A Portal to Yin-Yang Grid

インヤン格子の歴史についての短いコメント：インヤン格子を初めて思いついたのは2002年末でした。この時には新しい球格子として温めていたアイディアが他にも二つほどあったということもあり、しばらく放っておいたのですが、あることがきっかけで（非並列版の）インヤン格子を使った流体ソルバの実装をはじめたところ、一週間ほどでできあがりました。コードを書いているうちに、いろいろなものがなんとなく自然とうまく組み合わさっていくような感覚があり、これは悪くないな、と感じました。 2003年4月、当時わたしが在籍していた地球シミュレータセンターでインヤン格子の話をしました。その時、ソースコードとLaTeXのドキュメントも配布しました。 インヤン格子について地球シミュレータセンターの外で発表したのは2003年10月、核融合研で開催されたシミュレーションサイエンスシンポジウムが最初だったと思います。 2003年12月には数値流体力学シンポジウムで少々意気込んで発表しましたが、ほとんど反響がなく、あまりにもがっかりしたので質疑応答の最後に、少々ふてくされたような感じで「面白くなかったですか？」と聞いてしまったのを覚えています。

2004年の3月末に（まだろくに並列化もしていない段階だったにも関わらず）その年のSCでのGordon Bell賞にインヤン格子のコードで挑戦しなければいけないことになりました。それから一月でMPI並列化とチューニングまでしなければならず、実に大変でした。ジョブスクリプト関係は亀山さん（現在愛媛大）に手伝ってもらい、チューニング関係は津田さん（NEC）に色々と教えていただきましたが、それ以外は、ほとんど私一人でやったと言っていいと思います。まあ、いま思うと若かったからこそできたことだと思います。幸いGordon Bell賞は取れて地球シミュレータの面目を維持することができましたが、この時私が作ったインヤン格子を使ったMHDシミュレーションコードの計算性能はその2年も前の（同じ初代地球シミュレータでの）AFESコードでの記録を大きく下回っています。この年、たまたま国内には他の候補者が、国外には速い計算機がなかったというだけで、HPCの世界ではあまり意味のある記録ではないことは自分でもわかっています。そもそも私はそれまでHPCにはあまり縁がなく、Gordon Bell賞どころかSCという会議についてさえ聞いたことがなかったくらいです。SCにはこの2004年に行ったきりです。

About Yin-Yang Grid

Yin-Yang Grid is a kind of overset grid (or Chimera grid) applied to the spherical geometry. There are infinite variations of the spherical overset grids. Among them, the Yin-Yang grid is the simplest one in the following sense: The number of the component grids is two (minimum); The two component grids are the same size and shape; The component grid is nothing but a low latitude part of the usual spherical polar coordinate (latitude-longitude) grid, which is orthogonal and has the well-known simple metric. Details of the Yin-Yang grid can be found in the paper; Kageyama & Sato, Geochem. Geophys. Geosyst., 2004.

New (2015.12.28): An improved version of Yin-Yang grid, Yin-Yang-Zhong grid, is developed. See our recent paper in JCP. Yin-Yang-Zhong grid makes it possible to perform computations in a full sphere including the center.

Pictures

Source Codes

• A Mathematica code to draw Yin-Yang grid 130529_yin-yang.nb
• An OpenGL code to draw Yin-Yang grid by Mr. Hiroshi Hayashi hayashi_yin_yang_opengl_130917.tar.gz

