Variational Discretization Framework for Geophysical Flow Models

Bauer, Werner; Gay–Balmaz, François

doi:10.1007/978-3-030-26980-7_54

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…[75,76]. These ideas have been extended to magneto-hydrodynamics [77,78,79], incompressible flows [80], and geophysical flow [81,82].…”

Section: Overview Of Structure Preserving Methods For Fluid Flowsmentioning

confidence: 99%

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Zhang,

Palha,

Gerritsma

et al. 2021

Preprint

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We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization makes use of a conservative dual-field mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are sought for each variable. A temporal discretization, which staggers the evolution equations and handles the nonlinearity such that the resulting discrete algebraic systems are linear and decoupled, is constructed. The spatial discretization is mimetic in the sense that the finite dimensional function spaces form a discrete de Rham complex. Conservation of mass, kinetic energy and helicity in the absence of dissipative terms is proven at the discrete level. Proper dissipation rates of kinetic energy and helicity in the viscous case is also proven. Numerical tests supporting the method are provided.

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“…[75,76]. These ideas have been extended to magneto-hydrodynamics [77,78,79], incompressible flows [80], and geophysical flow [81,82].…”

Section: Overview Of Structure Preserving Methods For Fluid Flowsmentioning

confidence: 99%

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Zhang,

Palha,

Gerritsma

et al. 2021

Preprint

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show abstract

“…Structure‐preserving discretizations have a long history in atmospheric dynamical cores, going back to the celebrated Arakawa and Lamb scheme (Arakawa & Lamb, 1981). Some recent work in this area for variational formulations is found in Gawlik and Gay‐Balmaz (2021), Bauer and Gay‐Balmaz (2019), Brecht et al. (2019) and for Hamiltonian formulations in Dubos et al.…”

Section: Summary and Future Directionsmentioning

confidence: 99%

Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs)

Lauritzen

Kevlahan

Toniazzo

et al. 2022

J Adv Model Earth Syst

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This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles.

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A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Zhang

Palha

Gerritsma

et al. 2022

Journal of Computational Physics

View full text Add to dashboard Cite

Variational Discretization Framework for Geophysical Flow Models

Cited by 3 publications

References 11 publications

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs)

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

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