# VDW diffusion interface model

**URL:** <https://community.freefem.org/t/vdw-diffusion-interface-model/3064>\
**Category:** General Discussion\
**Created:** [March 25, 2024, 8:26am UTC](https://community.freefem.org/t/vdw-diffusion-interface-model/3064 "2024-03-25T08:26:52Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![111-1111](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/111-1111/32/2175_2.png) [@111-1111](https://community.freefem.org/u/111-1111)\
**Post date:** [March 25, 2024, 8:26am UTC](https://community.freefem.org/t/vdw-diffusion-interface-model/3064/1 "2024-03-25T08:26:52Z")

</div>

Hello developer, I am a beginner about this software.I encountered difficulties in solving the following problem  
 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/f/f60c3026b94b1391b35e1d98e0c81785116dc9f2.png)  
The code is as follows

func u0=0;  
func v0=0;  
real rhol=1.46,rhog=0.58,delta=0.05;  
func rho0=0.5\*(rhol+rhog)-0.5\*(rhol-rhog)\*tanh((((x-1)^2+(y-1)^2)^(1/2)-0.4)/delta);

real T=10,dt=0.1,Re=100,We=1000;  
real sigma=0.95;  
mesh Th = square(30,30,[2_x,2_y]);  
fespace Uh(Th,P2,periodic=[[1,x],[3,x],[2,y],[4,y]]); Uh u=u0,v=v0,rho=rho0,uu,vv,rhot,uold,vold,rhoold;  
fespace Ph(Th,P1,periodic=[[1,x],[3,x],[2,y],[4,y]]);Ph p,pp;  
problem cons(rho,rhot)=  
int2d(Th)(rho_rhot/dt)-int2d(Th)((convect([uold,vold],-dt,rhoold)rhot/dt))+int2d(Th)(rhodx(uold)rhot+rhody(vold)rhot);  
problem vdw(p,pp)=  
int2d(Th)((p-8rho_sigma/(3-rho))+3_rho^2)pp)  
problem NSK([u,v],[uu,vv])=  
int2d(Th)(rho(u_uu/dt+v_vv/dt))-int2d(Th)(rho_((convect([uold,vold],-dt,uold)\*uu+convect([uold,vold],-dt,vold)_vv)/dt))  
+int2d(Th)((1/Re)_(((4/3)\*dx(u)-(2/3)\*dy(v))\*dx(uu)+(dx(u)+dy(v))\*dy(uu)+(dx(v)+dy(u))\*dx(vv)+((4/3)\*dy(v)-(2/3)\*dx(u))\*dy(vv))  
-int2d(Th)((1/We)_rho_(dx(dx(dx(rho))+dy(dy(rho)))\*uu+dy(dx(dx(rho))+dy(dy(rho)))\*vv))  
+int2d(Th)(dx(p)\*uu+dy(p)\*vv);

