| Author | Message | |||
     John Michopoulos (johnm) Junior Member Username: johnm Post Number: 3 Registered: 10-2004 |
Is there anywhere a .pde example for fluid-structure interaction or multiple interacting domains with different PDEs/fields on each domain? Thanks greatly! | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 257 Registered: 06-2003 |
We don't have such an example. Maybe if you pose a problem, we can create one. | |||
| John Michopoulos (johnm) Member Username: johnm Post Number: 4 Registered: 10-2004 |
Here's an attempt to pose a simple one: Scenario: A flexible flat and long cantilever beam is mounted on the bottom of a container filled with water. Option 1: Find the deflection response (and stresses inside the beam) as a consequence of water disturbance or flow. Option 2: Find the disturbance of the water (distributions of u,v,w,p) as the beam vibrates because of remotely induced body forces varying in time sinusoidaly. We have 3 major issues to take care within the mechanics of flexPDE: 1. Two disjoint sets of PDEs applied on two disjoint domains: The Navier Stokes system of PDEs (5) governs the water and the Elasticity equations (3) govern the beam (although the last one could be converted to a lower dimensional system). 2. A moving boundary between water and beam material. 3. Conservation of momentum and energy has to be maintained on the interface of the two media at all times.... If this sounds something fightable/resonable I can provide the PDEs and geometry details in a .pde script If I knew it was doable and I am not limited by flexPDE then I would propably start with something like C:\Program Files\FlexPDE4\Samples\time_dependent\stress\vibrate.pde and modify it to fit in the scenario. Thanks immensely! | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 258 Registered: 06-2003 |
We cannot at this time explicitly move the boundary between the media, but on the assumption that these motions are small, it would seem feasible to convert the displacement of the beam into accelerations of the water (and vice versa) without actually moving the boundary. Other than this, the problem seems tractable, so lets pursue it. | |||
| souli (livermore) New member Username: livermore Post Number: 2 Registered: 04-2005 |
Hi, I have classical incompressible fluid flow in a channel, with the following BC: 1) prescribed velocity at inflow. 2) Zero pressure at outflow. A semi-implicit method is used to solve the fluid problem, implicit pressure with appropraite BC, and explicit velocity. If the channel is not a rigid wall, but a deformable structure. The nodes of the fluid mesh and the the structure are merged ( common nodes). What are the BC to apply for the pressure at the fluid structure interface ? Thank you very much | |||
| John Michopoulos (johnm) Member Username: johnm Post Number: 5 Registered: 10-2004 |
Well, I am still trying to formulate a coupled fluid structure interaction problem like the one you describe, aand with Robert's help and did not have time to finish it. In case you want to pursue it before I release my example here's the strategy I am following: Instead of solving Navier-Stokes PDEs in the fluid, solve: the system of 3 fields: 1. ALE formulation of N-S in terms of a fluid state vector W (with components comprised by the 5 field vars that are in the classical N-S) PDE, applied on the fluid mesh. 2. Elastic equilibrioum equations for the structure (in your case the channel) on the structural mesh 3. Assign pseudo elastic material properties on the fluid mesh with properties determined from the conservation of momentum and energy across the common fluid-structure meshes. So the boundary conditions between fluid and structure are implicitely determined for the elastic part since it s like having a two phase structure with stiff inclusion (your channel and my wing) inside a much more compliant medium (your fluid, my air). We have tried this with custom codes for aeroelastic problems and works beutifully but encoding in flexPDE appears trickier than I was originally thinking. Hope this helps a bit | |||
| gcb (gcb) New member Username: gcb Post Number: 1 Registered: 12-2008 |
