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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.
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.
Animal models are often needed in cancer research but some research questions may be answered with other models, e.g., 3D replicas of patient-specific data, as these mirror the anatomy in more detail. We, therefore, developed a simple eight-step process to fabricate a 3D replica from computer tomography (CT) data using solely open access software and described the method in detail. For evaluation, we performed experiments regarding endoscopic tumor treatment with magnetic nanoparticles by magnetic hyperthermia and local drug release. For this, the magnetic nanoparticles need to be accumulated at the tumor site via a magnetic field trap. Using the developed eight-step process, we printed a replica of a locally advanced pancreatic cancer and used it to find the best position for the magnetic field trap. In addition, we described a method to hold these magnetic field traps stably in place. The results are highly important for the development of endoscopic tumor treatment with magnetic nanoparticles as the handling and the stable positioning of the magnetic field trap at the stomach wall in close proximity to the pancreatic tumor could be defined and practiced. Finally, the detailed description of the workflow and use of open access software allows for a wide range of possible uses.
Automated force field optimisation of small molecules using a gradient-based workflow package
(2010)
In this study, the recently developed gradient-based optimisation workflow for the automated development of molecular models is for the first time applied to the parameterisation of force fields for molecular dynamics simulations. As a proof-of-concept, two small molecules (benzene and phosgene) are considered. In order to optimise the underlying intermolecular force field (described by the (12,6)-Lennard-Jones and the Coulomb potential), the energetic and diameter parameters ε and σ are fitted to experimental physical properties by gradient-based numerical optimisation techniques. Thereby, a quadratic loss function between experimental and simulated target properties is minimised with respect to the force field parameters. In this proof-of-concept, the considered physical target properties are chosen to be diverse: density, enthalpy of vapourisation and self-diffusion coefficient are optimised simultaneously at different temperatures. We found that in both cases, the optimisation could be successfully concluded by fulfillment of a pre-defined stopping criterion. Since a fairly small number of iterations were needed to do so, this study will serve as a good starting point for more complex systems and further improvements of the parametrisation task.
Liquid–liquid equilibria of dipropylene glycol dimethyl ether and water by molecular dynamics
(2011)
In dieser Dissertation stellen wir einen neuen Ansatz zur Modellierung von Polymersystemen vor. Es werden (von methodischer Seite her) zwei automatisierte Iterationschemata dazu eingeführt, Kraftfeldparameter mesoskopischer Polymersysteme systematisch zu optimieren: Das Simplex-Verfahren und das Struktur-Differenzen-Verfahren. So werden diejenigen Freiheitsgrade aus Polymersystemen eliminiert, die eine hohe Auflösung erfordern, was die Modellierung größerer Systeme ermöglicht. Nach Tests an einfachen Flüssigkeiten werden vergröberte Modelle von drei prototypischen Polymeren (Polyacrylsäure, Polyvinylalkohol und Polyisopren) in unterschiedlichen Umgebungen (gutes Lösungsmittel und Schmelze) entwickelt und ihr Verhalten auf der Mesoskala ausgiebig geprüft. Die zugehörige Abbildung (von physikalischer Seite her) so zu gestalten, daß sie die unverwechselbaren Charakteristiken jedes Systems auf die mesoskopische Längenskala überträgt, stellt eine entscheidende Anforderung an die automatisierten Verfahren dar.