Rayleigh-Benard convection at large Rayleigh number - convergence.

[ethrelfall]

Dear community,

I have been working with the Rayleigh-B(')enard convection example found at

https://www.firedrakeproject.org/demos/rayleigh-benard.py

and I would like to be able to access larger values of the Rayleigh number (Ra). As supplied, the example stops converging at Ra=8e5 (this is using the direct solve and so it seems to be a failure of nonlinear convergence).

My attempt to improve this is at

https://github.com/ethrelfall/Heat-transport/tree/main/Firedrake;

by increasing the element order and using a mesh that's refined near the boundaries (see repo) I have been able to run up to about Ra=2e6 ... but I want more. And I don't really understand why the solution is problematic because there is nothing obviously pathological, e.g. a very thin boundary layer, in the solution.

Note: it is known that the flows I am running are laminar i.e. the transition to turbulence happens at much larger Ra, above 5e10, as presented in

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/regime-transitions-in-thermally-driven-highrayleigh-number-vertical-convection/2C6892CA314FB35E39818039C64ED799.

Is is possible to initialize the nonlinear (=Newton?) solve with a flow field e.g. one calculated at a slightly lower Rayleigh number? (This is the sort of thing I do when running the same problem in Nektar++ using a time-dependent solver.)

One other little question - I am currently running Firedrake on one core; is it easy to get it to use multiple cores?

(Did search for matching discussions.)

Many thanks!

Ed.

[colinjcotter]

Hi Ed, For larger Re you’ll need a continuation method. For running in parallel, <http://firedrakeproject.org/parallelism.html#id2> Parallelism in Firedrake — Firedrake 0.13.0+5418.g660d46b5 documentation<http://firedrakeproject.org/parallelism.html#id2> firedrakeproject.org<http://firedrakeproject.org/parallelism.html#id2> [icon.ico]<http://firedrakeproject.org/parallelism.html#id2> all the best cjc On 30 Dec 2022, at 16:24, ethrelfall ***@***.***> wrote:  Dear community, I have been working with the Rayleigh-B(')enard convection example found at https://www.firedrakeproject.org/demos/rayleigh-benard.py and I would like to be able to access larger values of the Rayleigh number (Ra). As supplied, the example stops converging at Ra=8e5 (this is using the direct solve and so it seems to be a failure of nonlinear convergence). My attempt to improve this is at https://github.com/ethrelfall/Heat-transport/tree/main/Firedrake; by increasing the element order and using a mesh that's refined near the boundaries (see repo) I have been able to run up to about Ra=2e6 ... but I want more. And I don't really understand why the solution is problematic because there is nothing obviously pathological, e.g. a very thin boundary layer, in the solution. Note: it is known that the flows I am running are laminar i.e. the transition to turbulence happens at much larger Ra, above 5e10, as presented in https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/regime-transitions-in-thermally-driven-highrayleigh-number-vertical-convection/2C6892CA314FB35E39818039C64ED799. Is is possible to initialize the nonlinear (=Newton?) solve with a flow field e.g. one calculated at a slightly lower Rayleigh number? (This is the sort of thing I do when running the same problem in Nektar++ using a time-dependent solver.) One other little question - I am currently running Firedrake on one core; is it easy to get it to use multiple cores? (Did search for matching discussions.) Many thanks! Ed. — Reply to this email directly, view it on GitHub<#2698>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4T55FX4PV4QVGLKSQ3WP35BHANCNFSM6AAAAAATM6YIN4>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[colinjcotter]

