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tidalFLOW.m
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function [U,Ux,Uy,U1,Um1,UN,UmN]=flowBasin(A,MANN,h,ho,dx,DH,T,periodic,kro,tidalnonlinearflow,Ubase);
BAD
%cells 10 to 19 are river boundaries
% %added may 2019 to reduce compuation. check that doesnot mes sup
% A(ho<=0)=0; %eliminate the cells in which the water depth is too small
%
%A(A==11)=1; %the river front cells are normal cells
%Uo=max(0.1,sqrt(9.8*h)*0.1);
%manning=0*A+n_manning;
A(A==22)=1; %this behaves as normal flow %but do not update A!
%consider the pond cells as A==0
A(A==3)=1; %the isoalted pond behaves as normal cell (btu different depth...) %but do not update A!
% hfriction;
% csi=hfriction.^(1/3)./manning.^2./Uo*24*3600;
% D=csi.*hfriction.^2/(dx^2);
if tidalnonlinearflow==1
Uo=(Ubase+0.2)/2;
else
Uo=1;
end
%figure;imagesc(MANN);pause
MANN(isnan(MANN))=0.1;%
csi=h.^(1/3)./MANN.^2./Uo*24*3600;
%csi=1./MANN.^2./Uo*24*3600;
%fM=1+A*0;fM(VEG==1)=1/facMann^2;
%csi(VEG==1)=csi(VEG==1)./(facMann*B(VEG==1)).^2;
%csi=A*0+45^2/Uo*24*3600;
D=csi.*h.^2/(dx^2);
G=0*h;a=find(A~=0);NN=length(a);G(a)=[1:NN];
%rhs=ones(NN,1).*min(DH,max(0,d(a)))/(T/2*3600*24); %in m/s!!!
rhs=ones(NN,1).*DH(a)/(T/2*3600*24); %in m/s!!!
[N,M] = size(G);i=[];j=[];s=[];
%boundary conditions imposed water level
a=find(A==2 | A==21);
i=[i;G(a)]; j=[j;G(a)]; s=[s;ones(size(a))];rhs(G(a))=0;%water level zero
S=0*G;
%exclude the NOLAND CELLS (A==0)
p = find(A==1 | (A>=10 & A<=19));[row col]=ind2sub(size(A),p);
for k = [N -1 1 -N]
%avoid to the the cells out of the domain (risk to make it periodic...)
%if k==m; a=find(col+1<=n);end;if k==-m;a=find(col-1>0);end;if k==-1;a=find(row-1>0);end;if k==1; a=find(row+1<=m);end;
%the translated cells
if periodic==0
[a,q]=excludeboundarycell(k,N,M,p);
elseif periodic==1;
[a,q]=periodicY(k,N,M,p); %for the long-shore
end
a=a(A(q(a))>0);%exlcude the translated cell that are NOLAND cells
DD=(D(p(a))+D(q(a)))/2;%.*(fM(p(a))+fM(q(a)))/2; %THA BEST!!!! BESTA! WITH THIS MORE STABLE
%DD=min(D(p(a)),D(q(a))); %ABSOLUTO NO!!!!
%DD=max(D(p(a)),D(q(a))); %OK
S(p(a))=S(p(a))+DD; %exit from that cell
i=[i;G(q(a))]; j=[j;G(p(a))]; s=[s;-DD]; %gain from the neigborh cell
end
%summary of the material that exits the cell
i=[i;G(p)]; j=[j;G(p)]; s=[s;S(p)];
ds2 = sparse(i,j,s);%solve the matrix inversion
p=ds2\rhs;
P=G;P(G>0)=full(p(G(G>0)));
P(A==2)=0; %need when swtinching q and p
D=D./h*dx;
%D=D*dx;
U1=0*A;Um1=0*A;UN=0*A;UmN=0*A;
p = find(A==1 | A==10 | A==2);[row col]=ind2sub(size(A),p);
for k = [N -1 1 -N]
%the translated cell
if periodic==0
[a,q]=excludeboundarycell(k,N,M,p);
elseif periodic==1;
[a,q]=periodicY(k,N,M,p); %for the long-shore
end
a=a(A(q(a))>0);%exlcude the translated cell that are NOLAND cells
%DD=(D(p(a))+D(q(a)))/2;
DD=min(D(p(a)),D(q(a)));%.*(fM(p(a))+fM(q(a)))/2; MEGLIO
if (k==1); U1(p(a))=U1(p(a))+sign(k)*(P(p(a))-P(q(a))).*DD;%./h(p(a))*dx;
elseif (k==-1); Um1(p(a))=Um1(p(a))+sign(k)*(P(p(a))-P(q(a))).*DD;%./h(p(a))*dx;
elseif (k==N); UN(p(a))=UN(p(a))+sign(k)*(P(p(a))-P(q(a))).*DD;%./h(p(a))*dx;
elseif (k==-N); UmN(p(a))=UmN(p(a))+sign(k)*(P(p(a))-P(q(a))).*DD;%./h(p(a))*dx;
end
end
Uy=max(abs(U1),abs(Um1)).*sign(U1+Um1);
Ux=max(abs(UN),abs(UmN)).*sign(UN+UmN);
U=sqrt(Ux.^2+Uy.^2);
%%%
% %%%%%%%%%%%%%%%%%
% %To deal with the boundaries of the domain
% P1=[P(:,2:end) P(:,end)];P2=[P(:,1) P(:,1:end-1) ];P3=[P(2:end,:); P(end,:)];P4=[P(1,:); P(1:end-1,:)];
% D1=[D(:,2:end) D(:,end)];D2=[D(:,1) D(:,1:end-1) ];D3=[D(2:end,:); D(end,:)];D4=[D(1,:); D(1:end-1,:)];
% A1=[A(:,2:end) A(:,end)];A2=[A(:,1) A(:,1:end-1) ];A3=[A(2:end,:); A(end,:)];A4=[A(1,:); A(1:end-1,:)];
%
% %to deal with the NOLAND cells
% pp1=P(A1==0);pp2=P(A2==0);pp3=P(A3==0);pp4=P(A4==0);
% P1(A1==0)=pp1;P2(A2==0)=pp2;P3(A3==0)=pp3;P4(A4==0)=pp4;
% pp1=D(A1==0);pp2=D(A2==0);pp3=D(A3==0);pp4=D(A4==0);
% D1(A1==0)=pp1;D2(A2==0)=pp2;D3(A3==0)=pp3;D4(A4==0)=pp4;
%
% DD1=(D+D1)/2;DD2=(D+D2)/2;DD3=(D+D3)/2;DD4=(D+D4)/2;
%
% Ux=0.5*((P-P1).*DD1 + (P2-P).*DD2);Uy=0.5*((P-P3).*DD3 + (P4-P).*DD4);
% Ux(A==2 | A==21)=2*Ux(A==2 | A==21);Uy(A==2 | A==21)=2*Uy(A==2 | A==21);
% %%%%%%%%%%%%%%%%%%