{"id":92227,"date":"2026-04-16T13:00:49","date_gmt":"2026-04-16T13:00:49","guid":{"rendered":"https:\/\/gaeatech.com\/knowledge-center\/?p=92227"},"modified":"2026-04-13T22:58:35","modified_gmt":"2026-04-13T22:58:35","slug":"pollutev10-example-13-2d-dispersion-tdast-analytical-comparison","status":"publish","type":"post","link":"https:\/\/gaeatech.com\/knowledge-center\/pollutev10-example-13-2d-dispersion-tdast-analytical-comparison\/","title":{"rendered":"POLLUTEv10 Example 13: 2D Plane Dispersion vs Analytical Solution (TDAST)"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"h-benchmarking-against-analytical-2d-dispersion-models\">Benchmarking Against Analytical 2D Dispersion Models<\/h2>\n\n\n\n<p><strong>POLLUTEv10 Example 13<\/strong> provides another important <strong>model validation case<\/strong>, comparing numerical results from POLLUTEv10 with the analytical solution implemented in <strong>TDAST<\/strong>, developed by P. Javandel and colleagues in 1984.<\/p>\n\n\n\n<p>This example focuses on <strong>2-dimensional plane dispersion<\/strong> in an <strong>infinitely deep porous medium<\/strong>, offering insight into plume spreading under uniform flow conditions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Problem Overview<\/h2>\n\n\n\n<p>The simulation considers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>conservative contaminant<\/strong> (no sorption)<\/li>\n\n\n\n<li>A <strong>constant source concentration<\/strong><\/li>\n\n\n\n<li><strong>Uniform groundwater flow<\/strong><\/li>\n\n\n\n<li><strong>2D dispersion in an infinite domain<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Key Conditions<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Source concentration (<strong>co<\/strong>) = 1.0 g\/L<\/li>\n\n\n\n<li>Time of interest = <strong>4 years<\/strong><\/li>\n\n\n\n<li>Flow is steady and uniform<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Conceptual Model<\/h2>\n\n\n\n<p>The system represents:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>infinitely thick porous medium<\/strong><\/li>\n\n\n\n<li>A <strong>continuous source<\/strong> releasing contaminant<\/li>\n\n\n\n<li>Transport governed by <strong>advection and diffusion<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Although the domain is infinite:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Results are evaluated over the <strong>top 10 m<\/strong> for comparison<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Input Parameters<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Property<\/th><th>Value<\/th><th>Units<\/th><\/tr><\/thead><tbody><tr><td>Darcy Velocity (va)<\/td><td>1.0<\/td><td>m\/a<\/td><\/tr><tr><td>Diffusion Coefficient (D)<\/td><td>0.01<\/td><td>m\u00b2\/a<\/td><\/tr><tr><td>Distribution Coefficient<\/td><td>0.0<\/td><td>cm\u00b3\/g<\/td><\/tr><tr><td>Soil Porosity (n)<\/td><td>1.0<\/td><td>&#8211;<\/td><\/tr><tr><td>Dry Density<\/td><td>0.0<\/td><td>g\/cm\u00b3<\/td><\/tr><tr><td>Soil Thickness (H)<\/td><td>10.0<\/td><td>m<\/td><\/tr><tr><td>Sub-layers<\/td><td>20<\/td><td>&#8211;<\/td><\/tr><tr><td>Source Concentration<\/td><td>1.0<\/td><td>g\/L<\/td><\/tr><tr><td>Time of Interest<\/td><td>4<\/td><td>years<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Transport Processes<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Advection<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Driven by constant Darcy velocity (<strong>1 m\/a<\/strong>)<\/li>\n\n\n\n<li>Controls plume movement direction<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. Diffusion \/ Dispersion<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Causes plume spreading in all directions<\/li>\n\n\n\n<li>Governed by <strong>D = 0.01 m\u00b2\/a<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. No Sorption<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Conservative contaminant<\/li>\n\n\n\n<li>No retardation effects<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Analytical Comparison (TDAST)<\/h2>\n\n\n\n<p>The <strong>TDAST model<\/strong> provides an analytical solution for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2D plane dispersion<\/strong><\/li>\n\n\n\n<li><strong>Infinite domain conditions<\/strong><\/li>\n\n\n\n<li><strong>Uniform flow fields<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Purpose of Comparison<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Validate POLLUTEv10 numerical accuracy<\/li>\n\n\n\n<li>Ensure correct implementation of dispersion processes<\/li>\n\n\n\n<li>Benchmark plume geometry and concentration distribution<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-graphical-output-depth-vs-concentration\">Graphical Output: Depth vs Concentration<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1007\" height=\"910\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24.jpg\" alt=\"\" class=\"wp-image-92228\" srcset=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24.jpg 1007w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24-300x271.jpg 300w, https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/image-24-768x694.jpg 768w\" sizes=\"auto, (max-width: 