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Implementation of the Navier - Stokes Equation using the PDE interface
Posted 10 apr 2017, 12:30 GMT-4 Computational Fluid Dynamics (CFD), Modeling Tools & Definitions 0 Replies
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I'm trying to solve the Navier - Stokes Equations by using the PDE module.
To do it, i set two PDEs:
1) In the first PDE, representing the Continuity Equation, I have imposed as dependent variable the pressure, p, and, considering the "General Form Interface", i set:
f=-d(rho,t);
Tx=rho*u;
Ty=rho*v;
Tz=rho*w;
with rho=1[kg/m^3].
2) In the second PDE, representing the Momentun Conservation Equations, I have imposed as dependent variables the velocity of the fluid in the x, y and z directions and, considering the "General Form", I set:
Txx=-(-p+mu*(ux+ux)-2/3*mu*(ux+vy+wz));
Txy=-(mu*(uy+vx));
Txz=-(mu*(uz+wx));
Tyx=-(mu*(vx+uy));
Tyy=-(-p+mu*(uy+uy)-2/3*mu*(ux+vy+wz));
Tyz=-(mu*(vz+wy));
Tzx=-(mu*(wx+uz));
Tzy=-(mu*(wy+vz));
Tzz=-(-p+mu*(wz+wz)-2/3*mu*(ux+vy+wz));
fx=-d(rho*u,t)-u*(d(rho*u,x)+d(rho*v,y)+d(rho*w,z))-rho*gx;
fy=-d(rho*v,t)-v*(d(rho*u,x)+d(rho*v,y)+d(rho*w,z))-rho*gy;
fz=-d(rho*w,t)-w*(d(rho*u,x)+d(rho*v,y)+d(rho*w,z))-rho*gz;
As boundary conditions, i have set:
- Inlet: u=0 m/s, v=1 m/s, w=0 m/s;
- No slip: u=0 m/s, v=0 m/s, w=0 m/s;
- Outlet: T=0 (no flux);
I have created the study and unified the Solutors for pressure and for the three speed components but the model doesn't converge. Can someone help me? I can send te model for e-mail if required. Thank you very much.
Hello Federico Giai Pron
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