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

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

Journal Article · Thu Mar 30 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.03.052· OSTI ID:1369441

^[1]; Kent, James ^[2]; Krasny, Robert ^[3]; Jablonowski, Christiane ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of South Wales, Pontypridd (United Kingdom)
Univ. of Michigan, Ann Arbor, MI (United States)

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1369441

Report Number(s):: SAND-2015-6438J; 598993

Journal Information:: Journal of Computational Physics, Vol. 340, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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References (52)

Advances in viscous vortex methods?meshless spatial adaption based on radial basis function interpolation Barba, L. A.; Leonard, A.; Allen, C. B. International Journal for Numerical Methods in Fluids, Vol. 47, Issue 5 https://doi.org/10.1002/fld.811	journal	January 2005
Icosahedral Discretization of the Two-Sphere Baumgardner, John R.; Frederickson, Paul O. SIAM Journal on Numerical Analysis, Vol. 22, Issue 6 https://doi.org/10.1137/0722066	journal	December 1985
High order accurate vortex methods with explicit velocity kernels Beale, J. T.; Majda, A. Journal of Computational Physics, Vol. 58, Issue 2 https://doi.org/10.1016/0021-9991(85)90176-7	journal	April 1985
Evolution of Small-Scale Filaments in an Adaptive Advection Model for Idealized Tracer Transport Behrens, J.; Dethloff, K.; Hiller, W. Monthly Weather Review, Vol. 128, Issue 8 https://doi.org/10.1175/1520-0493(2000)128<2976:EOSSFI>2.0.CO;2	journal	August 2000
Grid-free adaptive semi-Lagrangian advection using radial basis functions Behrens, J.; Iske, A. Computers & Mathematics with Applications, Vol. 43, Issue 3-5 https://doi.org/10.1016/S0898-1221(01)00289-9	journal	February 2002
Multilevel Adaptive Particle Methods for Convection-Diffusion Equations Bergdorf, Michael; Cottet, Georges-Henri; Koumoutsakos, Petros Multiscale Modeling & Simulation, Vol. 4, Issue 1 https://doi.org/10.1137/040602882	journal	January 2005
Local adaptive mesh refinement for shock hydrodynamics Berger, M. J.; Colella, P. Journal of Computational Physics, Vol. 82, Issue 1 https://doi.org/10.1016/0021-9991(89)90035-1	journal	May 1989
Fast optimization-based conservative remap of scalar fields through aggregate mass transfer Bochev, Pavel; Ridzal, Denis; Shashkov, Mikhail Journal of Computational Physics, Vol. 246 https://doi.org/10.1016/j.jcp.2013.03.040	journal	August 2013
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
The remapped particle-mesh semi-Lagrangian advection scheme Cotter, C. J.; Frank, J.; Reich, S. Quarterly Journal of the Royal Meteorological Society, Vol. 133, Issue 622 https://doi.org/10.1002/qj.11	journal	January 2007
Trajectory-Tracking Scheme in Lagrangian Form for Solving Linear Advection Problems: Interface Spatial Discretization Dong, Li; Wang, Bin Monthly Weather Review, Vol. 141, Issue 1 https://doi.org/10.1175/MWR-D-12-00058.1	journal	January 2013
A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields Dritschel, David G.; Ambaum, Maarten H. P. Quarterly Journal of the Royal Meteorological Society, Vol. 123, Issue 540 https://doi.org/10.1002/qj.49712354015	journal	April 1997
Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations Dukowicz, John K.; Kodis, John W. SIAM Journal on Scientific and Statistical Computing, Vol. 8, Issue 3 https://doi.org/10.1137/0908037	journal	May 1987
Azimuthal instability of a vortex ring computed by a vortex sheet panel method Feng, Hualong; Kaganovskiy, Leon; Krasny, Robert Fluid Dynamics Research, Vol. 41, Issue 5 https://doi.org/10.1088/0169-5983/41/5/051405	journal	September 2009
Transport schemes on a sphere using radial basis functions Flyer, Natasha; Wright, Grady B. Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.05.009	journal	September 2007
Rotational transport on a sphere: Local node refinement with radial basis functions Flyer, Natasha; Lehto, Erik Journal of Computational Physics, Vol. 229, Issue 6 https://doi.org/10.1016/j.jcp.2009.11.016	journal	March 2010
