Re: [Libmesh-users] Example 13: Non-Dimensional From: Vikram Garg - 2011-06-28 22:05 ```Saumil,            If you are using PETSc, you can tack on the command line option -ksp_monitor_singular_value and check whether the linear solver is running into trouble. If that is indeed the case, you can try increasing the number of GMRES restart steps or use modified Gram Schmidt. Another approach is to use continuation in parameters, where you start with a smaller Reynolds number and then increment the Reynold number iteratively to the desired value. The solution at Re(i) is used as the starting guess for the solver at Re(i+1). Thanks. On Tue, Jun 28, 2011 at 9:03 AM, Saumil Patel wrote: > > Thank You, John.  This makes sense. I was able to get results for Re 100. > > I have been trying to get results for Re = 1000.  I've tried two approaches: > 1) to multiply the diffusion term by 1/Re and 2) Change the boundary > condition to U=1000.  BC's are still based on the Penalty formulation. > > In both cases I'm using a refined mesh of 500 by 500. > > I'm having trouble getting accurate results so I was wondering if the > K-matrix is becoming ill-conditioned when I multiply the diffusion term by > .001 (1/Re)?  Do you have any suggestions on getting around it this issue? > > Thanks for your help, > > Saumil > > On Mon, Jun 27, 2011 at 10:43 AM, John Peterson > > On Sun, Jun 26, 2011 at 1:37 PM, Saumil Patel > > wrote: > > > Hello, > > > > > > I am getting familiar with the LIBMESH code and I was wondering if the > > FEM > > > formulation for the Unsteady NSE in example 13 are in a non-dimensional > > > form?  If so, I would just need to multiply the diffusion terms in the > > Kuu > > > and Kvv submatrices by the inverse Reynolds number factor, correct? > > > > Well the *dimensional* incompressible NS equations typically contain > > only a single parameter: "nu", the kinematic viscosity, anyway. > > > > So if you multiply the diffusion terms in ex13 by some parameter, you > > can think of it as a dimensional viscosity or an inverse Reynold's > > number. > > > > > Furthermore, I wouldn't need to change the B.C. condition for the top > > lid, > > > correct? > > > > The velocity on the top lid, the size of the domain, and the timestep > > will all take on different physical meaning depending on whether the > > value multiplying the diffusion terms is thought of as the Reynolds > > number or the kinematic viscosity.  Consider: > > > > The default values for ex13 are domain size = "1", lid velocity="1". > > > > If the number multiplying the diffusion terms is thought of as the > > kinematic viscosity (in SI units of m^2/s, say) then the domain size > > is 1 meter, the lid velocity 1 m/s. > > > > On the other hand, if the number multiplying the diffusion terms is > > thought of as 1/Re, then setting the lid velocity="1" just means the > > lid velocity is equal to the "characteristic velocity used in defining > > the Reynold's number" and does not imply any particular units.  In > > this case, one can always assign a physical value to, for example, the > > lid velocity "U" by specifying particular values for the Re, the > > kinematic viscosity of the fluid, and the domain size "L": > > > > Ex1, air @ 300K (nu=15.68e-6 m^2/s) in a L=1cm enclosure, Re=1: U = Re > > * (nu/L) ~ 0.15 cm/s > > > > Ex2, water @ 50C (nu=0.553e-6 m^2/s) in a L=1m enclosure, Re=1: U ~ .55 > > micron/s > > > > That is, the same Re=1 solution could represent either of the two > > physical situations (and infinitely many others!) above. > > > > -- > > John > > > ------------------------------------------------------------------------------ > All of the data generated in your IT infrastructure is seriously valuable. > Why? It contains a definitive record of application performance, security > threats, fraudulent activity, and more. Splunk takes this data and makes > sense of it. IT sense. And common sense. > http://p.sf.net/sfu/splunk-d2d-c2 > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users -- Vikram Garg PhD Candidate Institute for Computational and Engineering Sciences The University of Texas at Austin http://users.ices.utexas.edu/~vikram/ http://www.runforindia.org/runners/vikramg ```

