Velocity Correction Scheme and Time Integration Methods
******************* This email originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list https://spam.ic.ac.uk/SpamConsole/Senders.aspx to disable email stamping for this address. ******************* Hello everyone, would somebody be so kind to briefly explain to me what exactly the TimeIntegrationScheme flag does in the session file when there is also a solver type that needs to be set? The Velocity Correction Scheme is a time integration algorithm in itself, so why exactly is setting TimeIntegrationScheme to e.g. IMEXOrder2 needed in addition to choosing VCS? All the best Alex Sicher versendet mit [Proton Mail](https://proton.me/).
Hi Alex, The solver type refers to how you approach solving the given equations. In the case of incompressible Navier-Stokes, there are different approaches. The most common is the velocity-correction scheme (VCS) and it's derivatives. However, there is also a coupled solver for the monolithic system. The TimeIntegrationScheme refers to standard time-stepping schemes. This includes Runge-Kutta, backwards difference formula (BDF), Euler-forward/backward and more specific schemes such as the Implicit-Explicit (IMEX) schemes. You can find a number of examples in e.g. the ADRSolver tests. Your specific combination VCS + IMEXOrder2 leads to a second-order accurate VCS. An alternative might be the first-order accurate scheme via IMEXOrder1. Best wishes, Henrik ________________________________ Von: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> im Auftrag von Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Dienstag, 9. Juli 2024 16:33 An: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: [Nektar-users] Velocity Correction Scheme and Time Integration Methods This email from alexander.schukmann@protonmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. Hello everyone, would somebody be so kind to briefly explain to me what exactly the TimeIntegrationScheme flag does in the session file when there is also a solver type that needs to be set? The Velocity Correction Scheme is a time integration algorithm in itself, so why exactly is setting TimeIntegrationScheme to e.g. IMEXOrder2 needed in addition to choosing VCS? All the best Alex Sicher versendet mit Proton Mail<https://proton.me/>.
Hi Henrik, thank you very much for your answer. But isn‘t the VCS a time integration scheme itself, thus dictating how the governing equations are advanced in time? All the best Alex Sent from [Proton Mail](https://proton.me/mail/home) for iOS Am Mittwoch, 10. Juli 2024 um 09:54, Henrik Wüstenberg <[henrik.wuestenberg@hotmail.de](mailto:Am Mittwoch, 10. Juli 2024 um 09:54, Henrik Wüstenberg <<a href=)> schrieb:
Hi Alex,
The solver type refers to how you approach solving the given equations. In the case of incompressible Navier-Stokes, there are different approaches. The most common is the velocity-correction scheme (VCS) and it's derivatives. However, there is also a coupled solver for the monolithic system.
The TimeIntegrationScheme refers to standard time-stepping schemes. This includes Runge-Kutta, backwards difference formula (BDF), Euler-forward/backward and more specific schemes such as the Implicit-Explicit (IMEX) schemes. You can find a number of examples in e.g. the ADRSolver tests.
Your specific combination VCS + IMEXOrder2 leads to a second-order accurate VCS. An alternative might be the first-order accurate scheme via IMEXOrder1.
Best wishes, Henrik
---------------------------------------------------------------
Von: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> im Auftrag von Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Dienstag, 9. Juli 2024 16:33 An: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: [Nektar-users] Velocity Correction Scheme and Time Integration Methods
This email from alexander.schukmann@protonmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your [safe senders list](https://spam.ic.ac.uk/SpamConsole/Senders.aspx) to disable email stamping for this address.
Hello everyone,
would somebody be so kind to briefly explain to me what exactly the TimeIntegrationScheme flag does in the session file when there is also a solver type that needs to be set? The Velocity Correction Scheme is a time integration algorithm in itself, so why exactly is setting TimeIntegrationScheme to e.g. IMEXOrder2 needed in addition to choosing VCS?
All the best Alex
Sicher versendet mit [Proton Mail](https://proton.me/).
