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eated_at":"2023-09-13T08:44:56.808Z","updated_at":"2026-04-14T01:30:23.165Z","avatar_url":"https://github.com/byuflowlab.png","language":"Julia","category":"Renewable Energy","sub_category":"Wind Energy","monthly_downloads":0,"total_dependent_repos":0,"total_dependent_packages":0,"readme":"\u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/flowunsteady-logo-wide03.png\" alt=\"FLOWUnsteady logo\" style=\"width:100%\"\u003e\n\n\u003cp align=\"right\"\u003e\n  \u003cspan style=\"color:#2f6990;\"\u003e\n    \u003ci\u003eInteractional aerodynamics solver for multirotor aircraft and wind energy\u003c/i\u003e\n  \u003c/span\u003e\n\u003c/p\u003e\n\n\u003cp align=\"right\"\u003e\n  \u003ca href=\"https://github.com/byuflowlab/FLOWUnsteady\"\u003e\n    \u003cimg src=\"https://img.shields.io/badge/code-open%20source-brightgreen.svg\"\u003e\n  \u003c/a\u003e\n  \u003ca href=\"https://flow.byu.edu/FLOWUnsteady/\"\u003e\n    \u003cimg src=\"https://img.shields.io/badge/docs-stable-blue.svg\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n---\n\nFLOWUnsteady is an open-source variable-fidelity framework for unsteady\naerodynamics and aeroacoustics based on the\n[reformulated vortex particle method](https://scholarsarchive.byu.edu/etd/9589/)\n(rVPM).\nThis suite brings together various tools developed by the\n[FLOW Lab](http://flow.byu.edu/) at Brigham Young University: Vortex lattice\nmethod, strip theory, blade elements, 3D panel method, and rVPM.\nThe suite also integrates an FW-H solver and a BPM code for tonal\nand broadband prediction of aeroacoustic noise.\nIn the low end of fidelity, simulations are similar to a free-wake method,\nwhile in the high end simulations become meshless large eddy simulations.\n\n\n* *Documentation:* [flow.byu.edu/FLOWUnsteady](https://flow.byu.edu/FLOWUnsteady)\n* *Code:* [github.com/byuflowlab/FLOWUnsteady](https://github.com/byuflowlab/FLOWUnsteady)\n\nNOTE (28 Aug 2025): The documentation is temporarily unavailable due to server issues. See the examples/ and docs/ folder in the meantime. It should be back up in the next few days.\n\n### What is the Reformulated VPM?\n\nThe [reformulated VPM](https://scholarsarchive.byu.edu/etd/9589/) is a meshless\nCFD method solving the LES-filtered incompressible Navier-Stokes equations in\ntheir vorticity form,\n\u003cp align=\"center\"\u003e\n    \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/vorticityns.png\" alt=\"img\" style=\"width:40%\"\u003e\n\u003c/p\u003e\nIt uses a Lagrangian (meshless) scheme, which not only\navoids the hurdles of mesh generation, but it also conserves vortical structures\nover long distances with minimal numerical dissipation.\n\nThe rVPM uses particles to discretize the Navier-Stokes equations, with the\nparticles representing radial basis functions that construct a continuous\nvorticity/velocity field. The basis functions become the LES filter, providing a\nvariable filter width and spatial adaptation as the particles are convected and\nstretched by the velocity field. The local evolution of the filter width\nprovides an extra degree of freedom to reinforce conservation laws, which makes\nthe reformulated VPM numerically stable (overcoming the numerical issues that\nplague the classic VPM).\n\nThis meshless LES has several advantages over conventional mesh-based CFD.\nIn the absence of a mesh,   \n1. the rVPM does not suffer from the numerical dissipation introduced by a mesh\n2. integrates over coarser discretizations without losing physical accuracy\n3. derivatives are calculated analytically rather than approximated through a stencil.\n\nFurthermore, rVPM is highly efficient since it uses computational elements only\nwhere there is vorticity (rather than meshing the entire space), usually being ~100x\nfaster than conventional mesh-based LES with comparable accuracy.