Stabilization of RBF-generated finite difference methods for convective PDEs Fornberg, Bengt; Lehto, Erik Journal of Computational Physics, Vol. 230, Issue 6 https://doi.org/10.1016/j.jcp.2010.12.014	journal	March 2011
Could a Pile of Slippery Sacks Behave Like an Ocean? Haertel, Patrick T.; Randall, David A. Monthly Weather Review, Vol. 130, Issue 12 https://doi.org/10.1175/1520-0493(2002)130<2975:CAPOSS>2.0.CO;2	journal	December 2002
An arbitrary Lagrangian-Eulerian computing method for all flow speeds Hirt, C. W.; Amsden, A. A.; Cook, J. L. Journal of Computational Physics, Vol. 14, Issue 3 https://doi.org/10.1016/0021-9991(74)90051-5	journal	March 1974
A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics Kaas, E.; Sørensen, B.; Lauritzen, P. H. Geoscientific Model Development, Vol. 6, Issue 6 https://doi.org/10.5194/gmd-6-2023-2013	journal	January 2013
Assessing implicit large eddy simulation for two-dimensional flow Kent, James; Thuburn, John; Wood, Nigel Quarterly Journal of the Royal Meteorological Society, Vol. 138, Issue 663 https://doi.org/10.1002/qj.925	journal	September 2011
Downscale cascades in tracer transport test cases: an intercomparison of the dynamical cores in the Community Atmosphere Model CAM5 Kent, J.; Jablonowski, C.; Whitehead, J. P. Geoscientific Model Development, Vol. 5, Issue 6 https://doi.org/10.5194/gmd-5-1517-2012	journal	January 2012
Dynamical core model intercomparison project: Tracer transport test cases: DCMIP tracer tests Kent, James; Ullrich, Paul A.; Jablonowski, Christiane Quarterly Journal of the Royal Meteorological Society, Vol. 140, Issue 681 https://doi.org/10.1002/qj.2208	journal	July 2013
High-resolution simulations of the flow around an impulsively started cylinder using vortex methods Koumoutsakos, P.; Leonard, A. Journal of Fluid Mechanics, Vol. 296 https://doi.org/10.1017/S0022112095002059	journal	August 1995
Block-Structured Adaptive Grids on the Sphere: Advection Experiments Jablonowski, Christiane; Herzog, Michael; Penner, Joyce E. Monthly Weather Review, Vol. 134, Issue 12 https://doi.org/10.1175/MWR3223.1	journal	December 2006
CAM-chem: description and evaluation of interactive atmospheric chemistry in the Community Earth System Model Lamarque, J. -F.; Emmons, L. K.; Hess, P. G. Geoscientific Model Development, Vol. 5, Issue 2 https://doi.org/10.5194/gmd-5-369-2012	journal	January 2012
A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid Lauritzen, Peter H.; Nair, Ramachandran D.; Ullrich, Paul A. Journal of Computational Physics, Vol. 229, Issue 5 https://doi.org/10.1016/j.jcp.2009.10.036	journal	March 2010
A standard test case suite for two-dimensional linear transport on the sphere Lauritzen, P. H.; Skamarock, W. C.; Prather, M. J. Geoscientific Model Development, Vol. 5, Issue 3 https://doi.org/10.5194/gmd-5-887-2012	journal	January 2012
A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes Lauritzen, P. H.; Ullrich, P. A.; Jablonowski, C. Geoscientific Model Development, Vol. 7, Issue 1 https://doi.org/10.5194/gmd-7-105-2014	journal	January 2014
Evaluating advection/transport schemes using interrelated tracers, scatter plots and numerical mixing diagnostics Lauritzen, P. H.; Thuburn, J. Quarterly Journal of the Royal Meteorological Society, Vol. 138, Issue 665 https://doi.org/10.1002/qj.986	journal	November 2011
Multidimensional Flux-Form Semi-Lagrangian Transport Schemes Lin, Shian-Jiann; Rood, Richard B. Monthly Weather Review, Vol. 124, Issue 9 https://doi.org/10.1175/1520-0493(1996)124<2046:MFFSLT>2.0.CO;2	journal	September 1996
A “Vertically Lagrangian” Finite-Volume Dynamical Core for Global Models Lin, Shian-Jiann Monthly Weather Review, Vol. 132, Issue 10 https://doi.org/10.1175/1520-0493(2004)132<2293:AVLFDC>2.0.CO;2	journal	October 2004
Accurate, non-oscillatory, remeshing schemes for particle methods Magni, Adrien; Cottet, Georges-Henri Journal of Computational Physics, Vol. 231, Issue 1 https://doi.org/10.1016/j.jcp.2011.09.005	journal	January 2012
Moving Vortices on the Sphere: A Test Case for Horizontal Advection Problems Nair, Ramachandran D.; Jablonowski, Christiane Monthly Weather Review, Vol. 136, Issue 2 https://doi.org/10.1175/2007MWR2105.1	journal	February 2008
A Discontinuous Galerkin Transport Scheme on the Cubed Sphere Nair, Ramachandran D.; Thomas, Stephen J.; Loft, Richard D. Monthly Weather Review, Vol. 133, Issue 4 https://doi.org/10.1175/MWR2890.1	journal	April 2005
