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Fluid dynamics building problem

Author: Riccardo Tosi

Kratos version: 9.0

XMC version: Kratos default version

PyCOMPSs version: Kratos default version to run in serial, >2.8 to run with runcompss

Source files: Asynchronous Monte Carlo and Asynchronous Multilevel Monte Carlo

Application dependencies: FluidDynamicsApplication, LinearSolversApplications, MappingApplication, MeshingApplication, MultilevelMonteCarloApplication

Case Specification

We solve the fluid dynamics problem 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 and a exponent of the law . The problem is taken from [1].

The problem can be run with four different algorithms:

  • Synchronous Monte Carlo (SMC),
  • Asynchronous Monte Carlo (AMC),
  • Synchronous Multilevel Monte Carlo (SMLMC),
  • Asynchronous Multilevel Monte Carlo (AMLMC),

and by default AMC and AMLMC are selected. If one is interested in running SMC or SMLMC, it is needed to select asynchronous = false in the solver wrapper settings. Please observe that for running you may want to increase the number of realizations per level and the time horizon of each realization.

The Quantities of Interest of the problem are the drag force and the pressure field. Statistical convergence is assessed for the drag force.

Similar settings are employed for Monte Carlo and Multilevel Monte Carlo. We refer, for example, to: deterministic number of samples estimation, deterministic number of indices estimation, maximum number of iterations, tolerance, confidence, etc. Such settings can be observed in the corresponding configuration file of each algorithm, located inside the problem_settings folder.

To run the examples, the user should go inside the folder-algorithm of interest and run the run_mc/mlmc_Kratos.py Python file. In case one wants to use PyCOMPSs, the user should execute run_runcompss.sh from inside the source folder.

Results

The velocity field evolution for the problem is shown next.

velocity

The power sums and the h-statistics of both the drag force and the pressure field can be found here.

References

[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