\n\n\nWhile rVPM is well suited for resolving unbounded flows (wakes), complications\narise when attempting to impose boundary conditions (solid boundaries) on the flow.\nThis is because (1) the method is meshless, and (2) boundary conditions must\nbe imposed on the Navier-Stokes equations in the form of vorticity.\nFLOWUnsteady is a framework designed to introduce solid boundaries into the rVPM\nusing actuator models.\nWings and rotors are introduced in the computational domain through actuator\nline and surface models that use low-fidelity aerodynamic methods\n(*e.g.*, VLM, lifting line,\npanels, etc) to compute forces and embed the associated\nvorticity back into the LES domain.\n\n\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=-6aR37Z6hig\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-vahanahi.png\" alt=\"youtube.com/watch?v=-6aR37Z6hig\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n### Variable Fidelity\n\nrVPM considerably reduces engineering time by avoiding the hurdles of mesh\ngeneration. Furthermore, since it is not limited by the time-step and stability\nconstraints of conventional mesh-based CFD, rVPM can be used across all levels\nof fidelity, all in the same framework by simply coarsening or refining the\nsimulation.\nIn the low end of fidelity, simulations are similar to a free-wake method,\nwhile in the high end simulations become meshless large eddy simulations.\nThus, FLOWUnsteady can be used as a high-fidelity tool that is orders of\nmagnitude faster than mesh-based CFD, or as a variable-fidelity tool for\nthe different stages of design.\n\n\u003cp align=\"left\"\u003e\n    \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/flowunsteady-variablefidelity.jpg\" alt=\"img\" style=\"width:100%\"\u003e\n\u003c/p\u003e\n\n### Capabilities\n\n  \u003e **Simulation:**\n  \u003e *Tilting wings and rotors*\n  \u003e *• Rotors with variable RPM and variable pitch*\n  \u003e *• Asymmetric and stacked rotors*\n  \u003e *• Maneuvering vehicle with prescribed kinematics*\n  \u003e\n  \u003e **rVPM Solver:**\n  \u003e *Fast-multipole acceleration through [ExaFMM](https://joss.theoj.org/papers/10.21105/joss.03145)*\n  \u003e *• CPU parallelization through OpenMP*\n  \u003e *• Second-order spatial accuracy and third-order RK time integration*\n  \u003e *• Numerically stable by reshaping particles subject to vortex stretching*\n  \u003e *• Subfilter-scale (SFS) model of turbulence associated to vortex stretching*\n  \u003e *• SFS model coefficient computed dynamically or prescribed*\n  \u003e *• Viscous diffusion through core spreading*\n  \u003e\n  \u003e **Wing Models:**\n  \u003e *Actuator line model through lifting line + VLM*\n  \u003e *• Actuator surface model through vortex sheet + VLM*\n  \u003e *• Parasitic drag through airfoil lookup tables*\n  \u003e\n  \u003e **Rotor Model:**\n  \u003e *Actuator line model through blade elements*\n  \u003e *• Airfoil lookup tables automatically generated through XFOIL*\n  \u003e *• Aeroacoustic noise through FW-H (PSU-WOPWOP) and BPM*\n  \u003e\n  \u003e **Geometry:**\n  \u003e *Simple lofts and bodies of revolution through FLOWUnsteady*\n  \u003e *• Import complex geometry from [OpenVSP](https://openvsp.org/)*\n  \u003e\n  \u003e **Under development *(*🤞*coming soon)*:**\n  \u003e *Advanced actuator surface models through 3D panel method (for ducts, wings, and fuselage)*\n  \u003e *• Unstructured surface grids*\n  \u003e *• Bluff bodies through vortex sheet method*\n  \u003e\n  \u003e **Limitations:**\n  \u003e *Viscous drag and separation is only captured through airfoil lookup tables, without attempting to shed separation wakes*\n  \u003e *• Incompressible flow only (though wave drag can be captured through airfoil lookup tables)*\n  \u003e *• CPU parallelization through OpenMP without support for distributed memory (no MPI, i.e., only single-node runs)*\n  \u003e\n  \u003e *Coded in [the Julia language](https://www.infoworld.com/article/3284380/what-is-julia-a-fresh-approach-to-numerical-computing.html) for Linux, MacOS, and Windows WSL.