High-order partitioned spectral deferred correction solvers for multiphysics problems
Abstract
We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verifymore »
- Authors:
-
[1];
[3];
[4]
- Stanford Univ., CA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of California, Berkeley, CA (United States)
- Univ. of Notre Dame, IN (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1736333
- Alternate Identifier(s):
- OSTI ID: 1701942
- Report Number(s):
- LLNL-JRNL-788544
Journal ID: ISSN 0021-9991; 986544; TRN: US2205489
- Grant/Contract Number:
- AC52-07NA27344; LLNL-JRNL-788544
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 412; Journal Issue: na; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Huang, Daniel Z., Pazner, Will, Persson, Per-Olof, and Zahr, Matthew J. High-order partitioned spectral deferred correction solvers for multiphysics problems. United States: N. p., 2020.
Web. doi:10.1016/j.jcp.2020.109441.
Huang, Daniel Z., Pazner, Will, Persson, Per-Olof, & Zahr, Matthew J. High-order partitioned spectral deferred correction solvers for multiphysics problems. United States. https://doi.org/10.1016/j.jcp.2020.109441
Huang, Daniel Z., Pazner, Will, Persson, Per-Olof, and Zahr, Matthew J. Wed .
"High-order partitioned spectral deferred correction solvers for multiphysics problems". United States. https://doi.org/10.1016/j.jcp.2020.109441. https://www.osti.gov/servlets/purl/1736333.
@article{osti_1736333,
title = {High-order partitioned spectral deferred correction solvers for multiphysics problems},
author = {Huang, Daniel Z. and Pazner, Will and Persson, Per-Olof and Zahr, Matthew J.},
abstractNote = {We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.},
doi = {10.1016/j.jcp.2020.109441},
journal = {Journal of Computational Physics},
number = na,
volume = 412,
place = {United States},
year = {Wed Jul 01 00:00:00 EDT 2020},
month = {Wed Jul 01 00:00:00 EDT 2020}
}
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Works referenced in this record:
A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry
journal, March 2016
- Pazner, Will E.; Nonaka, Andrew; Bell, John B.
- Combustion Theory and Modelling, Vol. 20, Issue 3
A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
journal, June 1993
- Chung, J.; Hulbert, G. M.
- Journal of Applied Mechanics, Vol. 60, Issue 2
A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
journal, January 2013
- Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S.
- SIAM Journal on Scientific Computing, Vol. 35, Issue 3
Partitioned procedures for the transient solution of coupled aeroelastic problems – Part II: energy transfer analysis and three-dimensional applications
journal, March 2001
- Piperno, Serge; Farhat, Charbel
- Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 24-25
Fluid-structure interaction with applications in biomechanics
journal, December 2007
- Hron, Jaroslav; Mádlík, Martin
- Nonlinear Analysis: Real World Applications, Vol. 8, Issue 5
Added-mass effect in the design of partitioned algorithms for fluid–structure problems
journal, October 2005
- Causin, P.; Gerbeau, J. F.; Nobile, F.
- Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 42-44
Fixed-point fluid–structure interaction solvers with dynamic relaxation
journal, February 2008
- Küttler, Ulrich; Wall, Wolfgang A.
- Computational Mechanics, Vol. 43, Issue 1
Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations
journal, December 1986
- Tezduyar, T. E.; Park, Y. J.
- Computer Methods in Applied Mechanics and Engineering, Vol. 59, Issue 3
Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity
journal, April 1998
- Farhat, C.; Lesoinne, M.; Le Tallec, P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 157, Issue 1-2
A Unified Proof for the Convergence of Jacobi and Gauss–Seidel Methods
journal, March 1995
- Bagnara, Roberto
- SIAM Review, Vol. 37, Issue 1
Incompressible Limit for Solutionsof the Isentropic Navier–Stokes Equationswith Dirichlet Boundary Conditions
journal, June 1999
- Desjardins, B.; Grenier, E.; Lions, P. -L.
- Journal de Mathématiques Pures et Appliquées, Vol. 78, Issue 5
Large-Eddy Simulation of Realistic Gas Turbine Combustors
journal, April 2006
- Moin, P.; Apte, S. V.