References

Papers on Yin-Yang grid

• Hiroshi Hayashi and Akira Kageyama, Yin-Yang-Zhong grid: An overset grid system for a sphere, Journal of Computational Physics, 305, 895-905 (2016)
• M. Zerroukat, T. Allen, On the monotonic and conservative transport on overset/Yin-Yang grids, Journal of Computational Physics, 302, 285-299 (2015)
• Xingliang Li, Chungang Chen, Feng Xiao and Xueshun Shen, A high-order multi-moment constrained finite-volume global shallow-water model on the Yin-Yang grid, Quarterly Journal of the Royal Meteorological Society, 141, 2090-2102 (2015)
• Jacqueline Clare Goddard, Viability of the Yin-Yang Grid as a Basis for Future Generations of Atmospheric Models, PhD Thesis, University of Exeter, (2014)
• Chungang Chen, Xingliang Li, Xueshun Shen, Feng Xiao, Global shallow water models based on multi-moment constrained finite volume method and three quasi-uniform spherical grids, Journal of Computational Physics, 271, 191-223 (2014)
• Xingliang Li, Xueshun Shen, Xindong Peng, Feng Xiao, Zhaorong Zhuang, Chungang Chen, Fourth order transport model on Yin-Yang grid by multi-moment constrained finite volume scheme, Procedia Computer Science, 9, 1004-1013 (2012)
• M. Zerroukat and T. Allen, On the Solution of Elliptic Problems on Overset/Yin–Yang Grids, Mon. Wea. Rev., 140, 2756-2767 (2012)
• Hall, David M., Ramachandran D. Nair, Discontinuous Galerkin Transport on the Spherical Yin-Yang Overset Mesh, Mon. Wea. Rev. 141, 264-282 (2013)
• A. Qaddouri, L. Laayouni, S. Loisel, J. Côté, and M. J. Gander, Optimized Schwarz methods with an overset grid for the shallow-water equations: preliminary results, Appl. Numer. Math., 58, 459-471 (2008)
• Akira Kageyama, Dissection of a Sphere and Yin-Yang Grids, J. Earth Sim., 3, 20-28 (2005)
• A. Kageyama, M. Kameyama, S. Fujihara, M. Yoshida, M. Hyodo, Y.Tsuda, A 15.2 TFlops Simulation of Geodynamo on the Earth Simulator, Proc. ACM/IEEE SC2004 Conf. (2004)
• A. Kageyama and T. Sato, "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005 (2004)

Books, reviews, and broad scope papers commenting on Yin-Yang grid

• Shi Tsan WU and Murray DRYER, Comparative analyses of current three-dimensional numerical solar wind models, Science China, Earth Sciences, 58, no.6, pp.839-858 (2015)
• A. Staniforth and J. Thuburn, Horizontal grids for global weather and climate prediction models: a review, Q. J. R. Meteorolog. Soc., 138, 1-26 (2012) [category: meteorology]
• Xuefeng Lü, Chengqui Cheng, Jianya Gong, Li Guan, Review of data storage and management technologies for massive remote sensing data, Sci. China Tech. Sci., 54, 3220-3232 (2011)
• R. J. Purser and M. Rancic, A standardized procedure for the derivation of smooth and partially overset grids on the sphere, associated with polyhedra that admit regular griddings of their surfaces. Part I: Mathematical principles of classification and construction, NOAA/NCEP Office Note 467 (2011)
• Alik Ismail-Zadeh and Paul Tackley, Computational Methods for Geodynamics, 332 pages, Cambridge University Press, 2010
• Peter Olson (editor), Core Dynamics: Treatise on Geophysics, Elsevier, ISBN 9780444534576 (2009)
• W. M. Washington, L. Buja and A. Craig, The computational future for climate and Earth system models: on the path to petaflop and beyond, Phil. Trans. R. Soc. A, 367, 833-846 (2009)
• U. R. Christensen and J. Wicht, 8.08 Numerical Dynamo Simulations, in Treatise on Geophysics, Volume 8. Core Dynamics, Edited by: G. Schubert (2007)
• David L. Williamson, The Evolution of Dynamical Cores for Global Atmospheric Models, Journal of the Meteorological Society of Japan, 85B, 241-269 (2007)
• Jishan Xue and Yan Liu, Numerical weather prediction in China in the new century—Progress, problems and prospects, Advances in Atmospheric Sciences, 24, 1099-1108 (2007)
• Jörn Behrens, Adaptive Atmospheric Modeling, 233 pages, Springer, 2006

Papers using Yin-Yang grid

Geodynamo

• T. Miyagoshi and Y. Hamano, Magnetic Field Variation Caused by Rotational Speed Change in a Magnetohydrodynamic Dynamo, Phys. Rev. Lett., 111, 124501 (2013)
• T. Miyagoshi, A. Kageyama and T. Sato, Formation of sheet plumes, current coils, and helical magnetic fields in a spherical magnetohydrodynamic dynamo, Phys. Plasmas, 18, 072901 (2011)
• T. Miyagoshi, A. Kageyama and T. Sato, Zonal flow formation in the Earth’s core, Nature, 463, 793-796 (2010)
• A. Kageyama, T. Miyagoshi and T. Sato, Formation of current coils in geodynamo simulations, Nature, 454, 1106-1109 (2008)
• A. Kageyama and M. Yoshida, Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid, J. Phys.: Conf. Ser., 16, 325 (2005)

