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Base_code_projet_NS_Time_v3.m
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Base_code_projet_NS_Time_v3.m
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% resoltion of the steady state navier stocke equation
%boundary condition
clear all; %close all;
X_domain=[0 1];
Y_domain=[0 0.5];
rho=1;
mu=0.1;
gx=0;
gy=0;
vx_in=10;
vx_out=1;
nbpoint_immersed=1000;
radius=0.02;
center=[0.2 0.25];
X=[];
randfactor=0.0 ;
%cercles
for i=1:nbpoint_immersed
X(i,1)=1*radius*cos((i-1)*2*pi/(nbpoint_immersed))+center(1);
X(i,2)=1*radius*sin((i-1)*2*pi/(nbpoint_immersed))+center(2)+rand()*randfactor-randfactor/2;
end
% for i=1:nbpoint_immersed
%
% X2(i,1)=1.01*radius*cos((i-1)*2*pi/(nbpoint_immersed))+center(1);
% X2(i,2)=1.01*radius*sin((i-1)*2*pi/(nbpoint_immersed))+center(2)+rand()*randfactor-randfactor/2;
% end
%
%
%
% for i=1:nbpoint_immersed
%
% X3(i,1)=1.01*radius*cos((i-1)*2*pi/(nbpoint_immersed))+center(1)+1;
% X3(i,2)=1.01*radius*sin((i-1)*2*pi/(nbpoint_immersed))+center(2)+rand()*randfactor-randfactor/2;
% end
% % theta=-pi/16
% X=X*[cos(theta) -sin(theta); sin(theta) cos(theta)]
% theta=10;
% rot=[cos(theta*pi/180) -sin(theta*pi/180); sin(theta*pi/180) cos(theta*pi/180)];
% load('Aero_profil/CH10_43_13');
% X_top=interp1(profil_top(:,1),profil_top(:,2),linspace(0,1,nbpoint_immersed),'pchip');
% X_bottom=interp1(profil_bottom(:,1),profil_bottom(:,2),linspace(0,1,nbpoint_immersed),'pchip');
% X_eval=linspace(0,1,nbpoint_immersed);
% top_profil_points=[X_eval' X_top'];
% bottom_profil_points=[X_eval(2:length(X_bottom-1))' X_bottom(2:length(X_bottom-1))'];
% X=[top_profil_points ; flip(bottom_profil_points)]*rot*radius+center;
% X=flip(X);
%%points must be distributed counter clockwise
renold_number=vx_in*rho*2*radius/mu;
disp('the reynolds number for that simulation is :')
disp(renold_number)
initial_Raffienement=6 ;
initial_immersed_refinement=1;
nb_refinement=1;
mesh_size_suggestion=radius*renold_number^(-3/4);
mesh_order_suggestion=log2(renold_number^(3/4));
load_mesh=0
load_mesh_file='mesh_circle_27540_elipse_0_05_0_03_c_015_015';
load_mesh_file=['Meshs/' load_mesh_file];
if load_mesh==1
load(load_mesh_file)
else
disp('mesh initialisation...')
mesh=cells_define(X_domain(1),X_domain(2),Y_domain(1),Y_domain(2),initial_Raffienement);
disp('mesh initialisation complete')
disp('mesh zones refinement...')
% mesh=raffine_zone(mesh,[0.0 1 0.1 0.4]);
% mesh=raffine_zone(mesh,[0.0 0.7 0.13 0.37]);
% mesh=raffine_zone(mesh,[0.0 0.5 0.16 0.34]);
% mesh=raffine_zone(mesh,[0.08 0.13 0.18 0.32]);
% mesh=raffine_zone(mesh,[0.1 0.13 0.2 0.3]);
% mesh=raffine_zone(mesh,[0.15 0.35 0.20 0.3]);
% mesh=raffine_zone(mesh,[0.28 0.3 0.23 0.245]);
% mesh=raffine_zone(mesh,[0.28 0.3 0.23 0.245]);
% mesh=raffine_zone(mesh,[0.28 0.3 0.23 0.245]);
% mesh=raffine_zone(mesh,[0.28 0.3 0.23 0.245]);
disp('mesh zones refinement complete')
disp('mesh refinement arrond immersed boundary...')