- AIAA Journal, Vol. 44, Issue 4
An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction
journal, October 2017
- Crockatt, Michael M.; Christlieb, Andrew J.; Garrett, C. Kristopher
- Journal of Computational Physics, Vol. 346
On the geometric conservation law in transient flow calculations on deforming domains
journal, January 2006
- Förster, Ch.; Wall, W. A.; Ramm, E.
- International Journal for Numerical Methods in Fluids, Vol. 50, Issue 12
Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow
journal, June 2006
- Bazilevs, Y.; Calo, V. M.; Zhang, Y.
- Computational Mechanics, Vol. 38, Issue 4-5
On the order of deferred correction
journal, August 2011
- Hansen, Anders C.; Strain, John
- Applied Numerical Mathematics, Vol. 61, Issue 8
Toward an efficient parallel in time method for partial differential equations
journal, January 2012
- Emmett, Matthew; Minion, Michael
- Communications in Applied Mathematics and Computational Science, Vol. 7, Issue 1
Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems
journal, February 2000
- Farhat, C.; Lesoinne, M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 182, Issue 3-4
A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations
journal, June 2014
- Christlieb, Andrew; Guo, Wei; Morton, Maureen
- Journal of Computational Physics, Vol. 267
Additive Semi-Implicit Runge–Kutta Methods for Computing High-Speed Nonequilibrium Reactive Flows
journal, October 1996
- Zhong, Xiaolin
- Journal of Computational Physics, Vol. 128, Issue 1
Torsional springs for two-dimensional dynamic unstructured fluid meshes
journal, September 1998
- Farhat, C.; Degand, C.; Koobus, B.
- Computer Methods in Applied Mechanics and Engineering, Vol. 163, Issue 1-4
The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes
journal, July 2000
- Tóth, Gábor
- Journal of Computational Physics, Vol. 161, Issue 2
Partitioned solver for strongly coupled fluid–structure interaction
journal, January 2013
- Habchi, Charbel; Russeil, Serge; Bougeard, Daniel
- Computers & Fluids, Vol. 71
Discontinuous Galerkin solution of the Navier–Stokes equations on deformable domains
journal, April 2009
- Persson, P. -O.; Bonet, J.; Peraire, J.
- Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 17-20
A monolithic approach to fluid–structure interaction
journal, June 2004
- Michler, C.; Hulshoff, S. J.; van Brummelen, E. H.
- Computers & Fluids, Vol. 33, Issue 5-6
High-order fluid–structure interaction in 2D and 3D application to blood flow in arteries
journal, July 2013
- Chabannes, Vincent; Pena, Gonçalo; Prud’homme, Christophe
- Journal of Computational and Applied Mathematics, Vol. 246
Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples
journal, October 2010
- Kassiotis, Christophe; Ibrahimbegovic, Adnan; Niekamp, Rainer
- Computational Mechanics, Vol. 47, Issue 3
Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows
journal, January 2007
- Förster, Christiane; Wall, Wolfgang A.; Ramm, Ekkehard
- Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 7
On the convergence of spectral deferred correction methods
journal, January 2019
- Causley, Mathew; Seal, David
- Communications in Applied Mathematics and Computational Science, Vol. 14, Issue 1
A high-order discontinuous Galerkin method for fluid–structure interaction with efficient implicit–explicit time stepping
journal, September 2014
- Froehle, Bradley; Persson, Per-Olof
- Journal of Computational Physics, Vol. 272
High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes
journal, October 2012
- Tang, Tao; Xie, Hehu; Yin, Xiaobo
- Journal of Scientific Computing, Vol. 56, Issue 1
An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems
journal, December 2016
- Zahr, M. J.; Persson, P. -O.
- Journal of Computational Physics, Vol. 326
A Solution for the Incompressibility Dilemma in Partitioned Fluid–Structure Interaction with Pure Dirichlet Fluid Domains
journal, March 2006
- Küttler, Ulrich; Förster, Christiane; Wall, Wolfgang A.
- Computational Mechanics, Vol. 38, Issue 4-5
Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981
- Roe, P. L.
- Journal of Computational Physics, Vol. 43, Issue 2
Semi-implicit spectral deferred correction methods for ordinary differential equations
journal, January 2003
- Minion, Michael L.
