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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.

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.

Automated parameterization of intermolecular pair potentials using global optimization techniques
(2014)

In this work, different global optimization techniques are assessed for the automated development of molecular force fields, as used in molecular dynamics and Monte Carlo simulations. The quest of finding suitable force field parameters is treated as a mathematical minimization problem. Intricate problem characteristics such as extremely costly and even abortive simulations, noisy simulation results, and especially multiple local minima naturally lead to the use of sophisticated global optimization algorithms. Five diverse algorithms (pure random search, recursive random search, CMA-ES, differential evolution, and taboo search) are compared to our own tailor-made solution named CoSMoS. CoSMoS is an automated workflow. It models the parameters’ influence on the simulation observables to detect a globally optimal set of parameters. It is shown how and why this approach is superior to other algorithms. Applied to suitable test functions and simulations for phosgene, CoSMoS effectively reduces the number of required simulations and real time for the optimization task.

A central goal of molecular simulations is to predict physical or chemical properties such that costly and elaborate experiments can be minimized. The reliable generation of molecular models is a critical issue to do so. Hence, striving for semiautomated and fully automated parameterization of entire force fields for molecular simulations, the authors developed several modular program packages in recent years. The programs run with limited user interactions and can be executed in parallel on modern computer clusters. Various interlinked resolutions of molecular modeling are addressed: For intramolecular interactions, a force-field optimization package named Wolf2Pack has been developed that transfers knowledge gained from quantum mechanics to Newtonian-based molecular models. For intermolecular interactions, especially Lennard–Jones parameters, a modular optimization toolkit of programs and scripts has been created combining global and local optimization algorithms. Global optimization is performed by a tool named CoSMoS, while local optimization is done by the gradient-based optimization workflow named GROW or by a derivative-free method called SpaGrOW. The overall goal of all program packages is to realize an easy, efficient, and user-friendly development of reliable force-field parameters in a reasonable time. The various tools are needed and interlinked since different stages of the optimization process demand different courses of action. In this paper, the conception of all programs involved is presented and how they communicate with each other.

The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.

Ionic liquids are highly relevant for industrial applications as they stand out due to their special chemical and physical features, e.g. low vapor pressure, low melting point or extraordinary solution properties. The goal of this work is to study the capability of the three ionic liquids [C2MIM][NTf2], [C12MIM][NTf2] and [C2MIM][EtSO4] to diffuse through a POPC membrane (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine). To achieve this, we used molecular simulation techniques, which on the one hand give insight into specific domains of the membrane and on the other hand compute partition coefficients and free energy profiles of solutes in lipid membranes, which cannot be measured by labor experiments. To be as accurate as possible we parameterized a new united atom force field for the ionic liquid of type 1-alkyl-3-methylimidazoliumethylsulfate [CnMIM][EtSO4] with n = 1,2,4,6,8. Like the other IL force field for [CnMIM][NTf2] (see Köddermann et al., ChemPhysChem 14, 3368–3374, 2013) used in this work, the new one was derived to reproduce experimental densities and self-diffusion coefficients. The new force field reproduces the experimental data extremely well. Using this force field, the influences of cation and anion exchanges as well as the variation of the chain length on the free energy could be analyzed. We performed umbrella-sampling to characterize the free energy profile of one ion pair, accompanied by a second one, in solution, at the membrane interface, and inside the membrane. In the outlook we present our intention to parameterize force fields in a systematic and user-friendly way. We will use the combination of two optimization toolkits, developed at SCAI: The global optimization toolkit CoSMoS and the local optimization techniques implemented in the software package GROW.

Molecular simulations are an important tool in the study of aqueous salt solutions. To predict the physical properties accurately and reliably, the molecular models must be tailored to reproduce experimental data. In this work, a combination of recent global and local optimization tools is used to derive force fields for MgCl2 (aq) and CaCl2 (aq). The molecular models for the ions are based on a Lennard-Jones (LJ) potential with a superimposed point charge. The LJ parameters are adjusted to reproduce the bulk density and shear viscosity of the different solutions at 1 bar and temperatures of 293.15, 303.15, and 318.15 K. It is shown that the σ-value of chloride consistently has the strongest influence on the system properties. The optimized force field for MgCl2 (aq) provides both properties in good agreement with the experimental data over a wide range of salt concentrations. For CaCl2 (aq), a compromise was made between the bulk density and shear viscosity, since reproducing the two properties requires two different choices of the LJ parameters. This is demonstrated by studying metamodels of the simulated data, which are generated to visualize the correlation between the parameters and observables by using projection plots. Consequently, in order to derive a transferable force field, an error of ∼3% on the bulk density has to be tolerated to yield the shear viscosity in satisfactory agreement with experimental data.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies
(2018)

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

The paper describes methods for calculating chemical equilibria based on a constrained Gibbs free energy minimization. The methods allow the treatment of multicomponent systems with multiple phases, including gaseous phases, condensed phases, and stoichiometric phases. A special aspect is the detection and treatment of miscibility gaps. The underlying mathematical problem is described in detail together with the algorithmic approach for its solution. Results are presented for some test cases, including the computation of phase diagrams for ternary systems.

In dieser Arbeit werden neuartige methodische Erweiterungen der Lattice-Boltzmann-Methode (LBM) entwickelt, die effizientere Simulationen inkompressibler Wirbelströmungen ermöglichen. Diese Erweiterungen beheben zwei Hauptprobleme der Standard-LBM: ihre Instabilität in unteraufgelösten turbulenten Simulationen und ihre Beschränkung auf reguläre Rechengitter. Dazu wird zunächst eine Pseudo-Entropische Stabilisierung (PES) entwickelt. Diese kombiniert Ansätze der Multiple-Relaxation-Time (MRT)-Modelle und der Entropischen LBM zu einem expliziten, lokalen und flexiblen Stabilisierungsoperator. Diese Modifikation des Kollisionsschritts erlaubt selbst auf stark unteraufgelösten Gittern stabile und qualitativ korrekte Simulationen. Zur Erweiterung der LBM auf irreguläre Rechengitter wird zunächst eine moderne Discontinuous-Galerkin-LBM untersucht und um stabilere Zeitintegratoren ergänzt. Diese Studie demonstriert die drastischen Schwächen existierender LBMAnsätze auf irregulären Gittern. Basierend auf den gewonnenen Erkenntnissen gelingt die Formulierung einer neuartigen Semi-Lagrangeschen LBM (SLLBM). Diese ermöglicht in einzigartigerWeise sowohl die Verwendung irregulärer Gitter und großer Zeitschritte als auch eine hohe räumliche Konvergenzordnung. Anhand von Beispielsimulationen wird demonstriert, wieso dieser Ansatz anderen aktuellen Off-Lattice-Boltzmann-Methoden (OLBMs) in Effizienz und Genauigkeit überlegen ist. Weitere neuartige Aspekte dieser Arbeit sind die Entwicklung eines modularen Off-Lattice-Boltzmann-Codes und die Erweiterung der LBM um implizite Mehrschrittverfahren, mit denen eine Erhöhung der zeitlichen Konvergenzordnung gelingt.