% mesh=raffine_immersed(mesh,initial_immersed_refinement,12,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,10,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,8,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,6,X);
% mesh=raffine_zone(mesh,[0.297 0.299 0.232 0.234]);
% mesh=raffine_zone(mesh,[0.297 0.299 0.232 0.234]);
% mesh=raffine_zone(mesh,[0.298 0.29855 0.2326 0.2328]);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,2,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,2,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,2,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,2,X);
% mesh=raffine_immersed(mesh,initial_immersed_refinement,2,X);
disp('mesh refinement arrond immersed boundary complete')
disp('update mesh connection...')
mesh=update_neighbors_v(mesh);
disp('update mesh connection complete')
end
% X=[]
%re=60 cd cercle =1.13 mesh order =8 mesh order =7 cd =1.38
% 40 =ok 200 reponse osiclle
% min(10/renold_number,1);
relaxation=1;
figure(1);
figure(2);
figure(3);
% figure(4);
% figure(5);
for j=1:nb_refinement
error=1;
iter=1;
disp('define immersed boundary value...')
cells_sum=eval_immersed_boundary_sum_in_cells_NS(mesh,X,1);
cells_sum_uy=eval_immersed_boundary_sum_in_cells_NS(mesh,X,2);
disp('define immersed boundary value complet')
disp('define initial solution...')
U_x=ones(length(mesh.points),1)*vx_in;
U_y=ones(length(mesh.points),1)*0;
for i = 1:length(mesh.points)
if isempty(find(mesh.connect(cells_sum.index,:)==i))==0
% if norm(mesh.points(i,:)-center)<radius*2
U_x(i)=0;
U_y(i)=0;
end
end
P=zeros(length(mesh.points),1)*1;
Solution=[U_x; U_y; P];
disp('define initial solution complete')
A_Sparse_index=[];
A_Sparse_index_dx=[];
A_Sparse_index_dy=[];
A_Sparse_index_L=[];
disp('define momentum matrix...')
parfor i=1:length(mesh.points)*2
if i<=length(mesh.points)
mesh_position=i;
else
mesh_position=i-length(mesh.points);
end
a_p=-get_stancil_dx(mesh,mesh_position,2);
a_p2=-get_stancil_dy(mesh,mesh_position,2);
a_p3=mu/rho*get_stancil_L_v2(mesh,mesh_position,2);
if i<=length(mesh.points)
a_p=[a_p zeros(1,length(mesh.points))];
a_p2=[a_p2 zeros(1,length(mesh.points))];
a_p3=[a_p3 zeros(1,length(mesh.points))];
else
a_p=[zeros(1,length(mesh.points)) a_p];
a_p2=[zeros(1,length(mesh.points)) a_p2];
a_p3=[zeros(1,length(mesh.points)) a_p3];
end
A_p=Solution(mesh_position)*a_p+Solution(mesh_position+length(mesh.points))*a_p2+a_p3
A_Sparse_index_dx=[A_Sparse_index_dx ;sparsematrix(a_p,i)];
A_Sparse_index_dy=[A_Sparse_index_dy ;sparsematrix(a_p2,i)];
A_Sparse_index_L=[A_Sparse_index_L ;sparsematrix(a_p3,i)];
A_Sparse_index=[A_Sparse_index;sparsematrix(A_p,i)];
end
disp('define momentum matrix complete')
disp('define pressure matrix...')
C_Sparse_index=[];
for i=1:length(mesh.points)*2
if i<=length(mesh.points)
mesh_position=i;
else
mesh_position=i-length(mesh.points);
end
a_p=zeros(1,length(mesh.points));
if i<=length(mesh.points)
a_p=get_stancil_dx_cross(mesh,mesh_position,2)/rho+get_stancil_L_v2(mesh,mesh_position,2)*0.00001;
else
a_p=get_stancil_dy_cross(mesh,mesh_position,2)/rho+get_stancil_L_v2(mesh,mesh_position,2)*0.00001;
end
% a_p=[zeros(1,length(mesh.points)*2) a_p];
C_Sparse_index=[C_Sparse_index ; sparsematrix(a_p,i)];
end
disp('define pressure matrix complete')
P_Sparse_index=C_Sparse_index;
C_Sparse_index=[];
disp('define pressure matrix conservation matrix...')
parfor i=1:length(mesh.points)
a_p1=get_stancil_dx(mesh,i,2);
a_p2=get_stancil_dy(mesh,i,2);
a_p=[a_p1 a_p2];
C_Sparse_index=[C_Sparse_index ; sparsematrix(a_p,i)];
end
disp('define pressure matrix conservation matrix complete')
%
% if isempty(C_Sparse_index)
% else
% P_Sparse_index=[C_Sparse_index(:,2) C_Sparse_index(:,1) C_Sparse_index(:,3)];
% end
B_immersed_ux=[];
B_immersed_uy=[];
D_Sparse_index=[];
disp('define immersed boundary condition...')
