{"id":1180,"date":"2015-08-17T16:17:32","date_gmt":"2015-08-17T16:17:32","guid":{"rendered":"https:\/\/www.ime.usp.br\/~pedrosp\/?page_id=1180"},"modified":"2024-08-29T13:14:15","modified_gmt":"2024-08-29T13:14:15","slug":"fluids-sphere","status":"publish","type":"page","link":"https:\/\/www.ime.usp.br\/~pedrosp\/fluids-sphere\/","title":{"rendered":"Numerical Methods and Fluid Dynamics"},"content":{"rendered":"\n<p>Main results and further information on the research area of numerical methods and computational geophysical fluid dynamics, mainly focused on the application on atmospheric modelling.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Selected Talks<\/h2>\n\n\n\n<div class=\"wp-block-ugb-icon-list ugb-icon-list ugb-57cb914 ugb-icon-list--v2 ugb-main-block\"><style>.ugb-57cb914 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ul{columns:1}<\/style><div class=\"ugb-inner-block\"><div class=\"ugb-block-content\"><ul><li>Results of a moist shallow-water model on locally refined Spherical Voronoi grids: The Andes Problem (SIAM-SCE-2021) &#8211; <a rel=\"noreferrer noopener\" href=\"https:\/\/www.ime.usp.br\/~pedrosp\/talks\/2021-SIAM-CSE.pdf\" target=\"_blank\">PDF<\/a><\/li><li>Challenges of mathematical and numerical modelling of the atmosphere dynamics (UNB-2021) &#8211; <a rel=\"noreferrer noopener\" href=\"https:\/\/www.ime.usp.br\/~pedrosp\/talks\/2020-UNB.pdf\" target=\"_blank\">PDF<\/a><\/li><li>Semi-Lagrangian Exponential Integration with application to the rotating shallow water equations (PDEs on the Sphere &#8211; 2019) &#8211; <a rel=\"noreferrer noopener\" href=\"https:\/\/www.ime.usp.br\/~pedrosp\/talks\/2019-PDEs.pdf\" target=\"_blank\">PDF<\/a><\/li><li>Current trends for global atmosphere dynamical core development: Traditional and modern approaches (CPTEC &#8211; 2019) &#8211; <a rel=\"noreferrer noopener\" href=\"https:\/\/www.ime.usp.br\/~pedrosp\/talks\/2019-CPTEC.pdf\" target=\"_blank\">PDF<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Selected Scientific Results (up to 2021)<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55.png\"><img loading=\"lazy\" decoding=\"async\" width=\"614\" height=\"608\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55.png\" alt=\"\" class=\"wp-image-1558\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55.png 614w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55-300x297.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55-150x150.png 150w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2021\/10\/Screenshot-from-2021-10-25-10-08-55-332x329.png 332w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Topography based local spherical Voronoi grid refinement<\/h3>\n\n\n\n<p>This paper describes how to generate SCVT grids that are locally refined in South America and that also captures the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite volume scheme employed in the MPAS dynamical core on this grid considering the non-linear classic and moist shallow-water equations on the sphere.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Santos, L.F. and Peixoto, P.S., 2021. Topography based local spherical Voronoi grid refinement on classical and moist shallow-water finite volume models. Geoscientific Model Development, pp.1-31. <a href=\"https:\/\/gmd.copernicus.org\/articles\/14\/6919\/2021\/\">https:\/\/gmd.copernicus.org\/articles\/14\/6919\/2021\/<\/a><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"660\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-1024x660.png\" alt=\"\" class=\"wp-image-1082\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-1024x660.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-300x193.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-768x495.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-700x451.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1-332x214.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-05-16-1.png 1427w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Comparing Numerical Accuracy of Icosahedral A-Grid and C-Grid Schemes in Solving the Shallow-Water Model<\/h3>\n\n\n\n<p>A collaborative study with NOAA-USA researchers comparing finite volume schemes currently used in two important models: MPAS (USA) and NICAM (Japan).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Yu, Y.G., Wang, N., Middlecoff, J., Peixoto, P.S. and Govett, M.W., 2020. Comparing Numerical Accuracy of Icosahedral A-Grid and C-Grid Schemes in Solving the Shallow-Water Model. Monthly Weather Review, 148(10), pp.4009-4033. <a href=\"https:\/\/doi.org\/10.1175\/MWR-D-20-0024.1\">https:\/\/doi.org\/10.1175\/MWR-D-20-0024.1<\/a><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"545\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-1024x545.png\" alt=\"\" class=\"wp-image-1089\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-1024x545.