Interface Flux Recovery coupling method for the ocean–atmosphere system

Sockwell, K. Chad; Peterson, Kara J.; Kuberry, Paul; Bochev, Pavel B.; Trask, Nat

doi:10.1016/j.rinam.2020.100110

Cited by 12 publications

(11 citation statements)

References 16 publications

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“…The overall accuracy and stability of the coupling schemes are not widely explored in the context of Earth system models because of their complexity and computational demands [14]. Recent efforts target various coupling strategies such as synchronous partitioned schemes for convection-diffusion equations [15,16], partitioned coupling algorithms for diffusion equations [14], global-in-time Schwarz methods for diffusion equations [17], operator splitting methods for incompressible Navier-Stokes equations [18], and sequential and concurrent coupling approaches for the Boussinesq convection model [19].…”

Section: Introductionmentioning

confidence: 99%

Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations

Kang,

Constantinescu,

Zhang

et al. 2021

Preprint

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Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study we focus on these issues. In particular, implicit-explicit (IMEX) tight and loose coupling strategies are explored for handling different time scales. For a simplified model for the air-sea interaction problem, we consider coupled compressible Navier-Stokes equations with an interface condition. Under the rigid-lid assumption, horizontal momentum and heat flux are exchanged through the interface. Several numerical experiments are presented to demonstrate the stability of the coupling schemes. We show both numerically and theoretically that our IMEX coupling methods are mass conservative for a coupled compressible Navier-Stokes system with the rigid-lid condition.

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Section: Introductionmentioning

confidence: 99%

Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations

Kang,

Constantinescu,

Zhang

et al. 2021

Preprint

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“…This puts the problem into the form of a system of differential algebraic equations (DAEs), in which the auxiliary equation is an algebraic condition in time. In following the solution methods for DAE formulations with coupled problems [20,28,13,2], the new auxiliary problem could then be solved before the individual subproblems to determine the fluxes over the coupling window. Then each subproblem can utilize the flux, which is now defined at all substeps.…”

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confidence: 99%

“…The L 2 -projection couples the data for all substeps on a window, so they would need to be computed together. In practice, this might be possible using dual Schur-complement technique of the monolithic system [22,23,13,20,28], that isolate the flux at the interface Γ that can then be utilized to construct a partitioned solve of the two subproblems. We therefore refer to the methods as monolithic.…”

mentioning

confidence: 99%

“…The DAE is trivial in some sense because it leads directly to an ODE through substitution of the interface condition in the model equations. Although we could work directly with the ODE, retaining the structure of a DAE lends itself to the development of coupling algorithms [28]. The algebraic constraints can be eliminated through the enforcement of a Neumann condition, leading to an equivalent set of ODE's with the variational form…”

mentioning

confidence: 99%

“…In a sense, the details of the ODE-DAE equivalence can be exploited to develop coupling algorithms through the implicit function of the algebraic constraint. In [22,23,13,20,28], the so-called dual-Schur complement methods that isolates the fluxes F i at the interface Γ leading to "implicitly-coupled" algorithms that are consistent with the underlying implicit discretization. We simply wish to note this relation to identify possible solution algorithms to be appliedwith our monolithic framework.…”

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confidence: 99%

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A Multirate Discontinuous-Galerkin-in-Time Framework for Interface-Coupled Problems

Connors¹,

Sockwell²

2021

Preprint

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A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution variables for both models to each other. The multirate aspect arises when numerical time integration is performed with different time step sizes for the component models. In this paper, we seek to identify a unified approach to develop multirate algorithms for these coupled problems. This effort is pursued though the use of discontinuous-Galerkin time stepping methods, acting as a general unified framework, with different time step sizes. The subproblems are coupled across user-defined intervals of time, called coupling windows, using polynomials that are continuous on the window. The coupling method is shown to reproduce the correct interfacial energy dissipation, discrete conservation of fluxes, and asymptotic accuracy. In principle, methods of arbitrary order are possible. As a first step, herein we focus on the presentation and analysis of monolithic methods for advection-diffusion models coupled via generalized Robintype conditions. The monolithic methods could be computed using a Schur-complement approach. We conclude with some discussion of future developments, such as different interface conditions and partitioned methods.

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

Sockwell

Bochev

Peterson

et al. 2023

Numerical Methods Partial

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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.

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Interface Flux Recovery coupling method for the ocean–atmosphere system

Cited by 12 publications

References 16 publications

Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations

Mass-Conserving Implicit-Explicit Methods for Coupled Compressible Navier-Stokes Equations

A Multirate Discontinuous-Galerkin-in-Time Framework for Interface-Coupled Problems

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

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