 Re: [Libmesh-users] Example 13: Non-Dimensional From: John Peterson - 2011-06-27 14:43 ```On Sun, Jun 26, 2011 at 1:37 PM, Saumil Patel wrote: > Hello, > > I am getting familiar with the LIBMESH code and I was wondering if the FEM > formulation for the Unsteady NSE in example 13 are in a non-dimensional > form?  If so, I would just need to multiply the diffusion terms in the Kuu > and Kvv submatrices by the inverse Reynolds number factor, correct? Well the *dimensional* incompressible NS equations typically contain only a single parameter: "nu", the kinematic viscosity, anyway. So if you multiply the diffusion terms in ex13 by some parameter, you can think of it as a dimensional viscosity or an inverse Reynold's number. > Furthermore, I wouldn't need to change the B.C. condition for the top lid, > correct? The velocity on the top lid, the size of the domain, and the timestep will all take on different physical meaning depending on whether the value multiplying the diffusion terms is thought of as the Reynolds number or the kinematic viscosity. Consider: The default values for ex13 are domain size = "1", lid velocity="1". If the number multiplying the diffusion terms is thought of as the kinematic viscosity (in SI units of m^2/s, say) then the domain size is 1 meter, the lid velocity 1 m/s. On the other hand, if the number multiplying the diffusion terms is thought of as 1/Re, then setting the lid velocity="1" just means the lid velocity is equal to the "characteristic velocity used in defining the Reynold's number" and does not imply any particular units. In this case, one can always assign a physical value to, for example, the lid velocity "U" by specifying particular values for the Re, the kinematic viscosity of the fluid, and the domain size "L": Ex1, air @ 300K (nu=15.68e-6 m^2/s) in a L=1cm enclosure, Re=1: U = Re * (nu/L) ~ 0.15 cm/s Ex2, water @ 50C (nu=0.553e-6 m^2/s) in a L=1m enclosure, Re=1: U ~ .55 micron/s That is, the same Re=1 solution could represent either of the two physical situations (and infinitely many others!) above. -- John ```
 Re: [Libmesh-users] Example 13: Non-Dimensional From: Saumil Patel - 2011-06-28 14:04 ```Thank You, John. This makes sense. I was able to get results for Re 100. I have been trying to get results for Re = 1000. I've tried two approaches: 1) to multiply the diffusion term by 1/Re and 2) Change the boundary condition to U=1000. BC's are still based on the Penalty formulation. In both cases I'm using a refined mesh of 500 by 500. I'm having trouble getting accurate results so I was wondering if the K-matrix is becoming ill-conditioned when I multiply the diffusion term by .001 (1/Re)? Do you have any suggestions on getting around it this issue? Thanks for your help, Saumil On Mon, Jun 27, 2011 at 10:43 AM, John Peterson On Sun, Jun 26, 2011 at 1:37 PM, Saumil Patel > wrote: > > Hello, > > > > I am getting familiar with the LIBMESH code and I was wondering if the > FEM > > formulation for the Unsteady NSE in example 13 are in a non-dimensional > > form? If so, I would just need to multiply the diffusion terms in the > Kuu > > and Kvv submatrices by the inverse Reynolds number factor, correct? > > Well the *dimensional* incompressible NS equations typically contain > only a single parameter: "nu", the kinematic viscosity, anyway. > > So if you multiply the diffusion terms in ex13 by some parameter, you > can think of it as a dimensional viscosity or an inverse Reynold's > number. > > > Furthermore, I wouldn't need to change the B.C. condition for the top > lid, > > correct? > > The velocity on the top lid, the size of the domain, and the timestep > will all take on different physical meaning depending on whether the > value multiplying the diffusion terms is thought of as the Reynolds > number or the kinematic viscosity. Consider: > > The default values for ex13 are domain size = "1", lid velocity="1". > > If the number multiplying the diffusion terms is thought of as the > kinematic viscosity (in SI units of m^2/s, say) then the domain size > is 1 meter, the lid velocity 1 m/s. > > On the other hand, if the number multiplying the diffusion terms is > thought of as 1/Re, then setting the lid velocity="1" just means the > lid velocity is equal to the "characteristic velocity used in defining > the Reynold's number" and does not imply any particular units. In > this case, one can always assign a physical value to, for example, the > lid velocity "U" by specifying particular values for the Re, the > kinematic viscosity of the fluid, and the domain size "L": > > Ex1, air @ 300K (nu=15.68e-6 m^2/s) in a L=1cm enclosure, Re=1: U = Re > * (nu/L) ~ 0.15 cm/s > > Ex2, water @ 50C (nu=0.553e-6 m^2/s) in a L=1m enclosure, Re=1: U ~ .55 > micron/s > > That is, the same Re=1 solution could represent either of the two > physical situations (and infinitely many others!) above. > > -- > John > ```