Solar / Astrophysics

• V. P. Utrobin, A. Wongwathanarat, H.-Th. Janka and E. Müller, Supernova 1987A: neutrino-driven explosions in three dimensions and light curves, Astronomy and Astrophysics, 581, A40 (2015)
• Jun Mabuchi, Youhei Masada, and Akira Kageyama, DIFFERENTIAL ROTATION IN MAGNETIZED AND NON-MAGNETIZED STARS, The Astrophysical Journal, 806:10, 16pp (2015)
• Hideyuki Hotta, Thermal Convection, Magnetic Field, and Differential Rotation in Solar-type Stars, Springer Theses, 2015
• A. Wongwathanarat, E. Müller and H.-Th. Janka, Three-dimensional simulations of core-collapse supernovae: from shock revival to shock breakout, Astronomy and Astrophysics, 577, A48 (2015)
• Tobias Melson, Hans-Thomas Janka, and Andreas Marek, NEUTRINO-DRIVEN SUPERNOVA OF A LOW-MASS IRON-CORE PROGENITOR BOOSTED BY THREE-DIMENSIONAL TURBULENT CONVECTION, The Astrophysical Journal Letters, 801:L24, 6pp (2015)
• H. Hotta, M. Rempel, and T. Yokoyama, HIGH-RESOLUTION CALCULATIONS OF THE SOLAR GLOBAL CONVECTION WITH THE REDUCED SPEED OF SOUND TECHNIQUE. I. THE STRUCTURE OF THE CONVECTION AND THE MAGNETIC FIELD WITHOUT THE ROTATION, The Astrophysical Journal, 786, 24 (2014)
• F. Hanke, B. Mueller, A. Wongwathanarat, A. Marek, H.-Th. Janka, SASI Activity in Three-Dimensional Neutrino-Hydrodynamics Simulations of Supernova Cores, Astrophys. J., 770:66, 16pp (2013)
• Eric J. Lentz, Stephen W. Bruenn, J. Austin Harris, Merek Austin Chertkow, W.Raphael Hix, Anthony Mezzacappa, O. E. Bronson Messer, John M. Bondin, Pedro Marronetti, Christopher M. Mauney, Konstantin N. Yakunin, Two- and three-dimensional simulations of core-collapse supernovae with CHIMERA, arXiv:1301.1326 (2013)
• Chaowei Jiang, Xueshang Feng, and Changqing Xiang, A New Code for Nonlinear Force-free Field Extrapolation of the Global Corona, The Astrophysical Journal, 755, 62 (2012)
• A. Wongwathanarat, H. Janka, and E. Müller, Three-dimensional Core-Collapse Supernova Simulations on the Yin-Yang Grid, Astronomical Society of the Pacific Conference Series, 453, 95 (2012)
• D. C. Warren, J. M. Blondin, Three-dimensional numerical investigations of the morphology of type Ia SNRs, MNRAS, 429, 3099-3113 (2013), arXiv:1210.7790
• A. Wongwathanarat, H.-Th. Janka, and E. Müller, Three-dimensional neutrino-driven supernovae: Neutron star kicks, spins, and asymmetric ejection of nucleosynthesis products, arXiv:1210.8148 (2012)
• Eric Raymer, Three-Dimensional Hydrodynamic Simulations of Accretion in Short Period Algols, Monthly Notices of the Royal Astronomical Society, 427, 1702-1712 (2012), arXiv:1209.2167 (2012)
• Xueshang Feng, Chaowei Jiang, Changqing Xiang, Xuepu Zhao, and S. T. Wu, A Data-driven Model for the Global Coronal Evolution, The Astrophysical Journal, 758, 62 (2012)
• E. Müller, H.-Th. Janka and A. Wongwathanarat, Parametrized 3D models of neutrino-driven supernova explosions: Neutrino emission asymmetries and gravitational-wave signals, Astronomy and Astrophysics, 537, A63 (2012)
• John M. Blondin and Eric Raymer, HOYLE-LYTTLETON ACCRETION IN THREE DIMENSIONS, The Astrophysical Journal, 752, 30 (2012)
• T. Lund, A. Wongwathanarat, H.-Th. Janka, E. Müller, and G. Raffelt, Fast time variations of supernova neutrino signals from 3-dimensional models, arXiv:1208.0043 (2012)
• Xueshang Feng, Shaohua Zhang, Changqing Xiang, Liping Yang, Chaowei Jiang, and S. T. Wu, A Hybrid Solar Wind Model of the CESE+HLL Method with a Yin-Yang Overset Grid and an AMR Grid, The Astrophysical Journal, 734, 50 (2011)
• A. Wongwathanarat, N. J. Hammer and E. Müller, An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows, Astronomy and Astrophysics, 514, A48 (2010)
• D. Shiota, K. Kusano, T. Miyoshi, and K. Shibata, Magnetohydrodynamic Modeling for a Formation Process of Coronal Mass Ejections: Interaction Between an Ejecting Flux Rope and an Ambient Field, The Astrophysical Journal, 718, 1305 (2010)