parfor i=1:length(cells_sum.boundary)
a_p=zeros(1,length(mesh.points));
a_p=get_lagrange_multiplier_stancil_weak_sum(mesh,cells_sum.index(i),X,cells_sum);
B_immersed_ux=[B_immersed_ux ; cells_sum.sum(i)];
B_immersed_uy=[B_immersed_uy ; cells_sum_uy.sum(i)];
a_p2=[zeros(1,length(mesh.points)) a_p];
D_Sparse_index=[D_Sparse_index ;sparsematrix(a_p,i)];
D_Sparse_index=[D_Sparse_index ;sparsematrix(a_p2,i+length(cells_sum.boundary))];
end
disp('define immersed boundary condition complete')
B=zeros(length(mesh.points)*3,1);
for i=1:length(mesh.points)
B(i)=0;
end
disp('define hanging node constraint...')
hanging_rhs=[];
%%hanging nods
parfor i=1:length(mesh.points)
if mesh.hanging(i)==true & mesh.points(i,1)~=X_domain(1) & mesh.points(i,1)~=X_domain(2)& mesh.points(i,2)~=Y_domain(1)& mesh.points(i,2)~=Y_domain(2)
hanging_rhs=[hanging_rhs ;0] ; % hanging ux
hanging_rhs=[hanging_rhs ;0] ;% hangign uy
hanging_rhs=[hanging_rhs ;0];% hangign p
end
end
H_Sparse_index=[];
l=0;
for i=1:length(mesh.points)
if mesh.hanging(i)==true & mesh.points(i,1)~=X_domain(1) & mesh.points(i,1)~=X_domain(2)& mesh.points(i,2)~=Y_domain(1)& mesh.points(i,2)~=Y_domain(2)
a_p=get_stancil_hanging(mesh,i);
l=l+1;
a_p2=[zeros(1,length(a_p)),a_p];
H_Sparse_index=[H_Sparse_index ; sparsematrix(a_p,l+2*length(cells_sum.boundary))];
l=l+1;
H_Sparse_index=[H_Sparse_index ; sparsematrix(a_p2,l+2*length(cells_sum.boundary))];
l=l+1;
a_p3=[zeros(1,length(a_p)*2),a_p];
H_Sparse_index=[H_Sparse_index ; sparsematrix(a_p3,l+2*length(cells_sum.boundary))];
end
end
disp('define hanging node constraint complete')
%boundary condition
Boundary_for_time_position=[]
boundary=[];
disp('define boundary condition...')
for i=1:length(mesh.points)
if mesh.points(i,1)==X_domain(1) & (mesh.points(i,2)==Y_domain(1) | mesh.points(i,2)==Y_domain(2))
boundary=[boundary; 0]; %speed value X
Boundary_for_time_position=[Boundary_for_time_position length(boundary)];
boundary=[boundary; 0]; %speed value Y
% boundary=[boundary; vx_in];
% elseif norm(mesh.points(i,:)-center)<0.02 %& mesh.points(i,1)>=X_domain(2)/4 & mesh.points(i,1)<=X_domain(2)*3/4
% boundary=[boundary; 0]; %speed value X
% boundary=[boundary; 0]; %speed value Y
% elseif mesh.points(i,1)==X_domain(2)
% boundary=[boundary; vx_in] %speed value X
% boundary=[boundary; 0] %speed value Y
elseif mesh.points(i,2)==Y_domain(1)
boundary=[boundary; 0]; %speed value X
Boundary_for_time_position=[Boundary_for_time_position length(boundary)];
boundary=[boundary; 0]; %speed value Y
elseif mesh.points(i,2)==Y_domain(2)
boundary=[boundary; 0]; %speed value X
Boundary_for_time_position=[Boundary_for_time_position length(boundary)];
boundary=[boundary; 0]; %speed value Y
elseif mesh.points(i,1)==X_domain(1)
% boundary=[boundary; vx_in]; %speed value X
% Boundary_for_time_position=[Boundary_for_time_position length(boundary)];
% % boundary=[boundary; (-(mesh.points(i,2)/0.5)^2+mesh.points(i,2)/0.5)*vx_in*6]; %speed value X
% boundary=[boundary; 0]; %speed value Y
boundary=[boundary; vx_in]; %speed value P
elseif mesh.points(i,1)==X_domain(2)
% boundary=[boundary; vx_in]; %speed value X
% boundary=[boundary; 0]; %speed value Y
boundary=[boundary; 0]; %speed value P
end
end
E_Sparse_index=[];
k=0;
for i=1:length(mesh.points)
a_p=zeros(1,2*length(mesh.points));
a_p2=zeros(1,2*length(mesh.points));
if mesh.points(i,1)==X_domain(1) & (mesh.points(i,2)==Y_domain(1) | mesh.points(i,2)==Y_domain(2))
a_p(1,i)=1; %speed value X
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
a_p2(1,i+length(mesh.points))=1; %speed value Y;
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
% a_p=zeros(1,3*length(mesh.points));
% a_p(1,i+length(mesh.points)*2)=1; %speed value Y
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+3*length(mesh.points)+2*length(cells_sum.boundary))];
%
% elseif norm(mesh.points(i,:)-center)<0.02% & mesh.points(i,1)>=X_domain(2)/4 & mesh.points(i,1)<=X_domain(2)*3/4
% a_p(1,i)=1; %speed value X