ah sorry, didn’t read carefully. You are describing a (basic) continuation method. To reuse the solution, just define Ra as a Constant. Then call the solver multiple times (it uses the contents of the field you want to solve to as an initial state), updating the value of the Constant using the .assign() method. On 30 Dec 2022, at 16:40, Cotter, Colin J ***@***.***> wrote:  Hi Ed, For larger Re you’ll need a continuation method. For running in parallel, <http://firedrakeproject.org/parallelism.html#id2> Parallelism in Firedrake — Firedrake 0.13.0+5418.g660d46b5 documentation<http://firedrakeproject.org/parallelism.html#id2> firedrakeproject.org<http://firedrakeproject.org/parallelism.html#id2> <http://firedrakeproject.org/parallelism.html#id2> <icon.ico> all the best cjc On 30 Dec 2022, at 16:24, ethrelfall ***@***.***> wrote:  Dear community, I have been working with the Rayleigh-B(')enard convection example found at https://www.firedrakeproject.org/demos/rayleigh-benard.py and I would like to be able to access larger values of the Rayleigh number (Ra). As supplied, the example stops converging at Ra=8e5 (this is using the direct solve and so it seems to be a failure of nonlinear convergence). My attempt to improve this is at https://github.com/ethrelfall/Heat-transport/tree/main/Firedrake; by increasing the element order and using a mesh that's refined near the boundaries (see repo) I have been able to run up to about Ra=2e6 ... but I want more. And I don't really understand why the solution is problematic because there is nothing obviously pathological, e.g. a very thin boundary layer, in the solution. Note: it is known that the flows I am running are laminar i.e. the transition to turbulence happens at much larger Ra, above 5e10, as presented in https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/regime-transitions-in-thermally-driven-highrayleigh-number-vertical-convection/2C6892CA314FB35E39818039C64ED799. Is is possible to initialize the nonlinear (=Newton?) solve with a flow field e.g. one calculated at a slightly lower Rayleigh number? (This is the sort of thing I do when running the same problem in Nektar++ using a time-dependent solver.) One other little question - I am currently running Firedrake on one core; is it easy to get it to use multiple cores? (Did search for matching discussions.) Many thanks! Ed. — Reply to this email directly, view it on GitHub<#2698>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4T55FX4PV4QVGLKSQ3WP35BHANCNFSM6AAAAAATM6YIN4>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***> <icon.ico>

[ethrelfall]

Thanks - that works. Awesome support!

[rckirby]

For continuation, you might also look at Patrick Farrel's code https://bitbucket.org/pefarrell/defcon/src/master/ and papers using it, such as https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.055106, where he does RB convection in 2d. On Fri, Dec 30, 2022 at 9:45 AM Colin J Cotter ***@***.***> wrote:

…

ah sorry, didn’t read carefully. You are describing a (basic) continuation method. To reuse the solution, just define Ra as a Constant. Then call the solver multiple times (it uses the contents of the field you want to solve to as an initial state), updating the value of the Constant using the .assign() method. On 30 Dec 2022, at 16:40, Cotter, Colin J ***@***.***> wrote:  Hi Ed, For larger Re you’ll need a continuation method. For running in parallel, <http://firedrakeproject.org/parallelism.html#id2> Parallelism in Firedrake — Firedrake 0.13.0+5418.g660d46b5 documentation< http://firedrakeproject.org/parallelism.html#id2> firedrakeproject.org<http://firedrakeproject.org/parallelism.html#id2> <http://firedrakeproject.org/parallelism.html#id2> <icon.ico> all the best cjc On 30 Dec 2022, at 16:24, ethrelfall ***@***.***> wrote:  Dear community, I have been working with the Rayleigh-B(')enard convection example found at https://www.firedrakeproject.org/demos/rayleigh-benard.py and I would like to be able to access larger values of the Rayleigh number (Ra). As supplied, the example stops converging at Ra=8e5 (this is using the direct solve and so it seems to be a failure of nonlinear convergence). My attempt to improve this is at https://github.com/ethrelfall/Heat-transport/tree/main/Firedrake; by increasing the element order and using a mesh that's refined near the boundaries (see repo) I have been able to run up to about Ra=2e6 ... but I want more. And I don't really understand why the solution is problematic because there is nothing obviously pathological, e.g. a very thin boundary layer, in the solution. Note: it is known that the flows I am running are laminar i.e. the transition to turbulence happens at much larger Ra, above 5e10, as presented in https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/regime-transitions-in-thermally-driven-highrayleigh-number-vertical-convection/2C6892CA314FB35E39818039C64ED799. Is is possible to initialize the nonlinear (=Newton?) solve with a flow field e.g. one calculated at a slightly lower Rayleigh number? (This is the sort of thing I do when running the same problem in Nektar++ using a time-dependent solver.) One other little question - I am currently running Firedrake on one core; is it easy to get it to use multiple cores? (Did search for matching discussions.) Many thanks! Ed. — Reply to this email directly, view it on GitHub< #2698>, or unsubscribe< https://github.com/notifications/unsubscribe-auth/ABOSV4T55FX4PV4QVGLKSQ3WP35BHANCNFSM6AAAAAATM6YIN4>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***> <icon.ico> — Reply to this email directly, view it on GitHub <#2698 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA4XUL4OBQKVJ6ZF7LFTS4TWP37TLANCNFSM6AAAAAATM6YIN4> . You are receiving this because you are subscribed to this thread.Message ID: <firedrakeproject/firedrake/repo-discussions/2698/comments/4556526@ github.com>

[ethrelfall]

Thanks for the advice - I'm now checking out that paper ...