1007px) 100vw, 1007px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-pdf-report\">PDF Report<\/h2>\n\n\n<div class=\"ead-preview\"><div class=\"ead-document\" style=\"position: relative;padding-top: 90%\"><div class=\"ead-iframe-wrapper\"><iframe src=\"\/\/docs.google.com\/viewer?url=https%3A%2F%2Fgaeatech.com%2Fknowledge-center%2Fwp-content%2Fuploads%2F2026%2F04%2Fpollute-example13.pdf&amp;embedded=true&amp;hl=en\" title=\"Embedded Document\" class=\"ead-iframe\" style=\"width: 100%;height: 100%;border: none;position: absolute;left: 0;top: 0;visibility: hidden;\"><\/iframe><\/div>\t\t\t<div class=\"ead-document-loading\" style=\"width:100%;height:100%;position:absolute;left:0;top:0;z-index:10\">\n\t\t\t\t<div class=\"ead-loading-wrap\">\n\t\t\t\t\t<div class=\"ead-loading-main\">\n\t\t\t\t\t\t<div class=\"ead-loading\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/loading.svg\" width=\"55\" height=\"55\" alt=\"Loader\">\n\t\t\t\t\t\t\t<span>Loading&#8230;<\/span>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"ead-loading-foot\">\n\t\t\t\t\t\t<div class=\"ead-loading-foot-title\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/EAD-logo.svg\" alt=\"EAD Logo\" width=\"36\" height=\"23\"\/>\n\t\t\t\t\t\t\t<span>Taking too long?<\/span>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<p>\n\t\t\t\t\t\t\t<div class=\"ead-document-btn ead-reload-btn\" role=\"button\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/reload.svg\" alt=\"Reload\" width=\"12\" height=\"12\"\/> Reload document\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<span>|<\/span>\n\t\t\t\t\t\t\t<a href=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/uploads\/2026\/04\/pollute-example13.pdf\" class=\"ead-document-btn\" target=\"_blank\">\n\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/gaeatech.com\/knowledge-center\/wp-content\/plugins\/embed-any-document\/images\/open.svg\" alt=\"Open\" width=\"12\" height=\"12\"\/> Open in new tab\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div><\/div>\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Key Insights<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analytical solutions remain essential for <strong>model verification<\/strong><\/li>\n\n\n\n<li>2D dispersion produces <strong>predictable plume geometries<\/strong><\/li>\n\n\n\n<li>Infinite domain assumptions simplify boundary effects<\/li>\n\n\n\n<li>POLLUTEv10 can accurately simulate <strong>multi-dimensional transport<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Importance of Discretization<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>20 sub-layers<\/strong> used for vertical resolution<\/li>\n\n\n\n<li>Adequate for capturing concentration gradients over 10 m<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"has-small-font-size\">Increasing sub-layers improves resolution for sharper gradients or shorter time scales<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Practical Applications<\/h2>\n\n\n\n<p>This example is relevant for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Groundwater contamination assessments<\/strong><\/li>\n\n\n\n<li><strong>Plume migration prediction<\/strong><\/li>\n\n\n\n<li><strong>Model calibration and validation<\/strong><\/li>\n\n\n\n<li><strong>Regulatory and environmental studies<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p>POLLUTEv10 Example 13 demonstrates the model\u2019s capability to accurately reproduce <strong>2D contaminant transport behavior<\/strong> and match analytical solutions such as TDAST.<\/p>\n\n\n\n<p>Key takeaways:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Advection controls plume direction<\/li>\n\n\n\n<li>Diffusion governs plume spreading<\/li>\n\n\n\n<li>Analytical comparisons build confidence in model results<\/li>\n<\/ul>\n\n\n\n<p>This example reinforces POLLUTEv10 as a reliable tool for <strong>groundwater contaminant transport modeling<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Benchmarking Against Analytical 2D Dispersion Models POLLUTEv10 Example 13 provides another important model validation case, comparing numerical results from POLLUTEv10 with the analytical solution implemented in TDAST, developed by P. Javandel and colleagues in 1984. This example focuses on 2-dimensional plane dispersion in an infinitely deep porous medium, offering insight into plume spreading under uniform [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":92230,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[858,1632],"tags":[1670,1669,501,24,469,821,1636,1236,1627,1671],"class_list":["post-92227","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contaminant-transport-modeling","category-pollute-examples","tag-2d-dispersion","tag-analytical-solution","tag-contaminant-transport","tag-environmental-engineering","tag-groundwater-modeling","tag-hydrogeology","tag-numerical-modeling","tag-plume-migration","tag-pollutev10","tag-tdast"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.4 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>2D Dispersion Modeling \u2013 POLLUTEv10 Example 13 Insights - 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