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
% a_p2(1,i+length(mesh.points))=1; %speed value Y
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
%
% % elseif mesh.points(i,1)==X_domain(2)
% a_p(1,i)=1; %speed value X
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+3*length(mesh.points)+2*length(cells_sum.boundary))];
% a_p2(1,i+length(mesh.points))=1; %speed value Y
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+3*length(mesh.points)+2*length(cells_sum.boundary))];
elseif mesh.points(i,2)==Y_domain(1)
a_p(1,i)=1; %speed value X
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
a_p2(1,i+length(mesh.points))=1; %speed value Y
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
elseif mesh.points(i,2)==Y_domain(2)
a_p(1,i)=1; %speed value X
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
a_p2(1,i+length(mesh.points))=1; %speed value Y
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
elseif mesh.points(i,1)==X_domain(1)
% a_p(1,i)=1; %speed value X
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
% a_p2(1,i+length(mesh.points))=1; %speed value Y
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
a_p=zeros(1,3*length(mesh.points));
a_p(1,i+length(mesh.points)*2)=1; %speed value Y
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
elseif mesh.points(i,1)==X_domain(2)
% a_p(1,i)=1; %speed value X
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
% a_p2(1,i+length(mesh.points))=1; %speed value Y
% k=k+1;
% E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p2,l+k+2*length(cells_sum.boundary))];
a_p=zeros(1,3*length(mesh.points));
a_p(1,i+length(mesh.points)*2)=1; %speed value Y
k=k+1;
E_Sparse_index=[E_Sparse_index ; sparsematrix(a_p,l+k+2*length(cells_sum.boundary))];
end
end
disp('define boundary condition complete')
disp('assembling matrix from sub matrix...')
A_Sparse_m_dx=sparse(A_Sparse_index_dx(:,1),A_Sparse_index_dx(:,2),A_Sparse_index_dx(:,3));
A_Sparse_m_dy=sparse(A_Sparse_index_dy(:,1),A_Sparse_index_dy(:,2),A_Sparse_index_dy(:,3));
A_sparse_matrix_index=[A_Sparse_index ];
A_sparse_matrix=sparse(A_sparse_matrix_index(:,1),A_sparse_matrix_index(:,2),A_sparse_matrix_index(:,3));
Constraint_sparse_matrix_index=[D_Sparse_index;E_Sparse_index;H_Sparse_index];
Constraint_sparse_matrix=sparse(Constraint_sparse_matrix_index(:,1),Constraint_sparse_matrix_index(:,2),Constraint_sparse_matrix_index(:,3),l+k+2*length(cells_sum.boundary),3*length(mesh.points));
Constraint_sparse_conservation=sparse(C_Sparse_index(:,1),C_Sparse_index(:,2),C_Sparse_index(:,3),1*length(mesh.points),2*length(mesh.points));
Constraint_sparse_pressure=sparse(P_Sparse_index(:,1),P_Sparse_index(:,2),P_Sparse_index(:,3),2*length(mesh.points),length(mesh.points));
A_1=[A_sparse_matrix Constraint_sparse_pressure; Constraint_sparse_conservation sparse(length(mesh.points),length(mesh.points))];
A_Sparse_global=[A_1 Constraint_sparse_matrix' ; Constraint_sparse_matrix sparse(l+k+2*length(cells_sum.boundary),l+k+2*length(cells_sum.boundary))];
disp('assembling matrix from sub matrix complete')
if iter==1
Solution=[Solution ; zeros(length(cells_sum.boundary)*2,1); zeros(k,1); zeros(l,1)];
end
%
% load('Solution')
% Solution(1:length(mesh.points)*3)=S2.Solution(1:length(mesh.points)*3)
time_sol=Solution;
mindt=0.01;
relative_tol=0.001;
max_time_step_modification=0.1;
dt=mindt;
t=0;
tmax=2
Boundary=[X_domain(1) Y_domain(1) Y_domain(2)];
I=speye(length(mesh.points)*2);
% back_euler_M=(I-A_Sparse_global*dt);
if isempty(A_Sparse_index_L)
A_Sparse_m_L=sparse(length(mesh.points)*2);
else
A_Sparse_m_L=sparse(A_Sparse_index_L(:,1),A_Sparse_index_L(:,2),A_Sparse_index_L(:,3));
end
B=[zeros(length(mesh.points),1);B_immersed_ux;B_immersed_uy ;hanging_rhs ;boundary];
Boundary_time_offset=length(B)-length(boundary);
nb_zeros=l+k+2*length(cells_sum.boundary);
disp('Simulation will run for ')
disp(tmax)
disp('seconds')
disp('solving the equation in time...')
