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ArcNum includes GUMP for automatic code generation from textual descriptions, and software components to create, register, and evaluate physical laws from defined inputs, outputs, and mathematical formulations. A Contribution component combines law evaluation with automatic differentiation to assemble linear systems efficiently. ArcNum is used to build the open-source ShArc porous-media flow proxy-app, which supports single- and two-phase simulations, including massively parallel HPC runs.","Comptes Rendus  \nMécanique  \nStéphane de Chaisemartin, Sylvain Desroziers, Guillaume Enchéry, Raphaël Gayno, Jean-Marc Gratien, Gilles Grospellier, Thomas Guignon, Pascal Havé, Benoît Lelandais, Alexandre l’Héritier, Anthony Michel, Aboul Karim Mohamed El Maarouf, Valentin Postat, Xavier Tunc and Soleiman Yousef  \nArcNum: an Arcane-based numerical framework used in porous media flow simulation applications  \nVolume 353 (2025), p. 1289-1314 Online since: 1 December 2025  \n[https://doi.org/10.5802/crmeca.336](https://doi.org/10.5802/crmeca.336)  \n This article is licensed under the  \nCreative Commons Attribution 4.0 International License.  \n[http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)  \nThe Comptes Rendus. Mécanique are a member of the Mersenne Center for open scientific publishing  \n[www.centre-mersenne.org](www.centre-mersenne.org)—e-ISSN : 1873-7234  \nComptes Rendus. Mécanique  \n2025, Vol. 353, p. 1289-1314 [https://doi.org/10.5802/crmeca.336](https://doi.org/10.5802/crmeca.336)  \nResearch article  \nArcNum: an Arcane-based numerical framework used in porous media flow simulation applications  \nStéphane de Chaisemartin ∗, a, Sylvain Desroziers a, b, Guillaume Enchéry a, Raphaël Gayno a, Jean-Marc Gratien a, Gilles Grospellier c, Thomas Guignon a, Pascal Havé a, d, Benoît Lelandais c, Alexandre l’Héritier c, Anthony Michel a, Aboul Karim Mohamed El Maarouf a, Valentin Postat c, Xavier Tunc a and Soleiman Yousef a  \na IFPEN, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex, France  \nb Michelin, 23 Place des Carmes Déchaux, 63040 Clermont Ferrand Cedex 9, France  \nc CEA, DAM, DIF, 91297 Arpajon, France  \nd NUANT, Baarerstrasse 20, 6300 Zug, Suisse  \nE-mail: [stephane.de-chaisemartin@ifpen.fr](stephane.de-chaisemartin@ifpen.fr)  \nAbstract. This article presents ArcNum, a framework built on the Arcane platform, designed to easily and efficiently develop and maintain the numerical core in finite-volume and finite-element applications. This framework first enables the automatic generation of code needed to instantiate and handle complex physical models from a textual description, through its component called GUMP. ArcNum also offers software components to create, register and evaluate a set of physical laws, requiring only the specification of their inputs, outputs, and corresponding mathematical formulations. Finally, the framework includes a component named Contribution, which combines law evaluation with automatic differentiation to assemble linear systems efficiently. The framework ArcNum has been used to develop an open source Arcane-based porous media flow simulation proxy-app, named ShArc. Single and two-phase porous media flow simulations performed with ShArc are presented to complete the framework description. In order to illustrate the ability to use ArcNum for High Performance Computing, massively parallel simulations conducted with ShArc are finally presented.  \nKeywords. Mathematical software framework, code generation, automatic differentiation, Arcane, proxyapp, multiphase porous media flow simulation, massively parallel computing.  \nNote. Article submitted by invitation.  \nManuscript received 9 January 2025, revised 13 October 2025, accepted 20 October 2025 .  \n1. Introduction  \nThe open source Arcane platform for scientific computing [1] is an advanced framework designed to facilitate the development and execution of complex scientific simulations applications. It provides researchers, scientists, and engineers with a comprehensive set of tools and libraries specifically tailored for high-performance computing (HPC) applications.  \n∗ Corresponding author  \nISSN (electronic): 1873-7234 [https://comptes-rendus.academie-sciences.fr/mecanique/](https://comptes-rendus.academie-sciences.fr/mecanique/)  \nArcane started being developed at the CEA-DAM, the Military Applications Division of the French Alternative Energies and Atomic Energy Commission, in the early 2000s, be","cbCaiq7RzsrJUeUO","https://ap.wps.com/l/cbCaiq7RzsrJUeUO","pdf",2403864,15,27,"English","en",105,"# Introduction\n## Arcane platform and open-source strategy\n## From linear solvers to numerical frameworks\n## Motivating development of ArcNum\n## ShArc proxy-application and HPC demonstration","[{\"question\":\"What is ArcNum and what problem does it address?\",\"answer\":\"ArcNum is a numerical framework on the Arcane platform designed to simplify the development and maintenance of numerical cores for porous media flow simulations in finite-volume and finite-element applications.\"},{\"question\":\"How does ArcNum support automatic generation and model handling?\",\"answer\":\"ArcNum provides GUMP for generating code from textual descriptions, and additional components to create, register, and evaluate physical laws using specified inputs, outputs, and mathematical formulations.\"},{\"question\":\"How are linear systems assembled efficiently within ArcNum?\",\"answer\":\"ArcNum’s Contribution component combines physical-law evaluation with automatic differentiation to assemble linear systems efficiently.\"}]","ArcNum - an Arcane-based numerical framework for porous media flow simulation applications | PDF",1787705378,68,{"code":4,"msg":83,"data":84},"ok",{"site_id":76,"language":75,"slug":85,"title":65,"keywords":86,"description":66,"schema_data":87,"social_meta":141,"head_meta":143,"extra_data":145,"updated_unix":80},"arcnum-an-arcane-based-numerical-framework-for-porous-media-flow-simulation-applications","",{"@graph":88,"@context":140},[89,103,123],{"@type":90,"itemListElement":91},"BreadcrumbList",[92,96,98,101],{"item":93,"name":94,"@type":95,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":97,"name":9,"@type":95,"position":14},"https://docshare.wps.com/document/",{"item":99,"name":40,"@type":95,"position":100},"https://docshare.wps.com/document/research-report/",3,{"item":102,"name":65,"@type":95,"position":19},"https://docshare.wps.com/document/arcnum-an-arcane-based-numerical-framework-for-porous-media-flow-simulation-applications/144595/",{"url":102,"name":65,"@type":104,"image":105,"author":110,"headline":65,"publisher":112,"fileFormat":115,"inLanguage":75,"description":66,"dateModified":116,"datePublished":117,"encodingFormat":115,"isAccessibleForFree":118,"interactionStatistic":119},"DigitalDocument",{"url":106,"@type":107,"width":108,"height":109},"https://docshare.wps.com/thumbnails/arcnum-an-arcane-based-numerical-framework-for-porous-media-flow-simulation-applications/144595.png","ImageObject",300,407,{"name":63,"@type":111},"Person",{"url":93,"name":113,"@type":114},"DocShare","Organization","application/pdf","2026-11-02","2026-08-26",true,{"@type":120,"interactionType":121,"userInteractionCount":72},"InteractionCounter",{"@type":122},"ViewAction",{"@type":124,"mainEntity":125},"FAQPage",[126,132,136],{"name":127,"@type":128,"acceptedAnswer":129},"What is ArcNum and what problem does it address?","Question",{"text":130,"@type":131},"ArcNum is a numerical framework on the Arcane platform designed to simplify the development and maintenance of numerical cores for porous media flow simulations in finite-volume and finite-element applications.","Answer",{"name":133,"@type":128,"acceptedAnswer":134},"How does ArcNum support automatic generation and model handling?",{"text":135,"@type":131},"ArcNum provides GUMP for generating code from textual descriptions, and additional components to create, register, and evaluate physical laws using specified inputs, outputs, and mathematical formulations.",{"name":137,"@type":128,"acceptedAnswer":138},"How are linear systems assembled efficiently within ArcNum?",{"text":139,"@type":131},"ArcNum’s Contribution component combines physical-law evaluation with automatic differentiation to assemble linear systems efficiently.","https://schema.org",{"og:url":102,"og:type":142,"og:title":65,"og:site_name":113,"og:description":66},"article",{"robots":144,"canonical":102},"index,follow",{"doc_id":61,"site_id":76}]