FEM Implementation of NS with SUPG Stabilization
Good Evening, I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information. Thank you in advance for your time. Brandon
Do you want to write a new code using only PETSc or would you be up for collaborating on ceed-fluids, which is a high-performance compressible SUPG solver based on DMPlex with good GPU support? It uses the metric to compute covariant length for stabilization. We have YZƁ shock capturing, though it hasn't been tested much beyond shock tube experiments. (Most of our work has been low Mach.) https://libceed.org/en/latest/examples/fluids/ https://github.com/CEED/libCEED/blob/main/examples/fluids/qfunctions/stabili... On Tue, Oct 10, 2023, at 7:34 PM, Brandon Denton via petsc-users wrote:
Good Evening,
I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information.
Thank you in advance for your time. Brandon
My initial plan was to write a new code using only PETSc. However, I don't see how to do what I want within the point-wise residual function. Am I missing something? Yes. I would be interested in collaborating on the ceed-fluids. I took a quick look at the links you provided and it looks interesting. I'll warn you though. I'm a Mechanical Engineer by trade/training. The calculus and programming sometimes take me a little while to wrap my head around. Let me know how I can help. In the meantime, I'll continue to review the information you sent over. ________________________________ From: Jed Brown <[email protected]> Sent: Tuesday, October 10, 2023 10:18 PM To: Brandon Denton <[email protected]>; [email protected] <[email protected]> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization Do you want to write a new code using only PETSc or would you be up for collaborating on ceed-fluids, which is a high-performance compressible SUPG solver based on DMPlex with good GPU support? It uses the metric to compute covariant length for stabilization. We have YZƁ shock capturing, though it hasn't been tested much beyond shock tube experiments. (Most of our work has been low Mach.) https://libceed.org/en/latest/examples/fluids/ https://github.com/CEED/libCEED/blob/main/examples/fluids/qfunctions/stabili... On Tue, Oct 10, 2023, at 7:34 PM, Brandon Denton via petsc-users wrote: Good Evening, I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information. Thank you in advance for your time. Brandon
On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users < [email protected]> wrote:
Good Evening,
I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information.
Are you sure you need those? Darsh and I implemented SUPG without that. You would need local second derivative information, which you can get using -dm_ds_jet_degree 2. If you check in an example, I can go over it. Thanks, Matt
Thank you in advance for your time. Brandon
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
I was thinking about trying to implement Ben Kirk's approach to Navier-Stokes (see attached paper; Section 5). His approach uses these quantities to align the orientation of the unstructured element/cell with the fluid velocity to apply the stabilization/upwinding and to detect shocks. If you have an example of the approach you mentioned, could you please send it over so I can review it? On Oct 11, 2023 6:02 AM, Matthew Knepley <[email protected]> wrote: On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users <[email protected]<mailto:[email protected]>> wrote: Good Evening, I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information. Are you sure you need those? Darsh and I implemented SUPG without that. You would need local second derivative information, which you can get using -dm_ds_jet_degree 2. If you check in an example, I can go over it. Thanks, Matt Thank you in advance for your time. Brandon -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice. https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure. Brandon Denton via petsc-users <[email protected]> writes:
I was thinking about trying to implement Ben Kirk's approach to Navier-Stokes (see attached paper; Section 5). His approach uses these quantities to align the orientation of the unstructured element/cell with the fluid velocity to apply the stabilization/upwinding and to detect shocks.
If you have an example of the approach you mentioned, could you please send it over so I can review it?
On Oct 11, 2023 6:02 AM, Matthew Knepley <[email protected]> wrote: On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users <[email protected]<mailto:[email protected]>> wrote: Good Evening,
I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information.
Are you sure you need those? Darsh and I implemented SUPG without that. You would need local second derivative information, which you can get using -dm_ds_jet_degree 2. If you check in an example, I can go over it.
Thanks,
Matt
Thank you in advance for your time. Brandon
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual. Matt
Brandon Denton via petsc-users <[email protected]> writes:
I was thinking about trying to implement Ben Kirk's approach to Navier-Stokes (see attached paper; Section 5). His approach uses these quantities to align the orientation of the unstructured element/cell with the fluid velocity to apply the stabilization/upwinding and to detect shocks.
If you have an example of the approach you mentioned, could you please send it over so I can review it?