disp('time step being solve...')
disp(0)
while t<tmax
U_x=Solution(1:length(mesh.points));
U_y=Solution(length(mesh.points)+1:length(mesh.points)*2);
P=Solution(length(mesh.points)*2+1:length(mesh.points)*3);
% U_x_a=avreage_whit_neighbors(mesh,U_x);
% U_y_a=avreage_whit_neighbors(mesh,U_y);
% Pa=avreage_whit_neighbors(mesh,P);
% Solution(1:length(mesh.points))=U_x_a;
% Solution(length(mesh.points)+1:length(mesh.points)*2)=U_y_a;
% Solution(length(mesh.points)*2+1:length(mesh.points)*3)=Pa;
speed=sqrt(U_x.^2+U_y.^2);
U_x_u=U_x./sqrt(U_x.^2+U_y.^2);
U_y_u=U_y./sqrt(U_x.^2+U_y.^2);
figure(1)
quiver(mesh.points(:,1),mesh.points(:,2),U_x,U_y,'color',[1 0 1]);
hold on
if isempty(X)==0
plot(X(:,1),X(:,2),'.r');
end
trisurf(mesh.connect_active,mesh.points(:,1),mesh.points(:,2),P);
hold off
pause(0.0001)
% %
V_inlet=1
% U_dx_sparse_m=sparse(A_Sparse_index_dx(:,1),A_Sparse_index_dx(:,2),A_Sparse_index_dx(:,3));
% U_dy_sparse_m=sparse(A_Sparse_index_dy(:,1),A_Sparse_index_dy(:,2),A_Sparse_index_dy(:,3));
% U=[U_x;U_y];
% %%%%%% a valider
% %%%%%% %%%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
% dU_dx=U_dx_sparse_m*U;
% dU_dy=U_dy_sparse_m*U;
% dux_dy=dU_dy(1:length(mesh.points));
% duy_dx=dU_dx(length(mesh.points)+1:length(mesh.points)*2);
%
% [F_v_x, F_v_y]=force_on_boundary_viscosity(mesh,dux_dy,duy_dx,mu,X);
% [F_p_x, F_p_y]=force_on_boundary_pressure(mesh,P,X);
%
% CD(iter)=(F_v_x+F_p_x)*2/(V_inlet^2*radius*rho);
% CL(iter)=(F_v_y+F_p_y)*2/(V_inlet^2*radius*rho);
reynolds(iter)=V_inlet*radius*2*rho/mu;
%
% figure(3)
% loglog(reynolds,CD)
% hold on
% loglog(reynolds,CL)
% hold off
% B(Boundary_time_offset+Boundary_for_time_position)=V_inlet;
disp('Reynolds value: ')
disp(reynolds(iter))
RHS=[Solution(1:2*length(mesh.points))/dt; B];
Solution=A_Sparse_global\RHS;
Solution(isnan(Solution))=0;
Solution(isinf(Solution))=0;
time_sol=[time_sol Solution];
t=t+dt;
I2=I/dt;
A_Sparse_global=update_matrix_NS(U_x,U_y,mesh,A_Sparse_index_dx,A_Sparse_index_dy,A_Sparse_m_L,Constraint_sparse_pressure,Constraint_sparse_conservation,Constraint_sparse_matrix,nb_zeros,I2);
iter=iter+1;
disp('time step being solve...')
disp(t)
end
if(j<nb_refinement)
mesh=raffine(mesh,speed,0.0,0,cells_sum.index);
end
mesh=update_neighbors_v(mesh);
% relaxation=relaxation
end