I have a problem about energy equation.It couldn`t raise to 1000K in 1.5 second.Can you help me to solve this problem?thanks. TITLE 'Weld pool' { the problem identification } COORDINATES cartesian3 { coordinate system, 1D,2D,3D, etc } VARIABLES { system variables } u(threshold=100) v(threshold=100) w(threshold=100) temp(threshold=100) p(threshold=100) { choose your own names } ! SELECT { method controls } DEFINITIONS { parameter definitions } ro=6900 g=9.8 lamuda=if (temp<=1798)then if(temp<=1768)then if(temp<=1082)then if(temp<=851)then 60.719-0.027857*temp else 78.542-0.0488*temp else 15.192+0.0097*temp else 349.99-0.1797*temp else 0 miu=if (temp<=1973)then if(temp<=1873)then if(temp<=1853)then if(temp<=1823)then 1e9 else (119-0.061*temp)*1e-3 else (10.603-0.025*temp)*1e-3 else (36.236-0.0162*temp)*1e-3 else 0 cp=if (temp<=1379)then if(temp<=1100)then if(temp<=1023)then if(temp<=973)then 513.76-0.335*temp+6.89e-4*temp^2 else -10539+11.7*temp else 11873-10.2*temp else 644 else 354.34+0.21*temp av=1e-4 a0=-0.35e-3 a=1 ac=80 i=110 u0=16 v0=1.5e-3 long=0.02 wide=0.02 high=0.01 yita=0.65 op=2e-3 r=sqrt((x-v0*t)^2+y^2) mium=4*pi*1e-7 oj=(1.4875+0.00123*i)*1e-3 gama=-0.35e-3 os=5.67e-8 e=0.4 source=yita*i*u0/(2*pi*op^2)*exp(-((x-v0*t)^2+y^2)/(2*op^2))-ac*(temp-298)-os*e* ((temp^2)^2-(298^2)^2) Fx=if(temp>=1973)then-mium*i^2/(4*pi^2*oj^2*r)*exp(-r^2/(2*oj^2))*(1-exp(-r^2/(2 *oj^2)))*(1-z/high)^2*x/r else 0 Fy=if(temp>=1973)then-mium*i^2/(4*pi^2*oj^2*r)*exp(-r^2/(2*oj^2))*(1-exp(-r^2/(2 *oj^2)))*(1-z/high)^2*y/r else 0 Fz=if(temp>=1973)then mium*i^2/(4*pi^2*high*r)*(1-exp(-r^2/(2*oj^2)))*(1-z/high)-ro*g*av*(temp-298)els e 0 INITIAL VALUES temp=298 u=0 v=0 w=0 EQUATIONS { PDE's, one for each variable } u:ro*(dt(u)+u*dx(u)+v*dy(u)+w*dz(u))=Fx-dx(p)+miu*(dxx(u)+dyy(u)+dzz(u)) v:ro*(dt(v)+u*dx(v)+v*dy(v)+w*dz(v))=Fy-dx(p)+miu*(dxx(v)+dyy(v)+dzz(v)) w:ro*(dt(w)+u*dx(w)+v*dy(w)+w*dz(w))=Fz-dx(p)+miu*(dxx(w)+dyy(w)+dzz(w)) temp:ro*cp*(dt(temp)+u*dx(temp)+v*dy(temp)+w*dz(temp))=lamuda*(dxx(temp)+dyy(tem p)+dzz(temp)) p  (Fx-dx(p)+miu*(dxx(u)+dyy(u)+dzz(u)))/ro-(dt(u)+v*dy(u)+w*dz(u)))*v*w+((Fy-dx(p) +miu*(dxx(v)+dyy(v)+dzz(v)))/ro-(dt(v)+u*dx(v)+w*dz(v)))*u*w+((Fz-dx(p)+miu*(dxx (w)+dyy(w)+dzz(w)))/ro-(dt(w)+u*dx(w)+v*dy(w)))*u*v=0 !p:dx(u)+dy(v)+dz(w)=0 !CONSTRAINTS{ Integral constraints } EXTRUSION surface 'top' z=0 surface 'bottom' z=high BOUNDARIES { The domain definition } surface 'bottom' natural(temp) =(ac*(temp-298)+os*e*((temp^2)^2-(298^2)^2))/lamuda value(u)=0 value(v)=0 value(w)=0 surface 'top' natural(temp)=-source/lamuda natural(u)=-gama*dx(temp)/miu natural(v)=-gama*dy(temp)/miu value(w)=0 REGION 1 { For each material region } START(-0.005,0) { Walk the domain boundary } natural(temp)=0 natural(u)=0 value(v)=0 natural(w)=0 LINE TO (long,0) value(u)=0 value(v)=0value(w)=0 line TO (long,wide/2) value(u)=0 value(v)=0value(w)=0 line TO(-0.005,wide/2) value(u)=0 value(v)=0value(w)=0 line TO CLOSE time 1e-5 to 10by 0.01 { if time dependent } MONITORS { show progress } PLOTS { save result displays } for t=1e-5 1e-4 1e-3 1e-2 by 0.01to endtime grid(x,y,z) contour(temp) on y=0 contour(temp) on z=0 contour(u) on y=0 contour(w) on y=0 vector(v,w) on x=0.015 vector(u,v) on z=0 vector(u,w) on y=0 END And the procedure is runing too slow,is there anyways to reduce the numbers of the mesh? Is there other ways to raise the runing speed? thanks. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1197 Registered: 06-2003 |
1. You should start with a simpler problem until you are familiar with the use of FlexPDE. Look at some of our example problems in the "Samples|Steady_State|Fluids" and "Samples|Time_dependent|Fluids" folders. Download Professor Backstrom's free book "Fields of Physics" from our bookstore.html page. 2. a) I believe your natural BCs to be incorrect. Look again at "Natural BC" items in the Help Index. b) I question the equation you present for the pressure. Where on earth did this come from? c) be sure that all the values defined by IF..THEN are continuous across the switch points. Discontinuous parameters can cause slow running and/or oscillation. | |||
| Fred Sachs (sachs) Member Username: sachs Post Number: 18 Registered: 01-2004 |
I have a simple moving boundary problem - a real problem I want to solve! A 2D problem of a flow through a rectangular channel, like viscous.pde, with a hemisphere of defomable media on one side, like replacing the square box in viscous with a hemisphere. Clearly the flow is not a problem, but how do you add i the elastic equations? I gather from the the forum that many people need an example of this kind of script. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1260 Registered: 06-2003 |
I assume you want to model the material inside the hemisphere (else what conditions determine the motion of the boundary?). So add the interior of the hemisphere to the domain. Then add the material deformation equations to the equation system. Make the elasticity in the fluid small compared to the material in the hemisphere. Now add two variables (e.g. Xm and Ym) for the surrogate mesh coordinates, as shown in the moving mesh examples. Give these variables the equations: Xm: dt(Xm) = dt(U) Ym: dt(Ym) = dt(V) This forces the mesh to move with the material. It will work best if the U and V equations are also evolution equations. So if you have steady-state stress equations, use dt(U) and dt(V) on the right, instead of 0. This establishes an evolution in pseudo-time (i.e. time of unknown scale). The attached script applies this technique to the BentBar.pde sample problem.
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