*\n\n\n\n\n\nMore about the models inside FLOWUnsteady:\n\u003cp align=\"center\"\u003e\n  \u003ca href=\"https://www.nas.nasa.gov/pubs/ams/2022/08-09-22.html\"\u003e\n    \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/nasaamsseminar2.png\" alt=\"https://www.nas.nasa.gov/pubs/ams/2022/08-09-22.html\" style=\"width:70%\"\u003e\n  \u003c/a\u003e\n\u003c/p\u003e\n\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\n### Selected Publications\nSee the following publications for an in-depth dive into the theory and validation:\n\n* E. J. Alvarez, J. Mehr, \u0026 A. Ning (2022), \"FLOWUnsteady: An Interactional Aerodynamics Solver for Multirotor Aircraft and Wind Energy,\" *AIAA AVIATION Forum*. [**[VIDEO]**](https://youtu.be/SFW2X8Lbsdw) [**[PDF]**](https://scholarsarchive.byu.edu/facpub/5830/)\n* E. J. Alvarez (2022), \"Reformulated Vortex Particle Method and Meshless Large Eddy Simulation of Multirotor Aircraft.,\" *Doctoral Dissertation, Brigham Young University*. [**[VIDEO]**](https://www.nas.nasa.gov/pubs/ams/2022/08-09-22.html) [**[PDF]**](https://scholarsarchive.byu.edu/etd/9589/)\n* E. J. Alvarez \u0026 A. Ning (2023), \"Stable Vortex Particle Method Formulation for Meshless Large-Eddy Simulation,\" *AIAA Journal*. [**[PDF]**](https://arc.aiaa.org/doi/epdf/10.2514/1.J063045)\n\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\n### Examples and Tutorials\n\n**Propeller:** [[Tutorial](https://flow.byu.edu/FLOWUnsteady/examples/propeller-J040)] [[Validation](https://flow.byu.edu/FLOWUnsteady/theory/validation/#Propeller)]\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=lUIytQybCpQ\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-prop.png\" alt=\"youtube.com/watch?v=lUIytQybCpQ\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n**Rotor in Hover:** [[Tutorial](https://flow.byu.edu/FLOWUnsteady/examples/rotorhover-aero)] [[Validation](https://flow.byu.edu/FLOWUnsteady/theory/validation/#Rotor)]\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=u9SgYbYhPpU\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-hover.png\" alt=\"youtube.com/watch?v=u9SgYbYhPpU\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n**Blown Wing:** [[Tutorial](https://flow.byu.edu/FLOWUnsteady/examples/blownwing-aero)] [[Validation](https://flow.byu.edu/FLOWUnsteady/theory/validation/#Rotor-Wing-Interactions)]\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=GfS3NoVrFfU\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-rotorwing.png\" alt=\"youtube.com/watch?v=GfS3NoVrFfU\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n**Ducted Fan:** [[Slides](http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/alvarez_2023-SLIDES-VPM_for_EDF_in_Non_Axisymmetric_Flow.pdf)]\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=BQpar3A0X-w\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-edf.png\" alt=\"youtube.com/watch?v=BQpar3A0X-w\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n**Airborne-Wind-Energy Aircraft:** [[Video](https://www.youtube.com/watch?v=iFM3B4_N2Ls)]\n\n\u003cp align=\"left\"\u003e\n  \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/circular-fdom-top02.jpg\" alt=\"img\" style=\"width:75%\"\u003e\n\u003c/p\u003e\n\n\n**eVTOL Transition:** [[Tutorial](https://flow.byu.edu/FLOWUnsteady/examples/vahana-vehicle/)]\n\nMid-fidelity\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=d__wNtRIBY8\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-vahanamid.png\" alt=\"youtube.com/watch?v=d__wNtRIBY8\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\nHigh-fidelity\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=-6aR37Z6hig\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-vahanahi.png\" alt=\"youtube.com/watch?v=-6aR37Z6hig\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\n**Aeroacoustic