A class of deformational flow test cases for linear transport problems on the sphere Nair, Ramachandran D.; Lauritzen, Peter H. Journal of Computational Physics, Vol. 229, Issue 23 https://doi.org/10.1016/j.jcp.2010.08.014	journal	November 2010
Rezoning for higher order vortex methods Nordmark, Henrik O. Journal of Computational Physics, Vol. 97, Issue 2 https://doi.org/10.1016/0021-9991(91)90005-6	journal	December 1991
On the accuracy of vortex methods Perlman, Mirta Journal of Computational Physics, Vol. 59, Issue 2 https://doi.org/10.1016/0021-9991(85)90142-1	journal	June 1985
The effects of mixing on tracer relationships in the polar vortices Plumb, R. Alan; Waugh, Darryn W.; Chipperfield, Martyn P. Journal of Geophysical Research: Atmospheres, Vol. 105, Issue D8 https://doi.org/10.1029/1999JD901023	journal	April 2000
Finite-volume transport on various cubed-sphere grids Putman, William M.; Lin, Shian-Jiann Journal of Computational Physics, Vol. 227, Issue 1 https://doi.org/10.1016/j.jcp.2007.07.022	journal	November 2007
Quantifying errors in trace species transport modeling Prather, M. J.; Zhu, X.; Strahan, S. E. Proceedings of the National Academy of Sciences, Vol. 105, Issue 50 https://doi.org/10.1073/pnas.0806541106	journal	December 2008
Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere Renka, Robert J. ACM Transactions on Mathematical Software, Vol. 23, Issue 3 https://doi.org/10.1145/275323.275329	journal	September 1997
Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension Renka, Robert J. ACM Transactions on Mathematical Software, Vol. 23, Issue 3 https://doi.org/10.1145/275323.275330	journal	September 1997
Numerical advection algorithms and their role in atmospheric transport and chemistry models Rood, Richard B. Reviews of Geophysics, Vol. 25, Issue 1 https://doi.org/10.1029/RG025i001p00071	journal	January 1987
Semi-Lagrangian Integration Schemes for Atmospheric Models—A Review Staniforth, Andrew; Côté, Jean Monthly Weather Review, Vol. 119, Issue 9 https://doi.org/10.1175/1520-0493(1991)119<2206:SLISFA>2.0.CO;2	journal	September 1991
A compatible and conservative spectral element method on unstructured grids Taylor, Mark A.; Fournier, Aimé Journal of Computational Physics, Vol. 229, Issue 17 https://doi.org/10.1016/j.jcp.2010.04.008	journal	August 2010
Numerical advection schemes, cross-isentropic random walks, and correlations between chemical species Thuburn, John; McIntyre, Michael E. Journal of Geophysical Research: Atmospheres, Vol. 102, Issue D6 https://doi.org/10.1029/96JD03514	journal	March 1997
Contour Advection with Surgery: A Technique for Investigating Finescale Structure in Tracer Transport Waugh, Darryn W.; Plumb, R. Alan Journal of the Atmospheric Sciences, Vol. 51, Issue 4 https://doi.org/10.1175/1520-0469(1994)051<0530:CAWSAT>2.0.CO;2	journal	February 1994
Modified interpolation kernels for treating diffusion and remeshing in vortex methods Wee, Daehyun; Ghoniem, Ahmed F. Journal of Computational Physics, Vol. 213, Issue 1 https://doi.org/10.1016/j.jcp.2005.08.009	journal	March 2006
A standard test set for numerical approximations to the shallow water equations in spherical geometry Williamson, David L.; Drake, John B.; Hack, James J. Journal of Computational Physics, Vol. 102, Issue 1 https://doi.org/10.1016/S0021-9991(05)80016-6	journal	September 1992
RBF-vortex methods for the barotropic vorticity equation on a sphere Xiao, Jianping; Wang, Lei; Boyd, John P. Journal of Computational Physics, Vol. 285 https://doi.org/10.1016/j.jcp.2015.01.005	journal	March 2015
SLICE: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems Zerroukat, Mohamed; Wood, Nigel; Staniforth, Andrew Quarterly Journal of the Royal Meteorological Society, Vol. 128, Issue 586 https://doi.org/10.1256/qj.02.69	journal	October 2002

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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tracer transport
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remeshing
adaptive refinement

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

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References (52)

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