- Communications in Mathematical Sciences, Vol. 1, Issue 3
Energy harvesting through flow-induced oscillations of a foil
journal, December 2009
- Peng, Zhangli; Zhu, Qiang
- Physics of Fluids, Vol. 21, Issue 12
Spectral Deferred Correction Methods for Ordinary Differential Equations
journal, June 2000
- Dutt, Alok; Greengard, Leslie; Rokhlin, Vladimir
- Bit Numerical Mathematics, Vol. 40, Issue 2, p. 241-266
Higher-order temporal integration for the incompressible Navier–Stokes equations in bounded domains
journal, December 2018
- Minion, M. L.; Saye, R. I.
- Journal of Computational Physics, Vol. 375
Numerical simulation of 3-D wing flutter with fully coupled fluid–structural interaction
journal, June 2007
- Chen, Xiangying; Zha, Ge-Cheng; Yang, Ming-Ta
- Computers & Fluids, Vol. 36, Issue 5
On the incompressible limit of the compressible navier-stokes equations
journal, January 1995
- Lin, Chi-Kun
- Communications in Partial Differential Equations, Vol. 20, Issue 3-4
Fluid–structure partitioned procedures based on Robin transmission conditions
journal, July 2008
- Badia, Santiago; Nobile, Fabio; Vergara, Christian
- Journal of Computational Physics, Vol. 227, Issue 14
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
journal, November 1997
- Ascher, Uri M.; Ruuth, Steven J.; Spiteri, Raymond J.
- Applied Numerical Mathematics, Vol. 25, Issue 2-3
Higher-order time integration through smooth mesh deformation for 3D fluid–structure interaction simulations
journal, May 2007
- van Zuijlen, A. H.; de Boer, A.; Bijl, H.
- Journal of Computational Physics, Vol. 224, Issue 1
Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations
journal, April 2017
- Pazner, Will; Persson, Per-Olof
- Journal of Computational Physics, Vol. 335
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
journal, August 2003
- Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.
- Journal of Computational Physics, Vol. 189, Issue 2
Added Mass
Effects of Compressible and Incompressible Flows in Fluid-Structure
Interaction
journal, January 2009
- van Brummelen, E. H.
- Journal of Applied Mechanics, Vol. 76, Issue 2
High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes
journal, April 2019
- Huang, D. Z.; Persson, P. -O.; Zahr, M. J.
- Computer Methods in Applied Mechanics and Engineering, Vol. 346
A monolithic approach to fluid–structure interaction using space–time finite elements
journal, June 2004
- Hübner, Björn; Walhorn, Elmar; Dinkler, Dieter
- Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 23-26
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
journal, January 2008
- Peraire, J.; Persson, P. -O.
- SIAM Journal on Scientific Computing, Vol. 30, Issue 4
Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution
journal, November 1995
- Farhat, Charbel; Lesoinne, Michel; Maman, Nathan
- International Journal for Numerical Methods in Fluids, Vol. 21, Issue 10
A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows
journal, July 2003
- Gerbeau, Jean-Frédéric; Vidrascu, Marina
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 37, Issue 4
On the spectral deferred correction of splitting methods for initial value problems
journal, January 2006
- Hagstrom, Thomas; Zhou, Ruhai
- Communications in Applied Mathematics and Computational Science, Vol. 1, Issue 1
An Implicit, Nonlinear Reduced Resistive MHD Solver
journal, May 2002
- Chacón, L.; Knoll, D. A.; Finn, J. M.
- Journal of Computational Physics, Vol. 178, Issue 1
Fluid–structure interaction for aeroelastic applications
journal, November 2004
- Kamakoti, Ramji; Shyy, Wei
- Progress in Aerospace Sciences, Vol. 40, Issue 8
Multiphysics simulations of rocket engine combustion
journal, June 2011
- Chen, Yen-Sen; Chou, T. H.; Gu, B. R.
- Computers & Fluids, Vol. 45, Issue 1
High-order fluid–structure interaction in 2D and 3D application to blood flow in arteries
journal, July 2013
- Chabannes, Vincent; Pena, Gonçalo; Prud’homme, Christophe
- Journal of Computational and Applied Mathematics, Vol. 246