Atmosphere / Ocean

• Mark Buehner, Ron McTaggart-Cowan, Alain Beaulne, Cécilien Charette, Louis Garand, Sylvain Heilliette, Ervig Lapalme, Stéphane Laroche, Stephen R. Macpherson, Josée Morneau, and Ayrton Zadra, Implementation of Deterministic Weather Forecasting Systems Based on Ensemble–Variational Data Assimilation at Environment Canada. Part I: The Global System, Monthly Weather Review, 143, 2532–2559 (2015)
• Jean de Grandpré, Monique Tanguay, Abdessamad Qaddouri, Mohamed Zerroukat, Chris A. McLinden, Semi-Lagrangian advection of stratospheric ozone on a Yin-Yang grid system, Monthly Weather Review, doi:10.1175/MWR-D-15-0142.1 (2015)
• 次世代非静力学モデルasuca, 気象庁数値予報部 数値予報課報告・別冊第 60 号, 1-151 (2014)
• Xingliang Li, Xueshun Shen, Xindong Peng, Feng Xiao, Zhaorong Zhuang, and Chungang Chen, An Accurate Multimoment Constrained Finite Volume Transport Model on Yin-Yang Grids, Advances in Atmospheric Sciences, 30, 1320-1330 (2013)
• K Takahashi, R Onishi, Y Baba, S Kida, K Matsuda, K Goto and H Fuchigami, Challenge toward the prediction of typhoon behaviour and down pour, Journal of Physics: Conference Series 454, 012072 (2013)
• A. Qaddouri, J. Pudykiewicz, M. Tanguay, C. Girard, and J. Côté, Experiments with different discretizations for the shallow-water equations on a sphere, Q. J. R. Meteorolog. Soc., 138, 989-1003 (2012)
• R. Onishi and K. Takahashi, A Warm-Bin–Cold-Bulk Hybrid Cloud Microphysical Model, J. Atmos. Sci., 69, 1474-1497 (2012)
• A. Qaddouri, Nonlinear shallow-water equations on the Yin-Yang grid, Q. J. R. Meteorolog. Soc., 137, 810-818 (2011)
• A. Qaddouri, V. Lee, The Canadian Global Environmental Multiscale model on the Yin-Yang grid system, Q. J. R. Meteorolog. Soc., 137, 1913-1926 (2011)
• K. Takahashi, K. Goto, H. Fuchigami, R. Onishi, Y. Baba, S. Kida and T. Sugimura, High Performance Computing of MSSG with Ultra High Resolution, PaCT 2011, Lecture Notes in Computer Science, 6873, 484-498 (2011)
• Y. Baba, K. Takahashi, and T. Sugimura, Dynamical Core of an Atmospheric General Circulation Model on a Yin–Yang Grid, Mon. Wea. Rev., 138, 3988-4005 (2010)
• Xingliang Li, Dehui Chen, Xindong Peng, Keiko Takahashi, Feng Xiao, A Multimoment Finite-Volume Shallow-Water Model on the Yin–Yang Overset Spherical Grid, Mon. Wea. Rev., 136, 3066-3086 (2008)
• Kazuo Saito, Jun-ichi Ishida, Kohei Aranami, Tabito Hara, Tomonori Segawa, Masami Narita and Yuuki Honda, Nonhydrostatic Atmospheric Models and Operational Development at JMA, Journal of the Meteorological Society of Japan, 85B, 271-304 (2007)
• Xindong Peng, Feng Xiao, Keiko Takahashi, Conservative constraint for a quasi-uniform overset grid on the sphere, Q. J. R. Meteorolog. Soc., 132, 979-996 (2006)