Noise:** [[Tutorial](https://flow.byu.edu/FLOWUnsteady/examples/rotorhover-acoustics)] [[Validation](https://flow.byu.edu/FLOWUnsteady/theory/validation/#Rotor)]\n\n\u003cp align=\"center\"\u003e \u003ca href=\"https://www.youtube.com/watch?v=ntQjP6KbZDk\u0026hd=1\"\u003e \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/youtube-vahananoise.png\" alt=\"youtube.com/watch?v=ntQjP6KbZDk\" style=\"width:70%\"\u003e \u003c/a\u003e \u003c/p\u003e\n\n\u003cp align=\"center\"\u003e\n  \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/cfdnoise_ningdji_multi_005D_03_20.gif\" alt=\"Vid\" style=\"width:60%\"/\u003e\n\u003c/p\u003e\n\n\n\n\n\n### Sponsors\n\n\u003cp align=\"center\"\u003e\n  \u003cimg src=\"http://edoalvar2.groups.et.byu.net/public/FLOWUnsteady/sponsors01.png\" alt=\"img\" style=\"width:100%\"\u003e\n  \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\n\u003c/p\u003e\n\n\n\n### About\n\nFLOWUnsteady is an open-source project jointly led by the\n[FLOW Lab](http://flow.byu.edu/) at Brigham Young University and\n[Whisper Aero](http://whisper.aero/).\nAll contributions are welcome.\n\nIf you find FLOWUnsteady useful in your work, we kindly request that you cite the following paper [[URL]](https://arc.aiaa.org/doi/10.2514/6.2022-3218) [[PDF]](https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=6735\u0026context=facpub):\n\n\u003eAlvarez, E. J., Mehr, J., and Ning, A., “FLOWUnsteady: An Interactional Aerodynamics Solver for Multirotor Aircraft and Wind Energy,” AIAA AVIATION 2022 Forum, Chicago, IL, 2022. DOI:[10.2514/6.2022-3218](https://doi.org/10.2514/6.2022-3218).\n\nIf you were to encounter any issues or have questions, please first read through\n[the documentation](https://flow.byu.edu/FLOWUnsteady/), [open/closed\nissues](https://github.com/byuflowlab/FLOWUnsteady/issues?q=is%3Aissue+is%3Aclosed),\nand [the discussion forum](https://github.com/byuflowlab/FLOWUnsteady/discussions?discussions_q=).\nIf the issue still persists, please participate in\n[the discussion forum](https://github.com/byuflowlab/FLOWUnsteady/discussions?discussions_q=)\nand/or [open a new issue](https://github.com/byuflowlab/FLOWUnsteady/issues).\n\n  * Developers/contributors : [Eduardo J. Alvarez](https://www.edoalvarez.com/) (main), [Cibin Joseph](https://github.com/cibinjoseph), [Judd Mehr](https://www.juddmehr.com/), [Ryan Anderson](https://flow.byu.edu/people/), [Eric Green](https://flow.byu.edu/people/), [Benjamin Varela](https://flow.byu.edu/people/)\n  * Created           : Sep 2017\n  * License           : MIT License\n","funding_links":[],"readme_doi_urls":["https://doi.org/10.2514/6.2022-3218"],"works":{"https://doi.org/10.2514/6.2022-3218":{"id":"https://openalex.org/W4283273277","doi":"https://doi.org/10.2514/6.2022-3218","title":"FLOWUnsteady: An Interactional Aerodynamics Solver for Multirotor Aircraft and Wind Energy","display_name":"FLOWUnsteady: An Interactional Aerodynamics Solver for Multirotor Aircraft and Wind Energy","publication_year":2022,"publication_date":"2022-06-20","ids":{"openalex":"https://openalex.org/W4283273277","doi":"https://doi.org/10.2514/6.2022-3218"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.2514/6.2022-3218","pdf_url":null,"source":{"id":"https://openalex.org/S4363604317","display_name":"AIAA AVIATION 2022 Forum","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://scholarsarchive.byu.edu/context/facpub/article/6735/viewcontent/Alvarez2022a.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080755264","display_name":"Eduardo J. 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