for(real t=0;t\<T;t+=dt)  
{  
uold=u;  
vold=v;  
rhoold=rho;  
cons;  
vdw;  
NSK;  
plot([u,v,rho],wait=false,value=true);  
}  
The error is as follows  
14 : problem vdw(p,pp)=  
15 : int2d(Th)((p-8_rho_sigma/(3-rho)) error operator - \<10LinearCombI7MGauche4C\_F0E\>,   
List of choices  
( : , )  
( \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> : \<14Matrice\_CreuseISt7complexIdEE\>, \<14Matrice\_CreuseISt7complexIdEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> : \<14Matrice\_CreuseISt7complexIdEE\>, \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\>, \<14Matrice\_CreuseISt7complexIdEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\>, \<NSt7\_\_cxx114listISt5tupleIJSt7complexIdEP13VirtualMatrixIiS3\_EbEESaIS7\_EEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> : \<14Matrice\_CreuseIdE\>, \<14Matrice\_CreuseIdE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> : \<14Matrice\_CreuseIdE\>, \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\>, \<14Matrice\_CreuseIdE\> )  
( \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> : \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\>, \<NSt7\_\_cxx114listISt5tupleIJdP13VirtualMatrixIidEbEESaIS5\_EEE\> )  
( \<10FormLinear\> : \<10FormLinear\> )  
( \<12FormBilinear\> : \<12FormBilinear\> )  
( \<6C\_args\> : \<6C\_args\>, \<10FormLinear\> )  
( \<6C\_args\> : \<6C\_args\>, \<12FormBilinear\> )  
( \<10LinearCombI7MGauche4C\_F0E\> : \<10LinearCombI7MGauche4C\_F0E\>, \<10LinearCombI7MGauche4C\_F0E\> )  
( \<10LinearCombI6MDroit4C\_F0E\> : \<10LinearCombI6MDroit4C\_F0E\>, \<10LinearCombI6MDroit4C\_F0E\> )  
( \<10LinearCombISt4pairI7MGauche6MDroitE4C\_F0E\> : \<10LinearCombISt4pairI7MGauche6MDroitE4C\_F0E\>, \<10LinearCombISt4pairI7MGauche6MDroitE4C\_F0E\> )  
( \<10LinearCombI7MGauche4C\_F0E\> : \<10LinearCombI7MGauche4C\_F0E\> )  
( \<10LinearCombI6MDroit4C\_F0E\> : \<10LinearCombI6MDroit4C\_F0E\> )  
( \<10LinearCombISt4pairI7MGauche6MDroitE4C\_F0E\> : \<10LinearCombISt4pairI7MGauche6MDroitE4C\_F0E\> )  
( : , )  
( \<4C\_F0\> : \<12TransE\_Array\>, \<12TransE\_Array\> )  
( \<4C\_F0\> : \<7E\_Array\>, \<12TransE\_Array\> )  
( \<4C\_F0\> : \<7E\_Array\>, \<7E\_Array\> )  
( \<4C\_F0\> : \<12TransE\_Array\>, \<7E\_Array\> )  
( \<12Add\_Mulc\_KN\_ISt7complexIdEE\> : \<8Mulc\_KN\_ISt7complexIdEE\>, \<3KN\_ISt7complexIdEE\> )  
( \<12Add\_Mulc\_KN\_ISt7complexIdEE\> : \<3KN\_ISt7complexIdEE\>, \<8Mulc\_KN\_ISt7complexIdEE\> )  
( \<12Add\_Mulc\_KN\_ISt7complexIdEE\> : \<8Mulc\_KN\_ISt7complexIdEE\>, \<8Mulc\_KN\_ISt7complexIdEE\> )  
( \<8Mulc\_KN\_ISt7complexIdEE\> : \<3KN\_ISt7complexIdEE\> )  
( \<7Sub\_KN\_ISt7complexIdEE\> : \<3KN\_ISt7complexIdEE\>, \<3KN\_ISt7complexIdEE\> )  
( \<12Add\_Mulc\_KN\_IdE\> : \<8Mulc\_KN\_IdE\>, \<3KN\_IdE\> )  
( \<12Add\_Mulc\_KN\_IdE\> : \<3KN\_IdE\>, \<8Mulc\_KN\_IdE\> )  
( \<12Add\_Mulc\_KN\_IdE\> : \<8Mulc\_KN\_IdE\>, \<8Mulc\_KN\_IdE\> )  
( \<8Mulc\_KN\_IdE\> : \<3KN\_IdE\> )  
( \<7Sub\_KN\_IdE\> : \<3KN\_IdE\>, \<3KN\_IdE\> )  
( \<12Add\_Mulc\_KN\_IlE\> : \<8Mulc\_KN\_IlE\>, \<3KN\_IlE\> )  
( \<12Add\_Mulc\_KN\_IlE\> : \<3KN\_IlE\>, \<8Mulc\_KN\_IlE\> )  
( \<12Add\_Mulc\_KN\_IlE\> : \<8Mulc\_KN\_IlE\>, \<8Mulc\_KN\_IlE\> )  
( \<8Mulc\_KN\_IlE\> : \<3KN\_IlE\> )  
( \<7Sub\_KN\_IlE\> : \<3KN\_IlE\>, \<3KN\_IlE\> )  
( : )  
( : )  
( : )  
( : **, )  
( : , )  
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( : , )  
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( : , )**

 

Error line number 15, in file vdw1.edp, before token )

current line = 15  
Compile error :  
line number :15, )  
error Compile error :  
line number :15, )  
code = 1 mpirank: 0  
How should I modify it