(P.psi.K(i-1,n)) == 0
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.K(i,n)-0.5 * 0 ) * (C.K(i,n)-C.K(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.K(i,n)-0.5 * 0 ) * (((C.K(i,n)-C.K(i-1,n))+(C.K(i,n+1)-C.K(i-1,n+1)))/2);
end
else
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.K(i,n)-0.5 * P.psi.K(i-1,n) / P.r.K(i-1,n) ) * (C.K(i,n)-C.K(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.K(i,n+1) = C.K(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.K(i,n)-0.5 * P.psi.K(i-1,n) / P.r.K(i-1,n) ) * (((C.K(i,n)-C.K(i-1,n))+(C.K(i,n+1)-C.K(i-1,n+1)))/2);
end
end
%Ca
if abs(P.psi.Ca(i-1,n)) == 0
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ca(i,n)-0.5 * 0 ) * (C.Ca(i,n)-C.Ca(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ca(i,n)-0.5 * 0 ) * (((C.Ca(i,n)-C.Ca(i-1,n))+(C.Ca(i,n+1)-C.Ca(i-1,n+1)))/2);
end
else
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ca(i,n)-0.5 * P.psi.Ca(i-1,n) / P.r.Ca(i-1,n) ) * (C.Ca(i,n)-C.Ca(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Ca(i,n+1) = C.Ca(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ca(i,n)-0.5 * P.psi.Ca(i-1,n) / P.r.Ca(i-1,n) ) * (((C.Ca(i,n)-C.Ca(i-1,n))+(C.Ca(i,n+1)-C.Ca(i-1,n+1)))/2);
end
end
%Mg
if abs(P.psi.Mg(i-1,n)) == 0
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Mg(i,n)-0.5 * 0 ) * (C.Mg(i,n)-C.Mg(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Mg(i,n)-0.5 * 0 ) * (((C.Mg(i,n)-C.Mg(i-1,n))+(C.Mg(i,n+1)-C.Mg(i-1,n+1)))/2);
end
else
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Mg(i,n)-0.5 * P.psi.Mg(i-1,n) / P.r.Mg(i-1,n) ) * (C.Mg(i,n)-C.Mg(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Mg(i,n+1) = C.Mg(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Mg(i,n)-0.5 * P.psi.Mg(i-1,n) / P.r.Mg(i-1,n) ) * (((C.Mg(i,n)-C.Mg(i-1,n))+(C.Mg(i,n+1)-C.Mg(i-1,n+1)))/2);
end
end
%Ba
if abs(P.psi.Ba(i-1,n)) == 0
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ba(i,n)-0.5 * 0 ) * (C.Ba(i,n)-C.Ba(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ba(i,n)-0.5 * 0 ) * (((C.Ba(i,n)-C.Ba(i-1,n))+(C.Ba(i,n+1)-C.Ba(i-1,n+1)))/2);
end
else
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ba(i,n)-0.5 * P.psi.Ba(i-1,n) / P.r.Ba(i-1,n) ) * (C.Ba(i,n)-C.Ba(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Ba(i,n+1) = C.Ba(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Ba(i,n)-0.5 * P.psi.Ba(i-1,n) / P.r.Ba(i-1,n) ) * (((C.Ba(i,n)-C.Ba(i-1,n))+(C.Ba(i,n+1)-C.Ba(i-1,n+1)))/2);
end
end
%Sr
if abs(P.psi.Sr(i-1,n)) == 0
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Sr(i,n)-0.5 * 0 ) * (C.Sr(i,n)-C.Sr(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Sr(i,n)-0.5 * 0 ) * (((C.Sr(i,n)-C.Sr(i-1,n))+(C.Sr(i,n+1)-C.Sr(i-1,n+1)))/2);
end
else
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Sr(i,n)-0.5 * P.psi.Sr(i-1,n) / P.r.Sr(i-1,n) ) * (C.Sr(i,n)-C.Sr(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Sr(i,n+1) = C.Sr(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Sr(i,n)-0.5 * P.psi.Sr(i-1,n) / P.r.Sr(i-1,n) ) * (((C.Sr(i,n)-C.Sr(i-1,n))+(C.Sr(i,n+1)-C.Sr(i-1,n+1)))/2);
