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Advection and rotation of tensor property in fluid flow
Posted 5 dic 2016, 11:33 GMT-5 Fluid & Heat 4 Replies
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Hi,
I would like to use the mathematics module to define a tensor property which is advected and rotated by the flow of a fluid (Fluid flow, single-phase creeping flow). Physically, I wish to model the average alignment and orientation of small crystals at the sub-continuum scale. Since Comsol already uses tensor quantities, I wonder whether such behavior is already implemented.
I can use the PDE interface in coefficient form to define a field with 6 entries (symmetric tensor in 3D). And advection is pre-defined in the interface. But how about rotations? Would I have to define them myself?
(I thought I would check the Heat Transfer module for help; but apparently the thermal diffusivity is neither advected nor rotated along with the flow).
I would like to use the mathematics module to define a tensor property which is advected and rotated by the flow of a fluid (Fluid flow, single-phase creeping flow). Physically, I wish to model the average alignment and orientation of small crystals at the sub-continuum scale. Since Comsol already uses tensor quantities, I wonder whether such behavior is already implemented.
I can use the PDE interface in coefficient form to define a field with 6 entries (symmetric tensor in 3D). And advection is pre-defined in the interface. But how about rotations? Would I have to define them myself?
(I thought I would check the Heat Transfer module for help; but apparently the thermal diffusivity is neither advected nor rotated along with the flow).
4 Replies Last Post 5 gen 2017, 11:03 GMT-5
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Posted:
8 years ago
Hi Christoph,
The Curvilinear Coordinates interface is probably what you need, and you should use the Flow Method in that.
Check this example out:
www.comsol.com/model/anisotropic-heat-transfer-through-woven-carbon-fibers-16709
For all physics alternatives for rotated tensor properties, see the COMSOL Multiphysics Reference Manual, and find the section called "The Curvilinear Coordinates Interface"
Niklas
The Curvilinear Coordinates interface is probably what you need, and you should use the Flow Method in that.
Check this example out:
www.comsol.com/model/anisotropic-heat-transfer-through-woven-carbon-fibers-16709
For all physics alternatives for rotated tensor properties, see the COMSOL Multiphysics Reference Manual, and find the section called "The Curvilinear Coordinates Interface"
Niklas
Hi,
I would like to use the mathematics module to define a tensor property which is advected and rotated by the flow of a fluid (Fluid flow, single-phase creeping flow). Physically, I wish to model the average alignment and orientation of small crystals at the sub-continuum scale. Since Comsol already uses tensor quantities, I wonder whether such behavior is already implemented.
I can use the PDE interface in coefficient form to define a field with 6 entries (symmetric tensor in 3D). And advection is pre-defined in the interface. But how about rotations? Would I have to define them myself?
(I thought I would check the Heat Transfer module for help; but apparently the thermal diffusivity is neither advected nor rotated along with the flow).
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Posted:
8 years ago
Hi Niklas,
Thanks for the information. It looks like deep inside, Comsol already has everything I need. But it appears difficult to get to it:
The curvilinear coordinates' flow interface assumes a type of flow that is different from the flow I want to model (e.g., free thermal calculation, not just inflows and outflows). But after the flow computation, the next step in the curvilinear coordinate module is almost exactly what I'm looking for: using a flow and its local direction to rotate a pre-defined tensor quantity.
Is there any way of using these built-in tools which are not openly available in the respective modules? What I'm looking for is:
1) I can define in the mathematics module a quantity which has 6 entries and might thus act as a tensor. Given a local angle at each timestep (e.g., calculated from the vorticity), is there a pre-defined way to rotate the tensor by that angle?
2) Solid mechanics provides eigenvalues and eigenvectors for stress and strain tensors. Is it possible to utilize these functions for other tensors (e.g., compute eigenvectors for my own tensor)?
Thanks for the information. It looks like deep inside, Comsol already has everything I need. But it appears difficult to get to it:
The curvilinear coordinates' flow interface assumes a type of flow that is different from the flow I want to model (e.g., free thermal calculation, not just inflows and outflows). But after the flow computation, the next step in the curvilinear coordinate module is almost exactly what I'm looking for: using a flow and its local direction to rotate a pre-defined tensor quantity.
Is there any way of using these built-in tools which are not openly available in the respective modules? What I'm looking for is:
1) I can define in the mathematics module a quantity which has 6 entries and might thus act as a tensor. Given a local angle at each timestep (e.g., calculated from the vorticity), is there a pre-defined way to rotate the tensor by that angle?
2) Solid mechanics provides eigenvalues and eigenvectors for stress and strain tensors. Is it possible to utilize these functions for other tensors (e.g., compute eigenvectors for my own tensor)?
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Posted:
8 years ago
Hi,
I am stuck with a tensor problem. Can you please help me solving these coupled pdes(Attached in the image). The unknowns are u, pw and T
I am stuck with a tensor problem. Can you please help me solving these coupled pdes(Attached in the image). The unknowns are u, pw and T
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Posted:
8 years ago
Hi,
I am stuck with a tensor problem. Can you please help me solving these coupled pdes(Attached in the image). The unknowns are u, pw and T
Dear Aminul,
Your problem is significantly different from mine. While I am trying to solve for a quantity which is a tensor field, you merely have a tensor as part of your coefficients.
I'm not saying your problem is trivial, but I think it can easily be handled by Comsol. From the Mathematics module's PDE interface, use either the coefficient form (easiest if you can put your problem into that format), or else the general form.
From the information provided, I cannot quite figure out the form of your problem. It looks to me that you have two coupled predictive equations (eqns 2 & 3), meaning they each have a time derivative d/dt. The third equation (eqn 1) looks like it is not needed for the time evolution but is only used to compute the vector field u after computation (but perhaps I misunderstand; perhaps eqn 1 provides a constraint on T and pw which I don't see because I don't understand what physics you are solving).
Regardless, you can select the PDE coefficient form several times, probably once for each equation. Using the source term, you can couple the equations. I have just tested this with a simpler system, and apparently it is OK to include constraint equations without time derivatives.