On Oct 11, 2023 6:02 AM, Matthew Knepley <[email protected]> wrote: On Tue, Oct 10, 2023 at 9:34 PM Brandon Denton via petsc-users < [email protected]<mailto:[email protected]>> wrote: Good Evening,
I am looking to implement a form of Navier-Stokes with SUPG Stabilization and shock capturing using PETSc's FEM infrastructure. In this implementation, I need access to the cell's shape function gradients and natural coordinate gradients for calculations within the point-wise residual calculations. How do I get these quantities at the quadrature points? The signatures for fo and f1 don't seem to contain this information.
Are you sure you need those? Darsh and I implemented SUPG without that. You would need local second derivative information, which you can get using -dm_ds_jet_degree 2. If you check in an example, I can go over it.
Thanks,
Matt
Thank you in advance for your time. Brandon
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/<; http://www.cse.buffalo.edu/~knepley/>
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
Matthew Knepley <[email protected]> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor).
Thank you for the discussion. Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions? Matt - Thank you for the command line option for the 2nd derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference. Jed - Thank you for the link. I will review the information on it. Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here). ________________________________ From: Jed Brown <[email protected]> Sent: Wednesday, October 11, 2023 1:38 PM To: Matthew Knepley <[email protected]> Cc: Brandon Denton <[email protected]>; petsc-users <[email protected]> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization Matthew Knepley <[email protected]> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor).
On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <[email protected]> wrote:
Thank you for the discussion.
Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions?
I am not sure what natural coordinates are. Do we just mean the Jacobian, derivatives of the map between reference and real coordinates? If so, yes the Jacobian is available. Right now I do not pass it directly, but passing it is easy. Thanks, Matt
Matt - Thank you for the command line option for the 2nd derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference.
Jed - Thank you for the link. I will review the information on it.
Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here). ------------------------------ *From:* Jed Brown <[email protected]> *Sent:* Wednesday, October 11, 2023 1:38 PM *To:* Matthew Knepley <[email protected]> *Cc:* Brandon Denton <[email protected]>; petsc-users < [email protected]> *Subject:* Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization
Matthew Knepley <[email protected]> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flibceed.or... <https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet>
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor).
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
By natural coordinates, I am referring to the reference element coordinates. Usually these are represented as (xi, eta, zeta) in the literature. Yes. I would like to have the Jacobian and the derivatives of the map available within PetscDSSetResidual() f0 and f1 functions. I believe DMPlexComputeCellGeometryFEM() function provides this information. Is there a way to get the cell, shape functions as well? It not, can we talk about this more? I would like to understand how the shape functions are addressed within PETSc. Dr. Kirk's approach uses the shape function gradients in its SUPG parameter. I'd love to talk with you about this is more detail. ________________________________ From: Matthew Knepley <[email protected]> Sent: Wednesday, October 11, 2023 3:13 PM To: Brandon Denton <[email protected]> Cc: Jed Brown <[email protected]>; petsc-users <[email protected]> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <[email protected]<mailto:[email protected]>> wrote: Thank you for the discussion. Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions? I am not sure what natural coordinates are. Do we just mean the Jacobian, derivatives of the map between reference and real coordinates? If so, yes the Jacobian is available. Right now I do not pass it directly, but passing it is easy. Thanks, Matt Matt - Thank you for the command line option for the 2nd derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference. Jed - Thank you for the link. I will review the information on it. Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here). ________________________________ From: Jed Brown <[email protected]<mailto:[email protected]>> Sent: Wednesday, October 11, 2023 1:38 PM To: Matthew Knepley <[email protected]<mailto:[email protected]>> Cc: Brandon Denton <[email protected]<mailto:[email protected]>>; petsc-users <[email protected]<mailto:[email protected]>> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization Matthew Knepley <[email protected]<mailto:[email protected]>> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]<mailto:[email protected]>> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor). -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
On Wed, Oct 11, 2023 at 4:15 PM Brandon Denton <[email protected]> wrote:
By natural coordinates, I am referring to the reference element coordinates. Usually these are represented as (xi, eta, zeta) in the literature.
Yes. I would like to have the Jacobian and the derivatives of the map available within PetscDSSetResidual() f0 and f1 functions.
Yes, we can get these passed an aux data.
I believe DMPlexComputeCellGeometryFEM() function provides this information. Is there a way to get the cell, shape functions as well? It not, can we talk about this more? I would like to understand how the shape functions are addressed within PETSc. Dr. Kirk's approach uses the shape function gradients in its SUPG parameter. I'd love to talk with you about this is more detail.
There should be a way to formulate this in a basis independent way. I would much prefer that to explicit inclusion of the basis. Thanks, Matt
*From:* Matthew Knepley <[email protected]> *Sent:* Wednesday, October 11, 2023 3:13 PM *To:* Brandon Denton <[email protected]> *Cc:* Jed Brown <[email protected]>; petsc-users <[email protected]> *Subject:* Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization
On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <[email protected]> wrote:
Thank you for the discussion.
Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions?
I am not sure what natural coordinates are. Do we just mean the Jacobian, derivatives of the map between reference and real coordinates? If so, yes the Jacobian is available. Right now I do not pass it directly, but passing it is easy.
Thanks,
Matt
Matt - Thank you for the command line option for the 2nd derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference.
Jed - Thank you for the link. I will review the information on it.
Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here). ------------------------------ *From:* Jed Brown <[email protected]> *Sent:* Wednesday, October 11, 2023 1:38 PM *To:* Matthew Knepley <[email protected]> *Cc:* Brandon Denton <[email protected]>; petsc-users < [email protected]> *Subject:* Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization
Matthew Knepley <[email protected]> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flibceed.or... <https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet>
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor).
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
How exactly does the aux data work? What is typically available there? Is it something the user can populate? ________________________________ From: Matthew Knepley <[email protected]> Sent: Wednesday, October 11, 2023 8:07 PM To: Brandon Denton <[email protected]> Cc: Jed Brown <[email protected]>; petsc-users <[email protected]> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization On Wed, Oct 11, 2023 at 4:15 PM Brandon Denton <[email protected]<mailto:[email protected]>> wrote: By natural coordinates, I am referring to the reference element coordinates. Usually these are represented as (xi, eta, zeta) in the literature. Yes. I would like to have the Jacobian and the derivatives of the map available within PetscDSSetResidual() f0 and f1 functions. Yes, we can get these passed an aux data. I believe DMPlexComputeCellGeometryFEM() function provides this information. Is there a way to get the cell, shape functions as well? It not, can we talk about this more? I would like to understand how the shape functions are addressed within PETSc. Dr. Kirk's approach uses the shape function gradients in its SUPG parameter. I'd love to talk with you about this is more detail. There should be a way to formulate this in a basis independent way. I would much prefer that to explicit inclusion of the basis. Thanks, Matt From: Matthew Knepley <[email protected]<mailto:[email protected]>> Sent: Wednesday, October 11, 2023 3:13 PM To: Brandon Denton <[email protected]<mailto:[email protected]>> Cc: Jed Brown <[email protected]<mailto:[email protected]>>; petsc-users <[email protected]<mailto:[email protected]>> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization On Wed, Oct 11, 2023 at 2:09 PM Brandon Denton <[email protected]<mailto:[email protected]>> wrote: Thank you for the discussion. Are we agreed then that the derivatives of the natural coordinates are required for the described approach? If so, is this something PETSc can currently do within the point-wise residual functions? I am not sure what natural coordinates are. Do we just mean the Jacobian, derivatives of the map between reference and real coordinates? If so, yes the Jacobian is available. Right now I do not pass it directly, but passing it is easy. Thanks, Matt Matt - Thank you for the command line option for the 2nd derivatives. Those will be needed to implement the discussed approach. Specifically in the stabilization and shock capture parameters. (Ref.: B. Kirk's Thesis). What is a good reference for the usual SUPG method you are referencing? I've been looking through my textbooks but haven't found a good reference. Jed - Thank you for the link. I will review the information on it. Sorry about the attachment. I will upload it to this thread later (I'm at work right now and I can't do it from here). ________________________________ From: Jed Brown <[email protected]<mailto:[email protected]>> Sent: Wednesday, October 11, 2023 1:38 PM To: Matthew Knepley <[email protected]<mailto:[email protected]>> Cc: Brandon Denton <[email protected]<mailto:[email protected]>>; petsc-users <[email protected]<mailto:[email protected]>> Subject: Re: [petsc-users] FEM Implementation of NS with SUPG Stabilization Matthew Knepley <[email protected]<mailto:[email protected]>> writes:
On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <[email protected]<mailto:[email protected]>> wrote:
I don't see an attachment, but his thesis used conservative variables and defined an effective length scale in a way that seemed to assume constant shape function gradients. I'm not aware of systematic literature comparing the covariant and contravariant length measures on anisotropic meshes, but I believe most people working in the Shakib/Hughes approach use the covariant measure. Our docs have a brief discussion of this choice.
Matt, I don't understand how the second derivative comes into play as a length measure on anistropic meshes -- the second derivatives can be uniformly zero and yet you still need a length measure.
I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor). -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/> -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
participants (3)
-
Brandon Denton -
Jed Brown -
Matthew Knepley