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September 3, 2012, 11:34 
Particle transport

#1 
Senior Member
Vishal Nandigana
Join Date: Mar 2009
Location: Champaign, Illinois, U.S.A
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Dear Foamers,
I would like to solve the following Newton's law of motion: dp/dt = F(x), where p is the position of the particle, and x corresponds to the current p value. I have the distribution of F with respect to x. In other words, in algebraic sense, p_new = p_old + (delta_t)*F(p_old). My query is how to calculate F(p_old) at every time step. Please let me know. Regards Vishal 

September 4, 2012, 05:12 

#2 
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Julien
Join Date: Jun 2012
Location: France
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Hi vishal
your question is quite strange here, in an OpenFOAM forum. OpenFOAM is a computing tool which works on FIELDS. A field is a concept of "something" which can vary respect to time and 3D space. Let say function f(x,y,z,t). This "something" can be a lot of different things: pressure, velocity, temperature, density, strain, stress, phase,... Mathematically, these "things" are described in terms of scalars, vectors, tensors. The power of OpenFOAM relies on a formal language which is able to solve for partial derivative equations. You can download here some documentation: www.openfoam.org/docs/ Mathematically, your problem seems to be "simply" a problem of integration. GNU Octave should be better tool for you. Physically, I think you are mysunderstanding: in this equation, p is not the position but the momentum, saying a product of a mass m and a velocity v. Velocity is the derivative of the position x. 

September 4, 2012, 10:25 

#3 
Senior Member
Vishal Nandigana
Join Date: Mar 2009
Location: Champaign, Illinois, U.S.A
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Hi Julien,
Thanks for the reply. Well, the equation I wanted to solve is the Langevin/Brownian dynamics with White noise, and neglecting the acceleration term in it. I wanted to couple this equation into Poisson  Nernst Planck equation which I have developed in OpenFOAM. However, before incorporating the noise and complicating it I wanted to know, if it is possible to calculate the variable f at a particular position, in the following equation. dp/dt = A*f(x=p_old) You are right, it is a momentum equation, however, I neglect the acceleration and consider a position dependent force. Please let me know, how to incorporate this equation in OF or in general how to solve for a Langevin equation. Thanks Regards Vishal 

September 4, 2012, 15:10 

#4 
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Bruno Santos
Join Date: Mar 2009
Location: Lisbon, Portugal
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Greetings to all!
@Vishal: If I understand you correctly, I think you can look into the Lagrangian capabilities that OpenFOAM has: http://www.openfoam.com/features/lagrangian.php Another possibility would be to look into the tutorial "mesh/moveDynamicMesh/simpleHarmonicMotion", which I think it solves a weight box hanging on elastics or cables... Best regards, Bruno edit: I've moved this thread to the programming section, which is where this fits the best...
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Last edited by wyldckat; September 4, 2012 at 15:12. Reason: see "edit:" 

September 4, 2012, 15:52 

#5 
Senior Member
Vishal Nandigana
Join Date: Mar 2009
Location: Champaign, Illinois, U.S.A
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Rep Power: 11 
Thanks Bruno. I would read it and would contact you.
Regards Vishal 

January 26, 2013, 23:02 

#6 
Senior Member
Vishal Nandigana
Join Date: Mar 2009
Location: Champaign, Illinois, U.S.A
Posts: 208
Rep Power: 11 
Hi Bruno,
I want to simulate a chain of particles, whose interaction potential is known (say a nonlinear spring potential + LennardJones potential). I want to study the dynamics of this chain using Lagrangian approach. However, I would like to know if it is possible to add a noise force with a Gaussian distribution in the Newton's equation. Also, is it possible to implement LennardJones type potential in OF while solving the dynamics. Kindly let me know where I could find some tutorials for such cases. Thanks a lot for the help Regards Vishal 

January 27, 2013, 07:04 

#7 
Super Moderator
Bruno Santos
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Location: Lisbon, Portugal
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Hi Vishal,
I don't know of any tutorials that have all of those characteristics, but here's a list of links that can help you start to track down this kind of information:
Bruno
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February 6, 2013, 11:16 

#8 
Senior Member
Vishal Nandigana
Join Date: Mar 2009
Location: Champaign, Illinois, U.S.A
Posts: 208
Rep Power: 11 
Hi Bruno,
I would like to solve the following equation fvm::laplacian(eps_r,Phi) == alpha * Z1*C1alpha*Z2*C2 where eps_r is spatially varying. I wrote the code to solve this problem when eps_r(x) at time t=0 is specified. However I would like to know if it is possible to define a function in OpenFOAM where eps_r is a function of time and space. Once this is defined, I want to read this variable at every time instant and solve the above governing equation. Please let me know. Thanks Regards Vishal 

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