Heliosphere / Magnetosphere / Ionosphere

• D. Shiota, R. Kataoka, Y. Miyoshi, T. Hara, C. Tao, K. Masunaga, Y. Futaana and N. Terada, Inner heliosphere MHD modeling system applicable to space weather forecasting for the other planets, Space Weather, 12, 187-204 (2014)
• Chester J. Weiss, An overset grid method for global geomagnetic induction, Geophysical Journal International, 198, 8-24 (2014)
• K. Sawada and T. Ogino, Three-Dimensional MHD Simulation of Magnetosphere-Ionosphere Coupling, Proceedings of ISSS-7 (2005)

Mantle / Plate dynamics

• Yang Li, Frédéric Deschamps, Paul J. Tackley, Effects of the post-perovskite phase transition properties on the stability and structure of primordial reservoirs in the lower mantle of the Earth, Earth and Planetary Science Letters, 432, 1-12 (2015)
• Masaki Yoshida, Yozo Hamano, Pangea breakup and northward drift of the Indian subcontinent reproduced by a numerical model of mantle convection, Scientific Reports, 5, Article number: 8407 (2015)
• Léa Bello, Nicolas Coltice, Paul J. Tackley, R. Dietmar Müller, John Cannon, Assessing the role of slab rheology in coupled plate-mantle convection models, Earth and Planetary Science Letters, 430, 191-201 (2015)
• Frédéric Deschamps, Yang Li, P. J. Tackley, Large-Scale Thermo-chemical Structure of the Deep Mantle: Observations and Models, The Earth's Heterogeneous Mantle, 479-515, Springer (2015)
• Yang Li, Frédéric Deschamps and Paul J. Tackley, The stability and structure of primordial reservoirs in the lower mantle: insights from models of thermochemical convection in three-dimensional spherical geometry, Geophysical Journal International, 199, 914-930 (2014)
• Yang Li, Frédéric Deschamps, Paul J. Tackley, Effects of low-viscosity post-perovskite on the stability and structure of primordial reservoirs in the lower mantle, Geophysical Research Letters, 41, 7089-7097 (2014)
• C. Yao, F. Deschamps, J. P. Lowman, C. Sanchez-Valle and P. J. Tackley, Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons, Journal of Geophysical Research: Planets (2014)
• Frédéric Deschamps, Chloé Yao, Paul J. Tackley, and C. Sanchez-Valle, High Rayleigh number thermal convection in volumetrically heated spherical shells, JOURNAL OF GEOPHYSICAL RESEARCH, 117, E09006 (2012)
• N. Coltice, T. Rolf, P. J. Tackley, S. Labrosse, Dynamic Causes of the Relation Between Area and Age of the Ocean Floor, Science, 336, 335-338 (2012)
• T. Rolf, N. Coltice, P.J. Tackley, Linking continental drift, plate tectonics and the thermal state of the Earth's mantle, Earth and Planetary Science Letters, 351–352, 134–146 (2012)
• F. Crameri, P. J. Tackley, I. Meilick, T. V. Gerya, and B. J. P. Kaus, A free plate surface and weak oceanic crust produce single-sided subduction on Earth, GEOPHYSICAL RESEARCH LETTERS, 39, L03306 (2012)
• Paul J. Tackley, Michael Ammann, John P. Brodholt, David P. Dobson, Diana Valencia, Mantle Dynamics in Super-Earths: Post-Perovskite Rheology and Self-Regulation of Viscosity, arXiv:1204.3539 (2013)
• T. Rolf and P. J. Tackley, Focussing of stress by continents in 3D spherical mantle convection with self-consistent plate tectonics, Geophys. Res. Lett., 38, L18301 (2011)
• F. Cammarano, P. Tackley, L. Boschi, Seismic, petrological and geodynamical constraints on thermal and compositional structure of the upper mantle: global thermochemical models, Geophysical Journal International, 187, 1301-1318 (2011)
• G. J. Golabek, T. Keller, T. V. Gerya, G. Zhu, P. J. Tackley, J. A. D. Connolly, Origin of the martian dichotomy and Tharsis from a giant impact causing massive magmatism, Icarus, 215, 346-357 (2011)
• P. J. Tackley, Living dead slabs in 3-D: The dynamics of compositionally-stratified slabs entering a "slab graveyard" above the core-mantle boundary, Physics of the Earth and Planetary Interiors, 188, 150-162 (2011)
• T. Nakagawa, P. J. Tackley, F. Deschamps, J. A. D. Connolly, Incorporating self-consistently calculated mineral physics into thermochemical mantle convection simulations in a 3-D spherical shell and its influence on seismic anomalies in Earth's mantle, Geochem. Geophys. Geosyst., 10, Q03004 (2009)
• M. Yoshida, T. Nakakuki, Effects on the long-wavelength geoid anomaly of lateral viscosity variations caused by stiff subducting slabs, weak plate margins and lower mantle rheology, Physics of the Earth and Planetary Interiors, 172, 278-288 (2009)
• T. Nakagawa and P. J. Tackley, Effects of low-viscosity post-perovskite on thermo-chemical mantle convection in a 3-D spherical shell, Geophys. Res. Lett., 38, L04309 (2011)
• M. Yoshida, Core-mantle boundary topography estimated from numerical simulations of instantaneous mantle flow, Geochem. Geophys. Geosyst., 9, Q07002 (2008)
• H. J. van Heck, P. J. Tackley, Planforms of self-consistently generated plates in 3D spherical geometry, Geophys. Res. Lett., 35, L19312 (2008)
• M. Kameyama, A. Kageyama, T. Sato, Multigrid-based simulation code for mantle convection in spherical shell using Yin–Yang grid, Physics of the Earth and Planetary Interiors, 171, 19-32 (2008)
• P. J. Tackley, Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Physics of the Earth and Planetary Interiors, 171, 7-18 (2008)
• M. Yoshida, and A. Kageyama, Low-degree mantle convection with strongly temperature- and depth-dependent viscosity in a three-dimensional spherical shell, J. Geophys. Res., 111, B03412 (2006)
• M. Yoshida and A. Kageyama, Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell, Geophys. Res. Lett., 31, L12609 (2004)

