Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions

Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil at a Reynolds number of Re = 40000 and finally, to access the model's performance for deforming meshes, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.Comment: submitted to Journal of Computational Physic

Entropic Multi-Relaxation Models for Simulation of Fluid Turbulence

A recently introduced family of lattice Boltzmann (LB) models (Karlin, B\"osch, Chikatamarla, Phys. Rev. E, 2014) is studied in detail for incompressible two-dimensional flows. A framework for developing LB models based on entropy considerations is laid out extensively. Second order rate of convergence is numerically confirmed and it is demonstrated that these entropy based models recover the Navier-Stokes solution in the hydrodynamic limit. Comparison with the standard Bhatnagar-Gross-Krook (LBGK) and the entropic lattice Boltzmann method (ELBM) demonstrates the superior stability and accuracy for several benchmark flows and a range of grid resolutions and Reynolds numbers. High Reynolds number regimes are investigated through the simulation of two-dimensional turbulence, particularly for under-resolved cases. Compared to resolved LBGK simulations, the presented class of LB models demonstrate excellent performance and capture the turbulence statistics with good accuracy.Comment: To be published in Proceedings of Discrete Simulation of Fluid Dynamics DSFD 201

Drops bouncing off macro-textured superhydrophobic surfaces

Recent experiments with droplets impacting a macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. We present here a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantify the role played by various external and internal forces that effect the dynamics of a drop impacting a complex surface. For the first time, three-dimensional simulations involving macro-textured surfaces are performed. Aside from demonstrating that simulations reproduce experiments in a quantitative manner, the study is focused on analyzing the flow situations beyond current experiments. We show that the experimentally observed reduction of contact time extends to higher Weber numbers, and analyze the role played by the texture density. Moreover, we report a non-linear behavior of the contact time with the increase of the Weber number for application relevant imperfectly coated textures, and also study the impact on tilted surfaces in a wide range of Weber numbers. Finally, we present novel energy analysis techniques that elaborate and quantify the interplay between the kinetic and surface energy, and the role played by the dissipation for various Weber numbers

Fluid-Structure Interaction with the Entropic Lattice Boltzmann Method

We propose a novel fluid-structure interaction (FSI) scheme using the entropic multi-relaxation time lattice Boltzmann (KBC) model for the fluid domain in combination with a nonlinear finite element solver for the structural part. We show validity of the proposed scheme for various challenging set-ups by comparison to literature data. Beyond validation, we extend the KBC model to multiphase flows and couple it with FEM solver. Robustness and viability of the entropic multi-relaxation time model for complex FSI applications is shown by simulations of droplet impact on elastic superhydrophobic surfaces

A note on the invariant distribution of a quasi-birth-and-death process

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution

An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys. Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study I present a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data I demonstrate high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19 pages, including 2 Tables and 4 Figure