# ALE method oscillating cylinder

**URL:** <https://community.freefem.org/t/ale-method-oscillating-cylinder/767>\
**Category:** General Discussion\
**Created:** [January 26, 2021, 10:25pm UTC](https://community.freefem.org/t/ale-method-oscillating-cylinder/767 "2021-01-26T22:25:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![tundo](https://avatars.discourse-cdn.com/v4/letter/t/8dc957/32.png) [@tundo](https://community.freefem.org/u/tundo)\
**Post date:** [January 26, 2021, 10:25pm UTC](https://community.freefem.org/t/ale-method-oscillating-cylinder/767/1 "2021-01-26T22:25:02Z")

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Good evening everyone,  
this is the code I wrote to study a cylinder that oscillates with an imposed motion in a direction perpendicular to the asymptotic flow. I have developed an ALE method. I put a dimensionless amplitude of oscillations of A = 0.25, a dimensionless frequency F = 1.1 (we should develop the phenomenon of the look in) and a Re = 100. I ask you if you think the code is correct, because the trends in the coefficient of lift and drag that I have seen in literature do not return. Thank you all.

ofstream Drug(“cd.txt”);  
ofstream Lift(“cl.txt”);

int n=20, nc=80, M=100;  
real Re=100, invRe=1/Re, KC=5. ,U=1, D=1, R=D/2., A=KC_D/(2_pi), F=1.1;  
real L=50_D, H=30_D;  
real K=20, S=10;  
real x0=(-1./2./pi)_sin(2_pi_0), y0=0, nu=1./Re, T=20, dt=0.01, a=1/dt, er=1e-8;  
border b1(t=-L,L){x=t;y=-H;label=1;}  
border b2(t=-H,H){x=L;y=t;label=2;}  
border b3(t=L,-L){x=t;y=H;label=1;}  
border b4(t=H,-H){x=-L;y=t;label=4;}  
border c(t=0,2_pi){x=x0+R_cos(t);y=y0+R_sin(t);label=3;}

//border b5(t=-K,K){x=t;y=-S;}  
//border b6(t=-S,S){x=K;y=t;}  
//border b7(t=K,-K){x=t; y=S;}  
//border b8(t=S,-S){x=-K; y=t;}

//border b5(t=0,1){x=-10+50_t;y=-5;}  
//border b6(t=0,1){x=40;y=-5+10_t;}  
//border b7(t=0,1){x=40-50_t;y=5;}  
//border b8(t=0,1){x=-10; y=5-10_t;}  
//border e(t=0, 2_pi){x=2_cos(t);y=2_sin(t);}  
//mesh Th=buildmesh(b1(50)+b2(50)+b3(50)+b4(n_H/L)+b5(200)+b6(100)+b7(200)+b8(100)+c(-80));  
//mesh Th=buildmesh(b1(80)+b2(80)+b3(80)+b4(80)+e(80)+c(-80));  
mesh Th=buildmesh(b1(n)+b2(n_H/L)+b3(n)+b4(n_H/L)+c(-nc));  
plot(Th, wait=1);

fespace Vh(Th,P2);  
Vh u, uu, v, vv, uold=0, vold=0,l;  
Vh a1, a2, w, s, f1=0, f2=0;  
Vh g1=uold-a1, g2=vold-a2;  
real[int] tmp(u[].n);  
fespace Ph(Th,P1);  
Ph p=0, pp;

problem MeshVelocity([a1,a2],[w,s]) //laplce eq: mesh MeshVelocity  
=int2d(Th,qforder=3)(dx(a1)_dx(w)+dy(a1)dy(w)+dx(a2)dx(s)+dy(a2)dy(s))  
+on(1,2,a1=0,a2=0)  
+on(3,a1=f1,a2=f2);_

 

_problem aleNS ([u,v,p],[uu,vv,pp],solver=UMFPACK)=  
int2d(Th,qforder=3)(a(uuu+v_vv)  
+((uold-a1)_dx(u)+(vold-a2)dy(u))uu+((uold-a1)dx(v)+(vold-a2)dy(v))vv  
-p(dx(uu)+dy(vv)) //pressione  
+invRe(dx(u)dx(uu)+dy(u)dy(uu)+dx(v)dx(vv)+dy(v)dy(vv))//termine diffusivo  
+pp(dx(u)+dy(v))+erppp)  
-int2d(Th,qforder=3)(a(uolduu+voldvv))  
//-int2d(Th,qforder=3)((dx(a1)+dy(a2))(u_uu+vvv))  
+on(3, u=a1,v=a2)  
+on(4,u=1,v=0)  
+on(1,v=0);  
//+on(b4,u=1,v=0)+on(b1,b3,v=0);

for(real t=0;t\<T;t+=dt){  
f2=-2_pi_0.25_0.16_1.1_cos(2_pi_0.16_1.1\*t);  
f1=0.;

aleNS;  
MeshVelocity;

Th=movemesh(Th,[x+dt_a1,y+dt_a2]);  
l=dx(v)-dy(u)+dx(a2)-dy(a1);  
tmp=u[]; uold=0; uold[]=tmp;  
tmp=v[]; vold=0; vold[]=tmp;  
tmp=a1[]; a1=0; a1[]=tmp;  
tmp=a2[]; a2=0; a2[]=tmp;  
tmp=g1[]; g1=0; g1[]=tmp;  
tmp=g2[]; g2=0; g2[]=tmp;  
//plot(coef=0.1,[u,v],value=1,fill=1);  
plot(coef=0.1,l,value=1,fill=1);  
//plot(coef=0.1,p,value=1,fill=1);  
fespace Mh(Th, P0);  
Mh h = hTriangle;  
cout \<\< "size of mesh = " \<\< h[].max \<\< endl;  
cout\<\< "size of mesh = " \<\< h[].min \<\<endl;

//Drug of cylinder  
real cd=int1d(Th,3,qforder=3)(-4_p_x+4_invRe_(2_dx(g1)x+(dy(g1)+dx(g2))y));  
//Lift of cylinder  
real cl=int1d(Th,3,qforder=3)(-4py+4_invRe\*((dy(g1)+dx(g2))_x+2_dy(g2)\*

Drug\<\<cd\<\<endl;  
Lift\<\<cl\<\<endl;

real i=0;  
i=i+1;  
cout\<\<i\<\<endl;  
cout\<\<t\<\<endl;  
}

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<div class="post-metadata">

**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [January 31, 2021, 2:56pm UTC](https://community.freefem.org/t/ale-method-oscillating-cylinder/767/2 "2021-01-31T14:56:21Z")

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I have test you example, but without math a formulation, I can’t help you.  
Remark: in this case I do not understand why your domain move because if you are the framework of the cylinder then just the boundary condition change and the mesh velocity.

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**Author:** ![tundo](https://avatars.discourse-cdn.com/v4/letter/t/8dc957/32.png) [@tundo](https://community.freefem.org/u/tundo)\
**Post date:** [February 4, 2021, 8:52am UTC](https://community.freefem.org/t/ale-method-oscillating-cylinder/767/3 "2021-02-04T08:52:04Z")

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Good morning,  
for the mathematical model I used a pseudo elastic problem to determine the speed of the mesh which I then inserted into the convective term of the NS equations. I made the mesh move in order to update it in each temporal step and simulate the oscillation of the cylinder. Do you think it is wrong? Thanks for the reply.