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dc.contributor.author
Furuichi, Mikito
dc.contributor.author
May, Dave A.
dc.date.accessioned
2023-06-14T13:08:25Z
dc.date.available
2017-06-11T17:15:39Z
dc.date.available
2023-06-14T13:08:25Z
dc.date.issued
2015-07
dc.identifier.issn
0010-4655
dc.identifier.issn
1879-2944
dc.identifier.other
10.1016/j.cpc.2015.02.011
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/100505
dc.identifier.doi
10.3929/ethz-b-000100505
dc.description.abstract
We present implicit time integration schemes suitable for modeling free surface Stokes flow dynamics with marker in cell (MIC) based spatial discretization. Our target is for example thermal convection surrounded by deformable surface boundaries to simulate the long term planetary formation process. The numerical system becomes stiff when the dynamical balancing time scale for the increasing/decreasing load by surface deformation is very short compared with the time scale associated with thermal convection. Any explicit time integration scheme will require very small time steps; otherwise, serious numerical oscillation (spurious solutions) will occur. The implicit time integration scheme possesses a wider stability region than the explicit method; therefore, it is suitable for stiff problems. To investigate an efficient solution method for the stiff Stokes flow system, we apply first (backward Euler (BE)) and second order (trapezoidal method (TR) and trapezoidal rule—backward difference formula (TR-BDF2)) accurate implicit methods for the MIC solution scheme. The introduction of implicit time integration schemes results in nonlinear systems of equations. We utilize a Jacobian free Newton Krylov (JFNK) based Newton framework to solve the resulting nonlinear equations. In this work we also investigate two efficient implicit solution strategies to reduce the computational cost when solving stiff nonlinear systems. The two methods differ in how the advective term in the material transport evolution equation is treated. We refer to the method that employs Lagrangian update as “fully implicit” (Imp), whilst the method that employs Eulerian update is referred to as “semi-implicit” (SImp). Using a finite difference (FD) method, we have performed a series of numerical experiments which clarify the accuracy of solutions and trade-off between the computational cost associated with the nonlinear solver and time step size. In comparison with the general explicit Euler method, the second order accurate Imp methods reduce total computational cost successfully through the utilization of a large time step without sacrificing accuracy and stability. Moreover, the proposed SImp method is effective in reducing the computational cost associated with evaluating the nonlinear residual while obtaining a solution similar to the Imp method.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Stokes flow
en_US
dc.subject
Free surface
en_US
dc.subject
Implicit time integration
en_US
dc.subject
JFNK
en_US
dc.subject
Geodynamics
en_US
dc.subject
TR-BDF2
en_US
dc.title
Implicit solution of the material transport in Stokes flow simulation: Toward thermal convection simulation surrounded by free surface
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2015-02-25
ethz.journal.title
Computer Physics Communications
ethz.journal.volume
192
en_US
ethz.journal.abbreviated
Comput. phys. commun.
ethz.pages.start
1
en_US
ethz.pages.end
11
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.identifier.nebis
000045256
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02330 - Dep. Erdwissenschaften / Dep. of Earth Sciences::02506 - Institut für Geophysik / Institute of Geophysics::03698 - Tackley, Paul / Tackley, Paul
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02330 - Dep. Erdwissenschaften / Dep. of Earth Sciences::02506 - Institut für Geophysik / Institute of Geophysics::03698 - Tackley, Paul / Tackley, Paul
ethz.date.deposited
2017-06-11T17:16:30Z
ethz.source
ECIT
ethz.identifier.importid
imp59365323c40dd99317
ethz.ecitpid
pub:157710
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-14T18:11:47Z
ethz.rosetta.lastUpdated
2024-02-03T00:06:58Z
ethz.rosetta.versionExported
true
ethz.COinS
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