{"id":1975,"date":"2021-11-11T13:40:43","date_gmt":"2021-11-11T12:40:43","guid":{"rendered":"https:\/\/s-ink.org\/?p=1975"},"modified":"2023-09-27T19:10:11","modified_gmt":"2023-09-27T17:10:11","slug":"governing-equations","status":"publish","type":"post","link":"https:\/\/s-ink.org\/governing-equations","title":{"rendered":"Governing equations"},"content":{"rendered":"\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><figure class=\"wp-block-post-featured-image\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1200\" height=\"733\" src=\"https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=1200%2C733&#038;ssl=1\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"The governing equations of numerical modelling include conservation of mass, momentum, and energy with different types of rheology.\" style=\"object-fit:cover;\" srcset=\"https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?w=2400&amp;ssl=1 2400w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=300%2C183&amp;ssl=1 300w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=1024%2C625&amp;ssl=1 1024w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=768%2C469&amp;ssl=1 768w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=1536%2C938&amp;ssl=1 1536w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=2048%2C1250&amp;ssl=1 2048w, https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?resize=1200%2C733&amp;ssl=1 1200w\" sizes=\"auto, (max-width: 1200px) 100vw, 1200px\" data-attachment-id=\"2172\" data-permalink=\"https:\/\/s-ink.org\/101modelling-governing-equations-fabio-crameri_2\" data-orig-file=\"https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?fit=2400%2C1465&amp;ssl=1\" data-orig-size=\"2400,1465\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"101Modelling-Governing-Equations-Fabio-Crameri_2\" data-image-description=\"&lt;p&gt;The governing equations of numerical modelling include conservation of mass, momentum, and energy with different types of rheology.&lt;\/p&gt;\n\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/s-ink.org\/wp-content\/uploads\/101Modelling-Governing-Equations-Fabio-Crameri_2.png?fit=1024%2C625&amp;ssl=1\" \/><\/figure>\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<p><strong>The governing equations of geodynamic numerical modelling include conservation of mass, momentum, and energy with different types of rheology. <em>\u03c1<\/em> is the density, <em>t<\/em> is time, <em>v<\/em> the velocity vector, <em>\u03c3<\/em> the stress tensor, <em>g<\/em> the gravitational acceleration vector, <em>Cp<\/em> the heat capacity, <em>T<\/em> the temperature, <em>k<\/em> the thermal conductivity, <em>H<\/em> a volumetric heat production term (e.g., due to radioactive decay) and the term <em>S = S + S2 + S3<\/em> accounts for friction heating, adiabatic heating, and the release or consumption of latent heat (e.g., associated with phase changes), respectively. Note that the plastic rheology depicted here is the geodynamic approximation of brittle failure.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Creator: <a href=\"https:\/\/www.fabiocrameri.ch\" target=\"_blank\" rel=\"noreferrer noopener\">Fabio Crameri<\/a><\/li>\n\n\n\n<li>This version: 19.01.2022<\/li>\n\n\n\n<li>License: <a href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\" target=\"_blank\" rel=\"noreferrer noopener\">Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)<\/a><\/li>\n\n\n\n<li>Specific citation: <em>This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.<\/em><\/li>\n\n\n\n<li>Related reference: van Zelst, I.,\u00a0F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583\u2013637,\u00a0<a href=\"https:\/\/doi.org\/10.5194\/se-13-583-2022\" target=\"_blank\" rel=\"noreferrer noopener\">doi:10.5194\/se-13-583-2022<\/a><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-columns coblocks-animate is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" data-coblocks-animation=\"slideInLeft\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<ul class=\"is-style-checkbox wp-block-list\">\n<li>Transparent background<\/li>\n\n\n\n<li>Dark background version<\/li>\n\n\n\n<li>Vector format<\/li>\n\n\n\n<li>Colour-vision deficiency friendly<\/li>\n\n\n\n<li>Readable in black&amp;white<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-buttons is-horizontal is-content-justification-left is-layout-flex wp-container-core-buttons-is-layout-7e5fce0a 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