Visualization / Image processing

• Kenji Hara, Kohei Inoue, Kiichi Urahama, Gradient operators for feature extraction from omnidirectional panoramic images, Pattern Recognition Letters, 54, 89-96 (2015)
• Masato Yoshida and Akira Kageyama, A Fortran visualization program for spherical data on a Yin-Yang grid, Geochemistry, Geophysics, Geosystems, 15, 1642-1647 (2014)
• Akira Kageyama and Tomoki Yamada, An Approach to Exascale Visualization: Interactive Viewing of In-Situ Visualization, arXiv:1301.4546 (2012)
• N. Ohno, A. Kageyama, Visualization of spherical data by Yin–Yang grid, Computer Physics Communications, 180, 1534-1538 (2009)
• J. B. S. G. Greensky, W. W. Czech, D. A. Yuen, M. R. Knox, M. R. Damon, S. S. Chen and M. C. Kameyama, Ubiquitous interactive visualization of 3D mantle convection using a web-portal with Java and Ajax framework, Visual Geosciences, 13, 105-115 (2008)
• K. Hara, R. Kurazume, K. Inoue, K.Urahama, Segmentation of Images on Polar Coordinate Meshes, Image Processing, 2007. ICIP 2007. IEEE International Conference on, 2, II-245-II-248 (2007)

Computational Fluid Dynamics

• Justin Merrick, Mark F. Reeder, Cavity-Store Interaction under Supersonic Freestream Conditions, AIAA Aviation, 22-26 June 2015, Dallas, TX, 33rd AIAA Applied Aerodynamics Conference
• Max Cubillos-Moraga, General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time, Dissertation (Ph.D.), California Institute of Technology, (2015)

Others

• Cédric Gillmann, Gregor J. Golabek, Paul J. Tackley, Effect of a single large impact on the coupled atmosphere-interior evolution of Venus, Icarus, doi:10.1016/j.icarus.2015.12.024 (2015)
• Tao Han, Analytical and Computational Studies of Compositional Lipid Microdomains in Bilayer Membranes, Dissertation (Ph.D.), Princeton University, (2015)
• J. Mazurek and L. Smolarek, Oil Spill Models: A State of the Art of the Grid Map as a Function of Wind, Current and Oil Parameters, International Journal on Marine Navigation and Safety of Sea Transportation, 7 (2013)
• C. C. Reese, C. P. Orth, V. S. Solomatov, Impact megadomes and the origin of the martian crustal dichotomy, Icarus, 213, 433-442 (2011)
• C. C. Reese, C. P. Orth, V. S. Solomatov, Impact origin for the Martian crustal dichotomy: Half emptied or half filled?, J. Geophys. Res., 115, E05004 (2010)