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Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.
Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation’s material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.
This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method , the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
Turbulent compressible flows are traditionally simulated using explicit Eulerian time integration applied to the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which elegantly circumvents this restriction. Previous lattice Boltzmann methods for compressible flows were mostly restricted to two dimensions due to the enormous number of discrete velocities needed in three dimensions. In contrast, this Rapid Communication demonstrates how cubature rules enhance the SLLBM to yield a three-dimensional velocity set with only 45 discrete velocities. Based on simulations of a compressible Taylor-Green vortex we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, even when the time step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization.
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.
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.
Force field (FF) based molecular modeling is an often used method to investigate and study structural and dynamic properties of (bio-)chemical substances and systems. When such a system is modeled or refined, the force field parameters need to be adjusted. This force field parameter optimization can be a tedious task and is always a trade-off in terms of errors regarding the targeted properties. To better control the balance of various properties’ errors, in this study we introduce weighting factors for the optimization objectives. Different weighting strategies are compared to fine-tune the balance between bulk-phase density and relative conformational energies (RCE), using n-octane as a representative system. Additionally, a non-linear projection of the individual property-specific parts of the optimized loss function is deployed to further improve the balance between them. The results show that the overall error is reduced. One interesting outcome is a large variety in the resulting optimized force field parameters (FFParams) and corresponding errors, suggesting that the optimization landscape is multi-modal and very dependent on the weighting factor setup. We conclude that adjusting the weighting factors can be a very important feature to lower the overall error in the FF optimization procedure, giving researchers the possibility to fine-tune their FFs.
This paper presents a novel approach to address noise, vibration, and harshness (NVH) issues in electrically assisted bicycles (e-bikes) caused by the drive unit. By investigating and optimising the structural dynamics during early product development, NVH can decisively be improved and valuable resources can be saved, emphasising its significance for enhancing riding performance. The paper offers a comprehensive analysis of the e-bike drive unit’s mechanical interactions among relevant components, culminating—to the best of our knowledge—in the development of the first high-fidelity model of an entire e-bike drive unit. The proposed model uses the principles of elastic multi body dynamics (eMBD) to elucidate the structural dynamics in dynamic-transient calculations. Comparing power spectra between measured and simulated motion variables validates the chosen model assumptions. The measurements of physical samples utilise accelerometers, contactless laser Doppler vibrometry (LDV) and various test arrangements, which are replicated in simulations and provide accessibility to measure vibrations onto rotating shafts and stationary structures. In summary, this integrated system-level approach can serve as a viable starting point for comprehending and managing the NVH behaviour of e-bikes.
Heutzutage werden alternative Mobilitätslösungen immer wichtiger. Dabei haben eBikes ihr Potential längst unter Beweis gestellt. Der zugehörige Markt ist über die letzten 10 Jahre enorm gewachsen und gleichermaßen auch die Erwartungen an das Produkt, wie bspw. eine Fahrt ohne störende Vibrationen und Geräusche zu haben. Der Motorfreilauf leistet dabei einen maßgeblichen Einfluss auf das dynamische Verhalten. In diesem Beitrag soll daher eine methodische Vorgehensweise vorgestellt werden, um mittels Versuch und Simulation den Einfluss des Motorfeilaufs auf das dynamische Verhalten der eBike Antriebseinheit zu bestimmen.
Integrating physical simulation data into data ecosystems challenges the compatibility and interoperability of data management tools. Semantic web technologies and relational databases mostly use other data types, such as measurement or manufacturing design data. Standardizing simulation data storage and harmonizing the data structures with other domains is still a challenge, as current standards such as the ISO standard STEP (ISO 10303 ”Standard for the Exchange of Product model data”) fail to bridge the gap between design and simulation data. This challenge requires new methods, such as ontologies, to rethink simulation results integration. This research describes a new software architecture and application methodology based on the industrial standard ”Virtual Material Modelling in Manufacturing” (VMAP). The architecture integrates large quantities of structured simulation data and their analyses into a semantic data structure. It is capable of providing data permeability from the global digital twin level to the detailed numerical values of data entries and even new key indicators in a three-step approach: It represents a file as an instance in a knowledge graph, queries the file’s metadata, and finds a semantically represented process that enables new metadata to be created and instantiated.
Wo Laborexperimente zu aufwendig, zu teuer, zu langsam oder zu gefährlich oder Stoffeigenschaften gar nicht erst experimentell zugänglich sind, können Computersimulationen von Atomen und Molekülen diese ersetzen oder ergänzen. Sie ermöglichen dadurch Reduktion von Kosten, Entwicklungszeit und Materialeinsatz. Die für diese Simulationen benötigten Molekülmodelle beinhalten zahlreiche Parameter, die der Simulant einstellen oder auswählen muss. Eine passende Parametrierung ist nur bei entsprechenden Kenntnissen über die Auswirkungen der Parameter auf die zu berechnenden Größen und Eigenschaften möglich. Eine Gruppe von Standardparametern in molekularen Simulationen sind die Partialladungen der einzelnen Atome innerhalb eines Moleküls. Die räumliche Ladungsverteilung innerhalb des Moleküls wird durch Punktladungen auf den Atomzentren angenähert. Für diese Annäherung existieren diverse Ansätze für verschiedene Molekülklassen und Anwendungen. In diesem Teilprojekt des Promotionsvorhabens wurde systematisch der Einfluss der Wahl des Partialladungssatzes auf potentielle Energien und ausgewählte makroskopische Eigenschaften aus Molekulardynamik-Simulationen evaluiert. Es konnte gezeigt werden, dass insbesondere bei stark polaren Molekülen die Auswahl des geeigneten Partialladungssatzes entscheidenden Einfluss auf die Simulationsergebnisse hat und daher nicht naiv, sondern nur ganz gezielt getroffen werden darf.