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Fusion energy development draws from a wide range of disciplines to describe design and to develop a functioning system. One challenging engineering task is to develop the fusion core component known as a "blanket." Because this component surrounds the burning plasma and must absorb almost all of the power from nuclear reactions, it must breed fuel, provide nuclear shielding, and provide energy deposition. Molten salt (MS) is a primary choice for cooling the blanket. A “salt blanket” in fusion energy is a layer of molten salt surrounding the fusion plasma. The molten salt acts as both a coolant and a material for neutron absorption, both of which are essential in fusion reactions. The salt blanket absorbs the high-energy neutrons produced by fusion, reducing the wear on reactor components, and converting some of the energy into heat for electricity generation. Molten salts have low electrical and thermal conductivity and experience lesser electromagnetic forces, but they are still turbulent. Heat transfer degradation in an MS flow caused by the reduction of turbulence by a magnetic field is a possible limitation of the MS blanket [@Smolentsev01042005].
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Two approaches are commonly adopted to model MS flows exposed to a magnetic field: high-fidelity modeling (large-eddy simulation [LES] or direct numerical simulation [DNS]), and Reynolds-averaged Navier-Stokes (RANS) turbulence models. LESs can resolve turbulences at temporal and spatial scales at the expense of large HPC resources. Blanket design with LES is not possible because of current HPC limitations. Design optimization often requires multiple simulation runs to investigate performance under various conditions. The main technique that reduces the computational requirements of the analysis is the RANS turbulence model. This approach filters out the instantaneous velocity component, and the influence of the turbulence is modeled solely by the closure models. Turbulence modeling is a complex problem, and many turbulence models are available as described in the literature [@Chen_2022][@Menter1992ImprovedTK], albeit with many limitations [@10.1023/a:1022818327584]. Furthermore, these models are not readily applicable to the MHD flows and would require modifications [@Smolentsev2002] because MHD effects introduce additional terms in the turbulence balance equations.
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Two approaches are commonly adopted to predict MS flows exposed to a magnetic field: high-fidelity simulation (large-eddy simulation (LES) or direct numerical simulation (DNS)), and Reynolds-averaged Navier-Stokes (RANS) turbulence models. LESs can resolve turbulences at temporal and spatial scales at the expense of large HPC resources. Blanket design with LES is not possible because of current HPC limitations. Design optimization often requires multiple simulation runs to investigate performance under various conditions. The main technique that reduces the computational requirements of the analysis is the RANS turbulence model. This approach filters out the instantaneous velocity component, and the influence of the turbulence is modeled solely by the closure models. Turbulence modeling is a complex problem, and many turbulence models are available as described in the literature [@Chen_2022][@Menter1992ImprovedTK], albeit with many limitations [@10.1023/a:1022818327584]. Furthermore, these models are not readily applicable to the MHD flows and would require modifications [@Smolentsev2002] because MHD effects introduce additional terms in the turbulence balance equations.
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VERTEX-CFD is a new open-source package designed to address the aforementioned challenges by leveraging and integrating artificial intelligence and machine learning (AI&ML) tools to enhance current turbulence models from high-fidelity datasets and also by relying on a robust multiphysics solver that scales on HPC platforms.
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## Dependencies and deployment
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The VERTEX-CFD package is an open-source code that is hosted on the Oak Ridge National Laboratory (ORNL) GitHub account [https://github.com/ORNL/VERTEX-CFD](https://github.com/ORNL/VERTEX-CFD). VERTEX-CFD is built on the [Trilinos package](https://trilinos.github.io/)[@trilinos-website] that provides a suite of tools for code development on HPC platforms. It has been deployed on a wide variety of HPC platforms, ranging from small clusters to exascale computers alike Summit [@olcf-web], Frontier [@olcf-web], and Perlmutter [@nersc-web].
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The VERTEX-CFD package is an open-source code that is hosted on the Oak Ridge National Laboratory (ORNL) GitHub account [https://github.com/ORNL/VERTEX-CFD](https://github.com/ORNL/VERTEX-CFD). VERTEX-CFD is built on the [Trilinos package](https://trilinos.github.io/)[@trilinos-website] that provides a suite of tools for code development on HPC platforms. It has been deployed on a wide variety of HPC platforms, ranging from small clusters to exascale computers including Summit [@olcf-web], Frontier [@olcf-web], and Perlmutter [@nersc-web].
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## Governing equations and discretization methods
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\right.
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\end{align}
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The set of equations presented above can be augmented with RANS turbulence models and the wall-adapting local eddy (WALE) viscosity model [@nicoud:hal-00910373] to model turbulent flows. Solvers, FEMs, and other relevant tools are provided by the [Trilinos package](https://trilinos.github.io/)[@trilinos-website]. The VERTEX-CFD software is designed to scale and to be compatible with various CPU and GPU architectures on HPC platforms by leveraging Kokkos [@kokkos] programming language. VERTEX-CFD software has demonstrated second-order temporal and spatial accuracy.
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The set of equations presented above can be augmented with RANS turbulence models and the wall-adapting local eddy (WALE) viscosity model [@nicoud:hal-00910373] to simulate turbulent flows. Solvers, FEMs, and other relevant tools are provided by the [Trilinos package](https://trilinos.github.io/)[@trilinos-website]. The VERTEX-CFD software is designed to scale and to be compatible with various CPU and GPU architectures on HPC platforms by leveraging Kokkos [@kokkos] programming language. VERTEX-CFD software has demonstrated second-order temporal and spatial accuracy[@vertexcfd-ans-2024].
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## Development workflow: testing, validation and verification
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# Conclusions and current development activities
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VERTEX-CFD is an open-source CFD solver that relies on a finite element discretization method to solve for the incompressible Navier-Stokes equations coupled to a temperature equation and MHD equation. Reynolds Averaged Navier-Stokes (RANS) turbulence models and large-eddy simulation (LES) models are also available. The code relies on the Trilinos package and offers a wide range of temporal integrators, solvers, and preconditioners to run on CPU- and GPU-enabled platforms. VERTEX-CFD software was verified and validated for steady and unsteady incompressible flows with benchmark cases taken from the published literature: natural convection, viscous heating, laminar flow over a circle, and turbulent channels. VERTEX-CFD software has also been demonstrated to scale on CPU (Perlmutter) and GPU (Perlmutter and Summit) architectures.
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VERTEX-CFD is an open-source CFD solver that relies on a finite element discretization method to solve for the incompressible Navier-Stokes equations coupled to a temperature equation and MHD equation. RANS turbulence models and LES models are also available. The code relies on the Trilinos package and offers a wide range of temporal integrators, solvers, and preconditioners to run on CPU- and GPU-enabled platforms. VERTEX-CFD software was verified and validated for steady and unsteady incompressible flows with benchmark cases taken from the published literature: natural convection, viscous heating, laminar flow over a circle, and turbulent channels. VERTEX-CFD software has also been demonstrated to scale on CPU (Perlmutter) and GPU (Perlmutter and Summit) architectures.
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Development tasks are currently focusing on the following three main activities:
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