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-300x160.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-768x409.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-700x373.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1-332x177.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-40-55-1.png 1228w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"402\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-1024x402.png\" alt=\"\" class=\"wp-image-1086\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-1024x402.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-300x118.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-768x302.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-700x275.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13-332x130.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/11\/Screenshot-from-2020-11-29-20-42-13.png 1253w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Semi-Lagrangian Exponential Integration with application to the rotating shallow water equations<\/h3>\n\n\n\n<p>In this paper, we propose a new class of numerical schemes formed from the fusion of two other classes of methods: Exponential integrators and semi-Lagrangian schemes. These new methods have the potential to allow larger time steps on equations with nonlinear advection with less impact on linear waves. Joint work with Martin Schreiber (TU Munich).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Peixoto, P.S. and Schreiber, M., 2019. Semi-Lagrangian Exponential Integration with application to the rotating shallow water equations.\u00a0<em>SIAM Journal on Scientific Computing<\/em>,\u00a0<em>41<\/em>(5), pp.B903-B928.  <a href=\"https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/18M1206497\">https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/18M1206497<\/a><a href=\"https:\/\/pedrosp.ime.usp.br\/papers\/PeixotoSchreiber2019-SISC.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"391\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-1024x391.jpg\" alt=\"\" class=\"wp-image-1129\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-1024x391.jpg 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-300x115.jpg 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-768x293.jpg 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-1536x587.jpg 1536w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-2048x782.jpg 2048w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-700x267.jpg 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/qj3191-fig-0002-m-332x127.jpg 332w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"404\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-1024x404.png\" alt=\"\" class=\"wp-image-1137\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-1024x404.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-300x119.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-768x303.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-700x277.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40-332x131.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-49-40.png 1324w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"431\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-1024x431.png\" alt=\"\" class=\"wp-image-1139\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-1024x431.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-300x126.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-768x323.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-1536x646.png 1536w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-700x295.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1-332x140.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-45-31-1.png 1911w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Numerical instabilities (Hollingsworth) on shallow water models with small equivalent depths<\/h3>\n\n\n\n<p>Research in collaboration with J. Thuburn (U. Exeter &#8211; UK) and M. Bell (UK MetOffice) about this intriguing numerical instability that has been affecting modern weather and climate models.<\/p>\n\n\n\n<p>Peixoto, P.S., Thuburn, J. and Bell, M.J., 2018. Numerical instabilities of spherical shallow\u2010water models considering small equivalent depths.\u00a0<em>Quarterly Journal of the Royal Meteorological Society<\/em>,\u00a0<em>144<\/em>(710), pp.156-171. <a href=\"https:\/\/doi.org\/10.1002\/qj.3191\">https:\/\/doi.org\/10.1002\/qj.3191<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><\/p>\n<\/div>\n<\/div>\n\n\n\n<p>Bell, M.J., Peixoto, P.S. and Thuburn, J., 2017. Numerical instabilities of vector\u2010invariant momentum equations on rectangular C\u2010grids.