Hi Alex, the VCS is a method to split the incompressible Navier-Stokes system into decoupled problems of scalar equations for pressure and each velocity component. The main idea is advancing the equations in time and, in that sense, you can consider it a time integration scheme. However, it is not a generic time integration scheme, because the VCS is tailored for the incompressible Navier-Stokes equations. It uses the incompressibility condition for decoupling the equations. If you consider other time integration schemes (Runge-Kutta, BDF, Euler-Forward/-Backward), they can be applied to any equation with a time derivative. As such, it makes sense to separate them as either a solver approach for a specific PDE or a generic time integration scheme. I hope this helps. Best wishes, Henrik ________________________________ Von: Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Mittwoch, 10. Juli 2024 11:37 An: Henrik Wüstenberg <henrik.wuestenberg@hotmail.de> Cc: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: AW: [Nektar-users] Velocity Correction Scheme and Time Integration Methods Hi Henrik, thank you very much for your answer. But isn‘t the VCS a time integration scheme itself, thus dictating how the governing equations are advanced in time? All the best Alex Sent from Proton Mail<https://proton.me/mail/home> for iOS Am Mittwoch, 10. Juli 2024 um 09:54, Henrik Wüstenberg <henrik.wuestenberg@hotmail.de<mailto:Am%20Mittwoch,%2010.%20Juli%202024%20um%2009:54,%20Henrik%20Wüstenberg%20<<a%20href=>> schrieb: Hi Alex, The solver type refers to how you approach solving the given equations. In the case of incompressible Navier-Stokes, there are different approaches. The most common is the velocity-correction scheme (VCS) and it's derivatives. However, there is also a coupled solver for the monolithic system. The TimeIntegrationScheme refers to standard time-stepping schemes. This includes Runge-Kutta, backwards difference formula (BDF), Euler-forward/backward and more specific schemes such as the Implicit-Explicit (IMEX) schemes. You can find a number of examples in e.g. the ADRSolver tests. Your specific combination VCS + IMEXOrder2 leads to a second-order accurate VCS. An alternative might be the first-order accurate scheme via IMEXOrder1. Best wishes, Henrik ________________________________ Von: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> im Auftrag von Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Dienstag, 9. Juli 2024 16:33 An: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: [Nektar-users] Velocity Correction Scheme and Time Integration Methods This email from alexander.schukmann@protonmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. Hello everyone, would somebody be so kind to briefly explain to me what exactly the TimeIntegrationScheme flag does in the session file when there is also a solver type that needs to be set? The Velocity Correction Scheme is a time integration algorithm in itself, so why exactly is setting TimeIntegrationScheme to e.g. IMEXOrder2 needed in addition to choosing VCS? All the best Alex Sicher versendet mit Proton Mail<https://proton.me/>.
Hello Henrik, thank you very much for the explanation! All the best Alex Sent from [Proton Mail](https://proton.me/mail/home) for iOS Am Freitag, 12. Juli 2024 um 10:33, Henrik Wüstenberg <[henrik.wuestenberg@hotmail.de](mailto:Am Freitag, 12. Juli 2024 um 10:33, Henrik Wüstenberg <<a href=)> schrieb:
Hi Alex,
the VCS is a method to split the incompressible Navier-Stokes system into decoupled problems of scalar equations for pressure and each velocity component.
The main idea is advancing the equations in time and, in that sense, you can consider it a time integration scheme. However, it is not a generic time integration scheme, because the VCS is tailored for the incompressible Navier-Stokes equations. It uses the incompressibility condition for decoupling the equations.
If you consider other time integration schemes (Runge-Kutta, BDF, Euler-Forward/-Backward), they can be applied to any equation with a time derivative. As such, it makes sense to separate them as either a solver approach for a specific PDE or a generic time integration scheme.
I hope this helps.
Best wishes, Henrik
---------------------------------------------------------------
Von: Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Mittwoch, 10. Juli 2024 11:37 An: Henrik Wüstenberg <henrik.wuestenberg@hotmail.de> Cc: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: AW: [Nektar-users] Velocity Correction Scheme and Time Integration Methods
Hi Henrik,
thank you very much for your answer. But isn‘t the VCS a time integration scheme itself, thus dictating how the governing equations are advanced in time?
All the best Alex
Sent from [Proton Mail](https://proton.me/mail/home) for iOS
Am Mittwoch, 10. Juli 2024 um 09:54, Henrik Wüstenberg <[henrik.wuestenberg@hotmail.de](mailto:Am Mittwoch, 10. Juli 2024 um 09:54, Henrik Wüstenberg <<a href=)> schrieb:
Hi Alex,
The solver type refers to how you approach solving the given equations. In the case of incompressible Navier-Stokes, there are different approaches. The most common is the velocity-correction scheme (VCS) and it's derivatives. However, there is also a coupled solver for the monolithic system.
The TimeIntegrationScheme refers to standard time-stepping schemes. This includes Runge-Kutta, backwards difference formula (BDF), Euler-forward/backward and more specific schemes such as the Implicit-Explicit (IMEX) schemes. You can find a number of examples in e.g. the ADRSolver tests.
Your specific combination VCS + IMEXOrder2 leads to a second-order accurate VCS. An alternative might be the first-order accurate scheme via IMEXOrder1.
Best wishes, Henrik
---------------------------------------------------------------
Von: nektar-users-bounces@imperial.ac.uk <nektar-users-bounces@imperial.ac.uk> im Auftrag von Alexander Schukmann <alexander.schukmann@protonmail.com> Gesendet: Dienstag, 9. Juli 2024 16:33 An: nektar-users@imperial.ac.uk <nektar-users@imperial.ac.uk> Betreff: [Nektar-users] Velocity Correction Scheme and Time Integration Methods
This email from alexander.schukmann@protonmail.com originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your [safe senders list](https://spam.ic.ac.uk/SpamConsole/Senders.aspx) to disable email stamping for this address.
Hello everyone,
would somebody be so kind to briefly explain to me what exactly the TimeIntegrationScheme flag does in the session file when there is also a solver type that needs to be set? The Velocity Correction Scheme is a time integration algorithm in itself, so why exactly is setting TimeIntegrationScheme to e.g. IMEXOrder2 needed in addition to choosing VCS?
All the best Alex
Sicher versendet mit [Proton Mail](https://proton.me/).
participants (2)
-
Alexander Schukmann
-
Henrik Wüstenberg