A Lagrangian particle method with remeshing for tracer transport on the sphere

Bosler, Peter Andrew; Kent, James; Krasny, Robert; Jablonowski, Christiane

doi:10.1016/j.jcp.2017.03.052

Cited by 12 publications

(5 citation statements)

References 53 publications

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“…However, since we use the Cartesian coordinate representation of the velocity field u in the trajectory reconstruction, the Lagrangian parcels may not reside on the sphere at time t = t m . Similar to [50], which also uses Cartesian coordinates (albeit in a fully Lagrangian scheme), we have found that the parcels remain very close to the sphere when a high-order integrator is used. In our experiments, we found that both the standard fourth-order Runge-Kutta (RK4) method and Fehlberg's fifth-order Runge-Kutta (RK5) scheme [51], worked well.…”

Section: Trajectory Reconstructionmentioning

confidence: 60%

Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions

Shankar

Wright

2018

Journal of Computational Physics

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We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surface-based coordinate systems. For problems involving tracer transport in a given velocity field, the semi-Lagrangian framework allows these new methods to avoid the use of any stabilization terms (such as hyperviscosity) during timeintegration, thus reducing the number of parameters that have to be tuned. The three new methods are based on interpolation using 1) global RBFs, 2) local RBF stencils, and 3) RBF partition of unity. For the latter two of these methods, we find that it is crucial to include some low degree spherical harmonics in the interpolants. Standard test cases consisting of solid body rotation and deformational flow are used to compare and contrast the methods in terms of their accuracy, efficiency, conservation properties, and dissipation/dispersion errors. For global RBFs, spectral spatial convergence is observed for smooth solutions on quasi-uniform nodes, while high-order accuracy is observed for the local RBF stencil and partition of unity approaches.

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Section: Trajectory Reconstructionmentioning

confidence: 60%

Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions

Shankar

Wright

2018

Journal of Computational Physics

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“…We note that the assumption of equal mass for all particles is convenient but not required, as many Lagrangian models allow for unequal particle masses that may also vary in time (Monaghan, 2012;Tartakovsky et al, 2016;Avesani et al, 2015;Cherfils et al, 2012;Bosler et al, 2017;Schmidt et al, 2020Schmidt et al, , 2019Engdahl et al, 2019;Jiao et al, 2022). The particles in this model are all independently and identically distributed-i.e., two particles beginning at the same position and under the same fluid conditions (or at identical times) will be governed by equivalent position and velocity densities and thus have the same underlying probability density function (PDF).…”

Section: Lagrangian Governing Equationsmentioning

confidence: 99%

Exploring ship track spreading rates with a physics-informed Langevin particle parameterization

McMichael,

Schmidt,

Wood

et al. 2024

Preprint

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Abstract. The rate at which aerosols spread from a point source injection, such as from a ship or other stationary pollution source, is critical for accurately representing subgrid plume spreading in a climate model. Such climate model results will guide future decisions regarding the feasibility and application of large-scale intentional marine cloud brightening (MCB). Prior modeling studies have shown that the rate at which ship plumes spread may be strongly dependent on meteorological conditions, such as precipitating versus non-precipitating boundary layers and shear. In this study, we apply a Lagrangian particle model (PM-ABL v1.0), governed by a Langevin stochastic differential equation, to create a simplified framework for predicting the rate of spreading from a ship-injected aerosol plume in sheared, precipitating, and non-precipitating boundary layers. The velocity and position of each stochastic particle is predicted with the acceleration of each particle being driven by the turbulent kinetic energy, dissipation rate, momentum variance, and mean wind. These inputs to the stochastic particle-velocity equation are derived from high-fidelity large-eddy simulations (LES) equipped with a prognostic aerosol-cloud microphysics scheme (UWSAM) to simulate an aerosol injection from a ship into a cloud-topped marine boundary layer. The resulting spreading rate from the reduced-order stochastic model is then compared to the spreading rate in the LES. The stochastic particle-velocity representation is shown to reasonably reproduce spreading rates in sheared, precipitating, and non-precipitating cases using domain-averaged turbulent statistics from the LES.

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“…The circumvention of issues related to the coordinate singularity inherent to the spherical coordinate system has been the subject of extensive study, notably in the atmospheric modelling community [41,42,43,44]. For linear advection, these issues may be quelled by performing the particle trajectory computations in a Cartesian coordinate system as in [29,20]. The coordinate representation of X [t,0] and its subsequent discretization chosen here is not unique to the method and alternative spatial discretizations are the subject of current research.…”

Section: Time Discretizationmentioning

confidence: 99%

“…Techniques to avoid excessive distortion include reseeding at regular time intervals [14,15,16,17] and adaptive methods [18,19]. Another more recent approach, called indirect remeshing, interpolates the inverse flow map for the Lagrangian trajectories and then re-samples the initial advected quantity [20,21,22]. Finally, the semi-Lagrangian (SL) framework maintains a spatial discretization using an Eulerian grid while computing the evolution in the Lagrangian frame.…”

Section: Introductionmentioning

confidence: 99%

A Characteristic Mapping Method for Tracer Transport on the Sphere

Taylor¹,

Nave²

2021

Preprint

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A semi-Lagrangian method for the solution of the transport equation on a sphere is presented. The method evolves the inverse flow-map using the Characteristic Mapping (CM) [1] and Gradient-Augmented Level Set (GALS) [2] frameworks. Transport of the advected quantity is then computed by composition with the numerically approximated inverse flow-map. This framework allows for the advection of complicated sets and multiple quantities with arbitrarily fine-features using a coarse computational grid. We discuss the CM method for linear transport on the sphere and its computational implementation. Standard test cases for solid body rotation, deformational and divergent flows, and numerical mixing are presented. The unique features of the method are demonstrated by the transport of a multi-scale function and a fractal set in a complex flow environment.

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A Lagrangian particle method with remeshing for tracer transport on the sphere

Cited by 12 publications

References 53 publications

Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions

Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions

Exploring ship track spreading rates with a physics-informed Langevin particle parameterization

A Characteristic Mapping Method for Tracer Transport on the Sphere

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