Mehrskalige Beschreibung von Mehrphasen-Fluidströmungen unter Verwendung datengesteuerter Verschlüsse
Zusammenfassung der Projektergebnisse
In this project, I tackled some of the issues that are fundamental and common in data-driven (moment-based) and continuum approximation of meso-scale models. These issues include high cost of data generation, expensive least-biased density estimator, non-realizablity and error in prediction among others. During my project, I provided solutions to some of these issues. • Costly Data Generation: I introduced a general purpose variance reduction method for kinetic theory based on the previous work which allows orders of magnitude speed-up in generating data with a minimal change in the base code compared to the benchmark Monte Carlo solution. • Expensive Least Biased Density Estimator: I found a simple and linear solution to the optimization problem associated with the maximum entropy distribution function which is the least biased density estimator given statistical samples. This allows using MED effectively in the framework of PDE-FIND in discovering partial differential equation (PDE) given samples of the underlying process, instead of using finite difference on histogram estimate. We note that the latter fails to find the PDE corresponding to the simple random walk. • Non-Realizability and Modelling Error: Given the data-driven moment-based model, it does not seem feasible to guarantee realizability for the the predicted solution or quantify the modelling error. The way around this problem is to generate particles given prediction, and perform a few iteration of the solver for the meso-scale model. I proposed a least-biased, efficient and robust sampling method given moments. Even if the moments are not realizable, the sampling method provide samples that are in the neighborhood of the target moments. I believe the remaining challenge in data-driven methods is modelling non-trivial boundary condition to incorporate the non-equilibrium effects (Knudsen layer). In particular, the boundary condition for the continuum/data-driven moment based model depends on the distance of boundary from all other boundaries as well as the solution inside the domain which makes it a great challenge. Although I worked on it for a while, I could not reach an appropriate solution within the time-frame of this funding.
Projektbezogene Publikationen (Auswahl)
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A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction. Journal of Computational Physics, 472, 111677.
Sadr, Mohsen & Hadjiconstantinou, Nicolas G.
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An efficient jump-diffusion approximation of the Boltzmann equation. Journal of Computational Physics, 490, 112308.
Mies, Fabian; Sadr, Mohsen & Torrilhon, Manuel
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Variance reduced particle solution of the Fokker-Planck equation with application to rarefied gas and plasma dynamics. Journal of Computational Physics, 492, 112402.
Sadr, Mohsen & Hadjiconstantinou, Nicolas G.