end
end
%Cl
if abs(P.psi.Cl(i-1,n)) == 0
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Cl(i,n)-0.5 * 0 ) * (C.Cl(i,n)-C.Cl(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Cl(i,n)-0.5 * 0 ) * (((C.Cl(i,n)-C.Cl(i-1,n))+(C.Cl(i,n+1)-C.Cl(i-1,n+1)))/2);
end
else
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Cl(i,n)-0.5 * P.psi.Cl(i-1,n) / P.r.Cl(i-1,n) ) * (C.Cl(i,n)-C.Cl(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Cl(i,n+1) = C.Cl(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Cl(i,n)-0.5 * P.psi.Cl(i-1,n) / P.r.Cl(i-1,n) ) * (((C.Cl(i,n)-C.Cl(i-1,n))+(C.Cl(i,n+1)-C.Cl(i-1,n+1)))/2);
end
end
%S
if abs(P.psi.S(i-1,n)) == 0
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.S(i,n)-0.5 * 0 ) * (C.S(i,n)-C.S(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.S(i,n)-0.5 * 0 ) * (((C.S(i,n)-C.S(i-1,n))+(C.S(i,n+1)-C.S(i-1,n+1)))/2);
end
else
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.S(i,n)-0.5 * P.psi.S(i-1,n) / P.r.S(i-1,n) ) * (C.S(i,n)-C.S(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.S(i,n+1) = C.S(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.S(i,n)-0.5 * P.psi.S(i-1,n) / P.r.S(i-1,n) ) * (((C.S(i,n)-C.S(i-1,n))+(C.S(i,n+1)-C.S(i-1,n+1)))/2);
end
end
%B
if abs(P.psi.B(i-1,n)) == 0
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.B(i,n)-0.5 * 0 ) * (C.B(i,n)-C.B(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.B(i,n)-0.5 * 0 ) * (((C.B(i,n)-C.B(i-1,n))+(C.B(i,n+1)-C.B(i-1,n+1)))/2);
end
else
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.B(i,n)-0.5 * P.psi.B(i-1,n) / P.r.B(i-1,n) ) * (C.B(i,n)-C.B(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.B(i,n+1) = C.B(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.B(i,n)-0.5 * P.psi.B(i-1,n) / P.r.B(i-1,n) ) * (((C.B(i,n)-C.B(i-1,n))+(C.B(i,n+1)-C.B(i-1,n+1)))/2);
end
end
%Al
if abs(P.psi.Al(i-1,n)) == 0
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Al(i,n)-0.5 * 0 ) * (C.Al(i,n)-C.Al(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Al(i,n)-0.5 * 0 ) * (((C.Al(i,n)-C.Al(i-1,n))+(C.Al(i,n+1)-C.Al(i-1,n+1)))/2);
end
else
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Al(i,n)-0.5 * P.psi.Al(i-1,n) / P.r.Al(i-1,n) ) * (C.Al(i,n)-C.Al(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Al(i,n+1) = C.Al(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Al(i,n)-0.5 * P.psi.Al(i-1,n) / P.r.Al(i-1,n) ) * (((C.Al(i,n)-C.Al(i-1,n))+(C.Al(i,n+1)-C.Al(i-1,n+1)))/2);
end
end
%Si
if abs(P.psi.Si(i-1,n)) == 0
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Si(i,n)-0.5 * 0 ) * (C.Si(i,n)-C.Si(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Si(i,n)-0.5 * 0 ) * (((C.Si(i,n)-C.Si(i-1,n))+(C.Si(i,n+1)-C.Si(i-1,n+1)))/2);
end
else
