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# Statement of need
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`SegregatedVMSSolver.jl` is a comprehensive Julia package designed for conducting high-fidelity simulations of complex flow phenomena within the incompressible regime, leveraging the VMS and SUPG method. VMS has been originally introduced by @Hughes:2000. The linearization adopted has been proposed in the SUPG method by @Banyai:2016.
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The package relies on the `Gridap.jl` package [@Verdugo:2022; @Badia:2020] to implement the mathematical model of FEM. Complementing this core functionality, `GridapDistributed.jl`[@BadiaD:2022] and `PartitionedArrays.jl`[@Verdugo:2025] allow the use of multi-core CPUs desktop computers to HPC clusters. The [`GridapPETSc.jl`](https://github.com/gridap/GridapPETSc.jl) package is used to solve the final linear system.
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The package relies on the `Gridap.jl` package [@Verdugo:2022; @Badia:2020] to implement the mathematical model of FEM. Complementing this core functionality, `GridapDistributed.jl`[@BadiaD:2022] and `PartitionedArrays.jl`[@Verdugo:2025] allow the use of multi-core CPUs desktop computers to HPC clusters. The `GridapPETSc.jl`[@GridapPETSc:2025] package is used to solve the final linear system.
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It solves a Linearized and Segregated version of VMS (LS-VMS) and SUPG. It is based on an iterative predictor-corrector scheme and it avoids the resolution of a non-linear problem. It uses the $\theta$ method to solve the time-marching problem.
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This package focuses on solving fluid dynamics problems, with a particular emphasis on the study of 2D and 3D airfoil aerodynamics at low Reynolds numbers (tested up to 500,000). The primary objective is to provide researchers and engineers with a versatile tool for analyzing aerodynamic features in this regime.
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-**Vortex shedding over a cylinder**: Available in both 2D and 3D.
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-**Airfoil aerodynamics**: Extensive support for both 2D and 3D simulations.
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It also has a suite of tools for post-processing the results like performing time and spanwise averaging. It is possible to control the simulation in real-time, enabling/disabling the creation of output files at each time-step. The user can load their own airfoil meshes also using the package [`AirfoilGmsh.jl`](https://github.com/carlodev/AirfoilGmsh.jl). Additionally, the package provides tools for initializing boundary layers in 2D simulations, enhancing its versatility and utility for researchers and practitioners in the field of fluid dynamics.
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It also has a suite of tools for post-processing the results like performing time and spanwise averaging. It is possible to control the simulation in real-time, enabling/disabling the creation of output files at each time-step. The user can load their own airfoil meshes also using the package `AirfoilGmsh.jl`[@BrunelliAirfoilGmsh:2023]. Additionally, the package provides tools for initializing boundary layers in 2D simulations, enhancing its versatility and utility for researchers and practitioners in the field of fluid dynamics.
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The field of fluid dynamics in Julia has seen significant growth, with several software packages emerging to address various computational challenges. This reflects the growing interest and engagement of the Julia community in this domain. A comprehensive list of packages can be found on [Julia Packages - Fluid Dynamics](https://juliapackages.com/c/fluid-dynamics). Among the most notable and well documented are:
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