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The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field.
Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauss-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauss-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor-Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor-Green vortex flows with Mach numbers Ma={0.5;1.0;1.5;2.0} on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.
In this contribution, we perform computer simulations to expedite the development of hydrogen storages based on metal hydride. These simulations enable in-depth analysis of the processes within the systems which otherwise could not be achieved. That is, because the determination of crucial process properties require measurement instruments in the setup which are currently not available. Therefore, we investigate the reliability of reaction values that are determined by a design of experiments.
Specifically, we first explain our model setup in detail. We define the mathematical terms to obtain insights into the thermal processes and reaction kinetics. We then compare the simulated results to measurements of a 5-gram sample consisting of iron-titanium-manganese (FeTiMn) to obtain the values with the highest agreement with the experimental data. In addition, we improve the model by replacing the commonly used Van’t-Hoff equation by a mathematical expression of the pressure-composition-isotherms (PCI) to calculate the equilibrium pressure.
Finally, the parameters’ accuracy is checked in yet another with an existing metal hydride system. The simulated results demonstrate high concordance with experimental data, which advocate the usage of approximated kinetic reaction properties by a design of experiments for further design studies. Furthermore, we are able to determine process parameters like the entropy and enthalpy.
Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauß-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauß-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor–Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor–Green vortex flows with Mach numbers on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.
The lattice Boltzmann method (LBM) stands apart from conventional macroscopic approaches due to its low numerical dissipation and reduced computational cost, attributed to a simple streaming and local collision step. While this property makes the method particularly attractive for applications such as direct noise computation, it also renders the method highly susceptible to instabilities. A vast body of literature exists on stability-enhancing techniques, which can be categorized into selective filtering, regularized LBM, and multi-relaxation time (MRT) models. Although each technique bolsters stability by adding numerical dissipation, they act on different modes. Consequently, there is not a universal scheme optimally suited for a wide range of different flows. The reason for this lies in the static nature of these methods; they cannot adapt to local or global flow features. Still, adaptive filtering using a shear sensor constitutes an exception to this. For this reason, we developed a novel collision operator that uses space- and time-variant collision rates associated with the bulk viscosity. These rates are optimized by a physically informed neural net. In this study, the training data consists of a time series of different instances of a 2D barotropic vortex solution, obtained from a high-order Navier–Stokes solver that embodies desirable numerical features. For this specific text case our results demonstrate that the relaxation times adapt to the local flow and show a dependence on the velocity field. Furthermore, the novel collision operator demonstrates a better stability-to-precision ratio and outperforms conventional techniques that use an empirical constant for the bulk viscosity.
Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing 100.000s of evaluations. Even with the assistance of surrogate models, quality diversity needs 100s or even 1000s of evaluations, which can make it use infeasible. In this study we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.