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Si(i,n)-0.5 * P.psi.Si(i-1,n) / P.r.Si(i-1,n) ) * (C.Si(i,n)-C.Si(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Si(i,n+1) = C.Si(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Si(i,n)-0.5 * P.psi.Si(i-1,n) / P.r.Si(i-1,n) ) * (((C.Si(i,n)-C.Si(i-1,n))+(C.Si(i,n+1)-C.Si(i-1,n+1)))/2);
end
end
%Li
if abs(P.psi.Li(i-1,n)) == 0
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Li(i,n)-0.5 * 0 ) * (C.Li(i,n)-C.Li(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Li(i,n)-0.5 * 0 ) * (((C.Li(i,n)-C.Li(i-1,n))+(C.Li(i,n+1)-C.Li(i-1,n+1)))/2);
end
else
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Li(i,n)-0.5 * P.psi.Li(i-1,n) / P.r.Li(i-1,n) ) * (C.Li(i,n)-C.Li(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.Li(i,n+1) = C.Li(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.Li(i,n)-0.5 * P.psi.Li(i-1,n) / P.r.Li(i-1,n) ) * (((C.Li(i,n)-C.Li(i-1,n))+(C.Li(i,n+1)-C.Li(i-1,n+1)))/2);
end
end
%H
if abs(P.psi.H(i-1,n)) == 0
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.H(i,n)-0.5 * 0 ) * (C.H(i,n)-C.H(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.H(i,n)-0.5 * 0 ) * (((C.H(i,n)-C.H(i-1,n))+(C.H(i,n+1)-C.H(i-1,n+1)))/2);
end
else
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.H(i,n)-0.5 * P.psi.H(i-1,n) / P.r.H(i-1,n) ) * (C.H(i,n)-C.H(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.H(i,n+1) = C.H(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.H(i,n)-0.5 * P.psi.H(i-1,n) / P.r.H(i-1,n) ) * (((C.H(i,n)-C.H(i-1,n))+(C.H(i,n+1)-C.H(i-1,n+1)))/2);
end
end
%C4
if abs(P.psi.C4(i-1,n)) == 0
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.C4(i,n)-0.5 * 0 ) * (C.C4(i,n)-C.C4(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.C4(i,n)-0.5 * 0 ) * (((C.C4(i,n)-C.C4(i-1,n))+(C.C4(i,n+1)-C.C4(i-1,n+1)))/2);
end
else
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.C4(i,n)-0.5 * P.psi.C4(i-1,n) / P.r.C4(i-1,n) ) * (C.C4(i,n)-C.C4(i-1,n));
%Is Euler modified to be used?
if P.EulerOrder==2
C.C4(i,n+1) = C.C4(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.C4(i,n)-0.5 * P.psi.C4(i-1,n) / P.r.C4(i-1,n) ) * (((C.C4(i,n)-C.C4(i-1,n))+(C.C4(i,n+1)-C.C4(i-1,n+1)))/2);
end
end
%HCO3
% if abs(P.psi.HCO3(i-1,n)) == 0
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.HCO3(i,n)-0.5 * 0 ) * (C.HCO3(i,n)-C.HCO3(i-1,n));
% %Is Euler modified to be used?
% if P.EulerOrder==2
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.HCO3(i,n)-0.5 * 0 ) * (((C.HCO3(i,n)-C.HCO3(i-1,n))+(C.HCO3(i,n+1)-C.HCO3(i-1,n+1)))/2);
% end
% else
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.HCO3(i,n)-0.5 * P.psi.HCO3(i-1,n) / P.r.HCO3(i-1,n) ) * (C.HCO3(i,n)-C.HCO3(i-1,n));
% %Is Euler modified to be used?
% if P.EulerOrder==2
% C.HCO3(i,n+1) = C.HCO3(i,n) - ((P.ut * P.dt * F.fw(i,n)) / (P.porosity * P.dx * F.Sw(i,n))) * (1+.5*P.psi.HCO3(i,n)-0.5 * P.psi.HCO3(i-1,n) / P.r.HCO3(i-1,n) ) * (((C.HCO3(i,n)-C.HCO3(i-1,n))+(C.HCO3(i,n+1)-C.HCO3(i-1,n+1)))/2);
% end
% end
end
end