\u00a0<em>Quarterly Journal of the Royal Meteorological Society<\/em>,\u00a0<em>143<\/em>(702), pp.563-581. <a href=\"https:\/\/doi.org\/10.1002\/qj.2950\">https:\/\/doi.org\/10.1002\/qj.2950<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"669\" height=\"727\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-58-04.png\" alt=\"\" class=\"wp-image-1142\" style=\"width:284px;height:308px\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-58-04.png 669w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-58-04-276x300.png 276w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-13-58-04-332x361.png 332w\" sizes=\"auto, (max-width: 669px) 100vw, 669px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Time parallelism in non-linear advection <\/h3>\n\n\n\n<p>Collaboration with researchers of TU Darmstadt (Germany) and   Univ. de Exeter (UK) on the proposition of a parallel in time method with a semi-Lagrangian coarse solver.<\/p>\n\n\n\n<p>Schmitt, A., Schreiber, M., Peixoto, P. and Sch\u00e4fer, M., 2018. A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation.\u00a0<em>Computing and Visualization in Science<\/em>,\u00a0<em>19<\/em>(1-2), pp.45-57. <a href=\"https:\/\/doi.org\/10.1007\/s00791-018-0294-1\">https:\/\/doi.org\/10.1007\/s00791-018-0294-1<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"584\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-1024x584.png\" alt=\"\" class=\"wp-image-1148\" style=\"width:282px;height:160px\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-1024x584.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-300x171.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-768x438.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-700x399.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12-332x189.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-12.png 1467w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"484\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-1024x484.png\" alt=\"\" class=\"wp-image-1149\" style=\"width:290px;height:136px\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-1024x484.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-300x142.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-768x363.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-700x331.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36-332x157.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-05-36.png 1054w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Massively parallel exponential integrator<\/h3>\n\n\n\n<p>Research in collaboration with researchers of the University of Exeter (UK) and Los Alamos Nat. Lab (USA) aiming to solve PDEs with linear oscillatory operators with a highly parallel exponential integration technique. <\/p>\n\n\n\n<p>Schreiber, M., Peixoto, P.S., Haut, T. and Wingate, B., 2018. Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems.\u00a0<em>The International Journal of High Performance Computing Applications<\/em>,\u00a0<em>32<\/em>(6), pp.913-933. <a href=\"https:\/\/doi.org\/10.1177\/1094342016687625\">https:\/\/doi.org\/10.1177\/1094342016687625<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"663\" height=\"410\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-14-44.png\" alt=\"\" class=\"wp-image-1160\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-14-44.png 663w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-14-44-300x186.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-14-44-332x205.png 332w\" sizes=\"auto, (max-width: 663px) 100vw, 663px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Accuracy analysis of mimetic finite volume operators on geodesic grids<\/h3>\n\n\n\n<p>Investigation on accuracy issues of finite volume schemes used in modern weather and climate models.<\/p>\n\n\n\n<p>Peixoto, P.S., 2016. Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative.\u00a0<em>Journal of Computational Physics<\/em>,\u00a0<em>310<\/em>, pp.127-160. <a href=\"https:\/\/doi.org\/10.1016\/j.jcp.2015.12.058\">https:\/\/doi.org\/10.1016\/j.jcp.2015.12.058<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"567\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-1024x567.png\" alt=\"\" class=\"wp-image-1164\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-1024x567.png 1024w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-300x166.png 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-768x425.png 768w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-1536x850.png 1536w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-700x388.png 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04-332x184.png 332w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/Screenshot-from-2020-12-01-14-19-04.png 1555w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Vector reconstructions on geodesic grids<\/h3>\n\n\n\n<p>A review and proposal of vector reconstruction schemes on geodesic grids and aiming to semi-Lagrangian transport schemes on the sphere.