High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

Huang, D. Z.; Persson, P. -O.; Zahr, M. J.

doi:10.1016/j.cma.2018.09.015

Title: High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes

Full Record
Other Related Research

Abstract

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the ith subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to bemore »« less

Authors:

Huang, D. Z. ^[1];

^[2];

^[3]

Stanford Univ., Stanford, CA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Notre Dame, Notre Dame, IN (United States)

Publication Date:: 2018-09-21

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1571989

Alternate Identifier(s):: OSTI ID: 1636028

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 346; Journal Issue: C; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Multiphysics simulations; Partitioned solvers; High-order methods; Implicit–explicit Runge–Kutta; Fluid–structure interaction

Citation Formats


                    Huang, D. Z., Persson, P. -O., and Zahr, M. J. High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes.  United States: N. p., 2018. 
Web.  doi:10.1016/j.cma.2018.09.015.

Copy to clipboard


                    Huang, D. Z., Persson, P. -O., & Zahr, M. J. High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes.  United States.  https://doi.org/10.1016/j.cma.2018.09.015

Copy to clipboard


                    Huang, D. Z., Persson, P. -O., and Zahr, M. J. Fri .  
"High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes".  United States.  https://doi.org/10.1016/j.cma.2018.09.015.  https://www.osti.gov/servlets/purl/1571989.

Copy to clipboard


                    
@article{osti_1571989,

  title        = {High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit–explicit Runge–Kutta schemes},

  author       = {Huang, D. Z. and Persson, P. -O. and Zahr, M. J.},

  abstractNote = {This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit–explicit Runge–Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the ith subsystem is coupled to the other subsystems through a coupling term that can depend on the state of all the other subsystems. This coupled system of partial differential equations reduces to a coupled system of ordinary differential equations via the method of lines where an appropriate spatial discretization is applied to each subsystem. The coupled system of ordinary differential equations is taken as a monolithic system and discretized using an IMEX-RK discretization with a specific implicit–explicit decomposition that introduces the concept of a predictor for the coupling term. We propose four coupling predictors that enable the monolithic system to be solved in a partitioned manner, i.e., subsystem-by-subsystem, and preserve the IMEX-RK structure and therefore the design order of accuracy of the monolithic scheme. The four partitioned solvers that result from these predictors are high-order accurate, allow for maximum re-use of existing single-physics software, and two of the four solvers allow the subsystems to be solved in parallel at a given stage and time step. We also analyze the stability of a coupled, linear model problem with a specific coupling structure and show that one of the partitioned solvers achieves unconditional linear stability for this problem, while the others are unconditionally stable only for certain values of the coupling strength. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection–diffusion–reaction systems, fluid–structure interaction problems, and particle-laden flows, where we verify the design order of the IMEX schemes and study various stability properties.},

  doi          = {10.1016/j.cma.2018.09.015},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = C,

  volume       = 346,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.cma.2018.09.015

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

High-order partitioned spectral deferred correction solvers for multiphysics problems

Journal Article Huang, Daniel Z. ; Pazner, Will ; Persson, Per-Olof ; ... - Journal of Computational Physics

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 tomore »« less
https://doi.org/10.1016/j.jcp.2020.109441

Full Text Available
Strong Stability Preserving Integrating Factor Two-Step Runge-Kutta Methods

Journal Article Isherwood, Leah ; Grant, Zachary J. ; Gottlieb, Sigal - Journal of Scientific Computing

In this report, problems with components that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, when nonlinear non-inner-product stability properties are of interest, such as in the evolution of hyperbolic partial differential equations with shocks or sharp gradients, linear inner-product stability is no longer sufficient for convergence, and so strong stability preserving (SSP) methods are often needed. Where the SSP property is needed, IMEX SSP Runge-Kutta (SSP-IMEX) methods have very restrictive time-steps. An alternative to SSP-IMEX schemes is to adoptmore »« less
https://doi.org/10.1007/s10915-019-01046-6

Full Text Available
Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Journal Article Conde, Sidafa ; Gottlieb, Sigal ; Grant, Zachary J. ; ... - Journal of Scientific Computing

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicitmore »« less
Cited by 9
https://doi.org/10.1007/s10915-017-0560-2

Full Text Available
Numerical Stability and Accuracy of Temporally Coupled Multi-Physics Modules in Wind-Turbine CAE Tools

Conference Gasmi, A ; Sprague, M A ; Jonkman, J M ; ...

In this paper we examine the stability and accuracy of numerical algorithms for coupling time-dependent multi-physics modules relevant to computer-aided engineering (CAE) of wind turbines. This work is motivated by an in-progress major revision of FAST, the National Renewable Energy Laboratory's (NREL's) premier aero-elastic CAE simulation tool. We employ two simple examples as test systems, while algorithm descriptions are kept general. Coupled-system governing equations are framed in monolithic and partitioned representations as differential-algebraic equations. Explicit and implicit loose partition coupling is examined. In explicit coupling, partitions are advanced in time from known information. In implicit coupling, there is dependence onmore »« less
https://doi.org/10.2514/6.2013-203

Full Text Available
Efficient IMEX Runge-Kutta Methods for Nonhydrostatic Dynamics

Journal Article Steyer, Andrew ; Vogl, Christopher J. ; Taylor, Mark ; ... - SIAM Journal on Scientific Computing

We develop new implicit-explicit Runge-Kutta (IMEX RK) methods for integrating horizontally explicit, vertically implicit (HEVI) partitionings of nonhydrostatic atmosphere models (HEVI models). These new methods, termed IMKG methods, are IMEX RK methods whose explicit part has optimal or near-optimal stability on the imaginary axis and whose implicit part is I-stable. A specialized stability region is presented for characterizing the stability of IMKG and other IMEX methods integrating HEVI models. Subsequently, we formulate two families of IMEX RK methods to enable deriving IMKG methods with a high explicit stage count for integrating HEVI models with large, stable time-steps. Here, we thenmore »« less
Full Text Available

Similar Records