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eig_scaling.m
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eig_scaling.m
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addpath('functions/')
% eigenvalues analysis
clc, clear all, close all
% Setup
xi = 0.5;
eta = 0.5;
Ulid = 1;
beta = sqrt(5.0);
Revec = [1, 100, 400, 1000];
%Revec = [2, 10, 25, 50, 100, 200, 400, 800, 1000, 2000, 5000];
Nvec = [8, 16, 24, 32];
Nmax = max(Nvec); %max Nx
nBndmax = 4*Nmax; %max boundary points in grid
Nlambda_max = 3*((Nmax-1)^2); %max number of eigenvalues
LAMBDA = zeros(length(Revec),length(Nvec),Nlambda_max);
LDT = zeros(length(Revec),length(Nvec),Nlambda_max);
NLAMBDA = zeros(length(Revec),length(Nvec));
for r = 1:length(Revec)
Re = Revec(r)
for n = 1:length(Nvec)
Nx = Nvec(n)
Ny = Nvec(n);
% %Choosing max values for velocities
% load(sprintf('../data/Re%i_Nx%i_Ny%i.mat',Re,Nx,Ny),...
% 'U','V')
% close all
% Umax = max(max(U));
% Vmax = max(max(V));
Umax = Ulid;
Vmax = 0;
[Rsmall,Rbig,idxBnd,X,Y] = SpatialOperator(Nx, Ny, xi, eta,Umax,Vmax,Re);
lambda = eig(full(Rsmall));
% storage eigenvalues
nlambda = length(lambda); %must be 3*(Nx-1)^2
NLAMBDA(r,n) = nlambda;
LAMBDA(r,n,1:length(lambda)) =lambda;
end
end
RL = real(LAMBDA);
IL = imag(LAMBDA);
maxRL = max(abs(RL),[],3);
maxIL = max(abs(IL),[],3);
% analisys of max eigen
%% Figure 1 .- maxRL scaling with Re
fig1 = figure(1); clf
subplot(1,1,1)
clear str_list
for n=1:length(Nvec)
loglog(Revec,maxRL(:,n),'.','Markersize',10)
if(n==1), hold on, end
str_list{n} = sprintf('$N_x =%i$',Nvec(n));
end
%auxiliar lines
loglog(Revec,500*Revec.^-1,'--k')
str_list{n+1}='$\mathcal{O}(R_e^{-1})$';
% loglog([Nvec 256],[Nvec 256].^-4,'-.k')
% str_list{r+2}='$\mathcal{O}(N_x^{-4})$';
% xlim([0 300])
% use latex legends and labels, set fontsize/name
legend(str_list,...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',14,...
'FontName','Computer Modern Roman',...
'Location','NorthWest');
% legend boxoff % if not outside plot?
set(gca,'FontSize',14)
xlabel('$R_e$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
ylabel('$max(Re(\lambda))$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
%print(fig1,'-depsc',sprintf('../Figs4Henrik/fig_scal_real_lambda_Rbig_Re'))
% Figure 2 .- maxIL scaling with Re
fig2 = figure(2); clf
subplot(1,1,1)
clear str_list
for n=1:length(Nvec)
loglog(Revec(1:end),maxIL(1:end,n),'.','Markersize',10)
if(n==1), hold on, end
str_list{n} = sprintf('$N_x =%i$',Nvec(n));
end
%auxiliar lines
loglog(Revec,50*Revec,'--k')
str_list{n+1}='$\mathcal{O}(Re)$';
axis([1 2000 0 10^5])
% loglog([Nvec 256],[Nvec 256].^-4,'-.k')
% str_list{r+2}='$\mathcal{O}(N_x^{-4})$';
% xlim([0 300])
% use latex legends and labels, set fontsize/name
legend(str_list,...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',14,...
'FontName','Computer Modern Roman',...
'Location','SouthWest');
% legend boxoff % if not outside plot?
set(gca,'FontSize',18)
xlabel('$R_e$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
ylabel('$max(Im(\lambda))$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
%print(fig2,'-depsc',sprintf('../Figs4Henrik/fig_scal_Imag_lambda_Rbig_Re'))
%% Figure 1 .- maxRL scaling with Nx
fig3 = figure(3); clf
subplot(1,1,1)
clear str_list
for r=1:length(Revec)
loglog(Nvec,maxRL(r,:)','.','Markersize',15)
if(r==1), hold on, end
str_list{r} = sprintf('$Re =%i$',Revec(r));
end
%auxiliar lines
loglog(Nvec,Nvec.^4,'--k')
str_list{r+1}='$\mathcal{O}(N_x^{4})$';
% loglog([Nvec 256],[Nvec 256].^-4,'-.k')
% str_list{r+2}='$\mathcal{O}(N_x^{-4})$';
% xlim([0 300])
% use latex legends and labels, set fontsize/name
legend(str_list,...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Computer Modern Roman',...
'Location','NorthWest');
% legend boxoff % if not outside plot?
set(gca,'FontSize',18)
xlabel('$N_x$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
ylabel('$max(Re(\lambda))$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
% print(fig3,'-depsc',sprintf('../Figs4Henrik/fig_scal_real_lambda_Rbig_Nx'))
%% Figure 4 .- maxIL scaling with Nx
fig4 = figure(4); clf
subplot(1,1,1)
clear str_list
for r=1:length(Revec)
if (r~=3)
loglog(Nvec,maxIL(r,:)','.','Markersize',15)
else
loglog(Nvec,maxIL(r,:)','o','Markersize',12)
end
if(r==1), hold on, end
str_list{r} = sprintf('$Re =%i$',Revec(r));
end
%auxiliar lines
% loglog(Nvec,Nvec,'--k')
% str_list{r+1}='$\mathcal{O}(N_x)$';
loglog(Nvec,5*Nvec.^2,'-.k')
str_list{r+1}='$\mathcal{O}(N_x^{2})$';
% xlim([0 300])
% use latex legends and labels, set fontsize/name
legend(str_list,...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Computer Modern Roman',...
'Location','NorthEast');
% legend boxoff % if not outside plot?
set(gca,'FontSize',18)
xlabel('$N_x$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
ylabel('$max(Im(\lambda))$',...
'FontUnits','points',...
'interpreter','latex',...
'FontSize',18,...
'FontName','Times')
% print(fig4,'-depsc',sprintf('../Figs4Henrik/fig_scal_imag_lambda_Rbig_Nx'))