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

Huang, Daniel Z.; Persson, Per‐Olof; Zahr, Matthew J.

doi:10.1016/j.cma.2018.09.015

Cited by 20 publications

(28 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This work extends the work in [1], and presents arbitrarily high-order partitioned spectral deferred correction schemes for general multiphysics systems. The SDC method, first proposed in [25], is a general class of methods for solving initial value problems determined by ordinary differential equations (ODEs), wherein high-order accuracy is attained by performing a series of correction sweeps using a low-order time-stepping method.…”

Section: Introductionsupporting

confidence: 53%

“…As in the works [1,2], we consider a general formulation for multiple interacting physical processes, described by a coupled system of partial differential equations,…”

Section: Governing Multiphysics Equations and Semi-discrete Formulationmentioning

confidence: 99%

“…The accuracy and stability properties of these partitioned multiphysics solvers are analyzed both analytically and numerically. The comparisons with the partitioned IMEX method in [1] are presented, which suggest the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers, while the IMEX are more efficient for the numerical examples considered in this work. Moreover, it is worth mentioning, the present SDC scheme is capable of handling differential-algebraic system of equations (DAE), which is demonstrated in section 5.3.…”

Section: Introductionmentioning

confidence: 99%

“…As for multiphysics systems, when a partitioned low-order solver is chosen, the proposed multiphysics solver can be both arbitrarily high-order accurate and partitioned. In the present work, these low-order partitioned solvers are designed using the weakly coupled Gauss-Seidel predictor proposed in [1], which features good stability. The accuracy and stability properties of these partitioned multiphysics solvers are analyzed both analytically and numerically.…”

Section: Introductionmentioning

confidence: 99%

“…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, 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.…”

mentioning

confidence: 99%

See 4 more Smart Citations

High-order partitioned spectral deferred correction solvers for multiphysics problems

Huang

Pazner

Persson

et al. 2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

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 including a simple 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.

show abstract

Section: Introductionsupporting

confidence: 53%

“…As in the works [1,2], we consider a general formulation for multiple interacting physical processes, described by a coupled system of partial differential equations,…”

Section: Governing Multiphysics Equations and Semi-discrete Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

High-order partitioned spectral deferred correction solvers for multiphysics problems

Huang

Pazner

Persson

et al. 2020

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Cao

Huang

2022

Numerical Meth Engineering

View full text Add to dashboard Cite

Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative-free and non-intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate. The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an aircraft wing under transonic buffeting.

show abstract

Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods

Sockwell

Bochev

Peterson

et al. 2023

Numerical Methods Partial

View full text Add to dashboard Cite

A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. In this article, we present a novel framework for partitioned heterogeneous time-integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system. We use these estimates to construct a polynomial-in-time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time-integrators for the individual subproblems without compromising the time-accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time-integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air-sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different † K. Chad Sockwell, the lead author of this article, passed away unexpectedly in May of 2022. He was a great friend, brimming with ideas and a contagious enthusiasm for his research. He is dearly missed and we appreciate his very significant contribution to this work.

show abstract

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

Cited by 20 publications

References 37 publications

High-order partitioned spectral deferred correction solvers for multiphysics problems

High-order partitioned spectral deferred correction solvers for multiphysics problems

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Interface flux recovery framework for constructing partitioned heterogeneous time‐integration methods

Contact Info

Product

Resources

About