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multilevel_monte_carlo/use_cases/fluid_dynamics_building/README.md

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**Application dependencies:** `FluidDynamicsApplication`, `LinearSolversApplications`, `MappingApplication`, `MeshingApplication`, `MultilevelMonteCarloApplication`
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## Case Specification
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We solve the [fluid dynamics problem](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/FluidDynamicsApplication) of a fluid passing through a bluff body. The problem is characterized by stochastic wind inlet velocity, which follows a power law. Uncertainty is provided by the mean velocity <img src="https://render.githubusercontent.com/render/math?math=u\sim\mathcal{N}(10.0,0.1)"> and a exponent of the law <img src="https://render.githubusercontent.com/render/math?math=\alpha\sim\mathcal{N}(0.12,0.012)">.
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We solve the [fluid dynamics problem](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/FluidDynamicsApplication) of a fluid passing through a bluff body. The problem is characterized by stochastic wind inlet velocity, which follows a power law. Uncertainty is provided by the mean velocity <img src="https://render.githubusercontent.com/render/math?math=u\sim\mathcal{N}(10.0,0.1)"> and a exponent of the law <img src="https://render.githubusercontent.com/render/math?math=\alpha\sim\mathcal{N}(0.12,0.012)">. The problem is taken from [1].
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The problem can be run with four different algorithms:
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## Results
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The velocity field evolution for the problem is shown next.
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![velocity](data/velocity.gif)
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<img src="data/velocity.gif" alt="velocity" width="750"/>
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The power sums and the h-statistics of both the drag force and the pressure field can be found [here](source/power_sums_outputs).
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## References
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[1] Tosi, R., Amela, R., Badia, R., & Rossi, R. (2021). A parallel dynamic asynchronous framework for Uncertainty Quantification by hierarchical Monte Carlo algorithms. Journal of Scientific Computing, 89(28), 25. https://doi.org/10.1007/s10915-021-01598-6

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