<\/p>\n\n\n\n<p>Peixoto, P.S. and Barros, S.R., 2014. On vector field reconstructions for semi-Lagrangian transport methods on geodesic staggered grids.\u00a0<em>Journal of Computational Physics<\/em>,\u00a0<em>273<\/em>, pp.185-211. <a href=\"https:\/\/doi.org\/10.1016\/j.jcp.2014.04.043\">https:\/\/doi.org\/10.1016\/j.jcp.2014.04.043<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"274\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0021999112007218-gr9.jpg\" alt=\"\" class=\"wp-image-1167\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0021999112007218-gr9.jpg 334w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0021999112007218-gr9-300x246.jpg 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0021999112007218-gr9-332x272.jpg 332w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Grid imprinting on geodesic grids<\/h3>\n\n\n\n<p>A theoretical result that explains the appearance of grid imprinting on finite volume schemes on icosahedral spherical grids.<\/p>\n\n\n\n<p>Peixoto, P.S. and Barros, S.R., 2013. Analysis of grid imprinting on geodesic spherical icosahedral grids.\u00a0<em>Journal of Computational Physics<\/em>,\u00a0<em>237<\/em>, pp.61-78. <a href=\"https:\/\/doi.org\/10.1016\/j.jcp.2012.11.041\">https:\/\/doi.org\/10.1016\/j.jcp.2012.11.041<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"715\" height=\"514\" src=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0898122110009892-gr4.jpg\" alt=\"\" class=\"wp-image-1169\" srcset=\"https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0898122110009892-gr4.jpg 715w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0898122110009892-gr4-300x216.jpg 300w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0898122110009892-gr4-700x503.jpg 700w, https:\/\/www.ime.usp.br\/~pedrosp\/wp\/wordpress\/wp-content\/uploads\/2020\/12\/1-s2.0-S0898122110009892-gr4-332x239.jpg 332w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\">Wavelets and PDEs<\/h3>\n\n\n\n<p>The proposition of a wavelet-based spectral scheme for 1D PDEs and an application to a precipitation (rain) model.<\/p>\n\n\n\n<p>Barros, S.R. and Peixoto, P.S., 2011. Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model.\u00a0<em>Computers &amp; Mathematics with Applications<\/em>,\u00a0<em>61<\/em>(4), pp.1217-1227. <a href=\"https:\/\/doi.org\/10.1016\/j.camwa.2010.12.073\">https:\/\/doi.org\/10.1016\/j.camwa.2010.12.073<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Main results and further information on the research area of numerical methods and computational geophysical fluid dynamics, mainly focused on the application on atmospheric modelling. Selected Talks Results of a moist shallow-water model on locally refined Spherical Voronoi grids: The Andes Problem (SIAM-SCE-2021) &#8211; PDF Challenges of mathematical and numerical modelling of the atmosphere dynamics [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-1180","page","type-page","status-publish","hentry"],"featured_image_urls_v2":{"full":"","thumbnail":"","medium":"","medium_large":"","large":"","1536x1536":"","2048x2048":""},"post_excerpt_stackable_v2":"<p>Main results and further information on the research area of numerical methods and computational geophysical fluid dynamics, mainly focused on the application on atmospheric modelling. Selected Talks Results of a moist shallow-water model on locally refined Spherical Voronoi grids: The Andes Problem (SIAM-SCE-2021) &#8211; PDFChallenges of mathematical and numerical modelling of the atmosphere dynamics (UNB-2021) &#8211; PDFSemi-Lagrangian Exponential Integration with application to the rotating shallow water equations (PDEs on the Sphere &#8211; 2019) &#8211; PDFCurrent trends for global atmosphere dynamical core development: Traditional and modern approaches (CPTEC &#8211; 2019) &#8211; PDF Selected Scientific Results (up to 2021) Topography based local&hellip;<\/p>\n","category_list_v2":"","author_info_v2":{"name":"Pedro","url":"https:\/\/www.ime.usp.br\/~pedrosp\/author\/pedrosp\/"},"comments_num_v2":"0 comments","_links":{"self":[{"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/pages\/1180","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/comments?post=1180"}],"version-history":[{"count":2,"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/pages\/1180\/revisions"}],"predecessor-version":[{"id":1969,"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/pages\/1180\/revisions\/1969"}],"wp:attachment":[{"href":"https:\/\/www.ime.usp.br\/~pedrosp\/wp-json\/wp\/v2\/media?parent=1180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}