 Re: [Libmesh-users] Example 13: Non-Dimensional From: John Peterson - 2011-06-28 14:30 ```On Tue, Jun 28, 2011 at 8:03 AM, Saumil Patel wrote: > Thank You, John.  This makes sense. I was able to get results for Re 100. > > I have been trying to get results for Re = 1000.  I've tried two approaches: > 1) to multiply the diffusion term by 1/Re and 2) Change the boundary > condition to U=1000.  BC's are still based on the Penalty formulation. > > In both cases I'm using a refined mesh of 500 by 500. > > I'm having trouble getting accurate results so I was wondering if the > K-matrix is becoming ill-conditioned when I multiply the diffusion term by > .001 (1/Re)?  Do you have any suggestions on getting around it this issue? The matrix condition number goes like h^-2 for the Laplacian, so the fine mesh will certainly hurt you there. The cell Reynolds number, Re*(h/L) = 1000/500 = 2 for your case, which is right on the borderline of Galerkin instability. The timestep, linear, and nonlinear tolerances will all need to be different from what they were in the Re=1 case. You'll need to play with those and see which ones work. -- John ```
 Re: [Libmesh-users] Example 13: Non-Dimensional From: Vikram Garg - 2011-06-28 22:05 ```Saumil,            If you are using PETSc, you can tack on the command line option -ksp_monitor_singular_value and check whether the linear solver is running into trouble. If that is indeed the case, you can try increasing the number of GMRES restart steps or use modified Gram Schmidt. Another approach is to use continuation in parameters, where you start with a smaller Reynolds number and then increment the Reynold number iteratively to the desired value. The solution at Re(i) is used as the starting guess for the solver at Re(i+1). Thanks. On Tue, Jun 28, 2011 at 9:03 AM, Saumil Patel wrote: > > Thank You, John.  This makes sense. I was able to get results for Re 100. > > I have been trying to get results for Re = 1000.  I've tried two approaches: > 1) to multiply the diffusion term by 1/Re and 2) Change the boundary > condition to U=1000.  BC's are still based on the Penalty formulation. > > In both cases I'm using a refined mesh of 500 by 500. > > I'm having trouble getting accurate results so I was wondering if the > K-matrix is becoming ill-conditioned when I multiply the diffusion term by > .001 (1/Re)?  Do you have any suggestions on getting around it this issue? > > Thanks for your help, > > Saumil > > On Mon, Jun 27, 2011 at 10:43 AM, John Peterson > > On Sun, Jun 26, 2011 at 1:37 PM, Saumil Patel > > wrote: > > > Hello, > > > > > > I am getting familiar with the LIBMESH code and I was wondering if the > > FEM > > > formulation for the Unsteady NSE in example 13 are in a non-dimensional > > > form?  If so, I would just need to multiply the diffusion terms in the > > Kuu > > > and Kvv submatrices by the inverse Reynolds number factor, correct? > > > > Well the *dimensional* incompressible NS equations typically contain > > only a single parameter: "nu", the kinematic viscosity, anyway. > > > > So if you multiply the diffusion terms in ex13 by some parameter, you > > can think of it as a dimensional viscosity or an inverse Reynold's > > number. > > > > > Furthermore, I wouldn't need to change the B.C. condition for the top > > lid, > > > correct? > > > > The velocity on the top lid, the size of the domain, and the timestep > > will all take on different physical meaning depending on whether the > > value multiplying the diffusion terms is thought of as the Reynolds > > number or the kinematic viscosity.  Consider: > > > > The default values for ex13 are domain size = "1", lid velocity="1". > > > > If the number multiplying the diffusion terms is thought of as the > > kinematic viscosity (in SI units of m^2/s, say) then the domain size > > is 1 meter, the lid velocity 1 m/s. > > > > On the other hand, if the number multiplying the diffusion terms is > > thought of as 1/Re, then setting the lid velocity="1" just means the > > lid velocity is equal to the "characteristic velocity used in defining > > the Reynold's number" and does not imply any particular units.  In > > this case, one can always assign a physical value to, for example, the > > lid velocity "U" by specifying particular values for the Re, the > > kinematic viscosity of the fluid, and the domain size "L": > > > > Ex1, air @ 300K (nu=15.68e-6 m^2/s) in a L=1cm enclosure, Re=1: U = Re > > * (nu/L) ~ 0.15 cm/s > > > > Ex2, water @ 50C (nu=0.553e-6 m^2/s) in a L=1m enclosure, Re=1: U ~ .55 > > micron/s > > > > That is, the same Re=1 solution could represent either of the two > > physical situations (and infinitely many others!) above. > > > > -- > > John > > > ------------------------------------------------------------------------------ > All of the data generated in your IT infrastructure is seriously valuable. > Why? It contains a definitive record of application performance, security > threats, fraudulent activity, and more. Splunk takes this data and makes > sense of it. IT sense. And common sense. > http://p.sf.net/sfu/splunk-d2d-c2 > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users -- Vikram Garg PhD Candidate Institute for Computational and Engineering Sciences The University of Texas at Austin http://users.ices.utexas.edu/~vikram/ http://www.runforindia.org/runners/vikramg ```