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

Entropic Lattice Boltzmann Models for Fluid Dynamics

The lattice Boltzmann method (LBM) is a modern and highly successful approach to computational fluid dynamics based on a fully discrete kinetic equation and offers an attractive alternative to direct discretizations of the macroscopic continuum equations. However, the original single relaxation-time formulation (LBGK) was plagued by numerical instabilities and prevented the simulation of highly turbulent flows unless prohibitively high resolutions were employed. A number of improvements and variations of LBM attempted to alleviate this issue. In particular, the multiple relaxation-times methods (MRT) take advantage of the additional degrees of freedom in the LBM kinetic system in order to stabilize the solution and improve accuracy. However, the introduction of additional tunable constants must be chosen appropriately depending on the physics and the flow at hand and are not universal, and thus, the problem of stability could not be solved consistently. With the inception of the entropic lattice Boltzmann method (ELBM) which reintroduced the discrete-time equivalent of Boltzmann's H-theorem, the application range has grown widely not only for incompressible turbulent flows, but also for thermal flows, two-phase systems with non-ideal equations of state and has made the simulation of compressible and high Mach number flows possible. The ELBM, however, comes at the price of introducing a fluctuating viscosity. The main result of this thesis is the development of a new class of entropic MRT models which combine the salient advantages from MRT and ELBM while trying to circumvent their respective disadvantages. J. W. Gibbs' seminal prescription for constructing optimal states by maximizing the entropy under pertinent constraints is used to derive a novel lattice kinetic theory and the the notion of modifying the viscosity to stabilize sub-grid simulations is challenged in this kinetic framework. By exploiting the degrees of freedom of MRT and by compliance to the discrete-time H-theorem, the advantages of both MRT and ELBM can be retained and the problems of parameter tuning and fluctuating viscosity can be solved. The resulting models are accurate, adaptive, parameter-free, efficient and, more importantly, very stable The entropic MRT models are studied extensively for two- and three- dimensional benchmark simulations at turbulent conditions and compared to experiments, theory and other numerical methods. While the entropic MRT models yield the same results as the LBGK in the resolved limit, and converge towards the Navier-Stokes equations with second-order accuracy, sufficiently accurate results are obtained also at coarse resolutions without the use of sub-grid turbulence models. This made the simulation of high Reynolds number flows with complex boundaries possible which are most relevant for engineering applications. Due to the general nature of the entropic MRT methods, a number of extensions beyond the incompressible low Mach number regimes were explored and extensions for thermal flows and two-phase flows are presented. Moreover, a novel model for miscible binary mixtures is presented in combination with the entropic MRT collision step. The salient features of this model are the lack of interpolation and the use of thermal multi-speed lattices to account for the different sound speed of the two unequally heavy substances involved. Independent adjustment of the diffusion coefficient and kinematic viscosity of the mixture is assured and the diffusion follows the Stefan-Maxwell model. To conclude it is shown that entropy maximisation principle can be extended to multiple relaxation-time lattice Boltzmann models to create more stable and computationally efficient LBM models. This principle of entropy maximization is applied without nominal modification of viscosity and is extended to not only high Reynolds number flows but also thermal, mixture and multi-phase flows. This principle is also shown to be lattice independent and generic nature thus opening a possibility of new class of LB models that are more robust to under-resolution and have a wide range of applications

Entropic Multi-Relaxation Models for Simulation of Fluid Turbulence

A recently introduced family of lattice Boltzmann (LB) models (Karlin, Bösch, Chikatamarla, Phys. Rev. E, 2014; Ref [22]) 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

Lattice Boltzmann model for compressible flows on standard lattices: Variable Prandtl number and adiabatic exponent

ISSN:1539-3755ISSN:1063-651XISSN:1095-3787ISSN:1550-237

Semi-Lagrangian lattice Boltzmann model for compressible flows on unstructured meshes

Compressible lattice Boltzmann model on standard lattices [M. H. Saadat, F. Bösch, and I. V. Karlin, Phys. Rev. E 99, 013306 (2019).] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.ISSN:1539-3755ISSN:1063-651XISSN:1095-3787ISSN:1550-237

Entropy-Assisted Computing of Low-Dissipative Systems

Entropy feedback is reviewed and highlighted as the guiding principle to reach extremely low dissipation. This principle is illustrated through turbulent flow simulations using the entropic lattice Boltzmann scheme.ISSN:1099-430

Entropic multi-relaxation time lattice Boltzmann model for complex flows

Entropic lattice Boltzmann methods were introduced to overcome the stability issues of lattice Boltzmann models for high Reynolds number turbulent flows. However, to date their validity has been investigated only for simple flows due to the lack of appropriate boundary conditions. We present here an extension of these models to complex flows involving curved and moving boundaries in three dimensions. Apart from a thorough investigation of resolved and under-resolved simulations for periodic flow and turbulent flow in a round pipe, we study in detail the set-up of a simplified internal combustion engine with a valve/piston arrangement. This arrangement allows us to probe the non-trivial interactions between various flow features such as jet breakup, jet–wall interaction, and formation and breakup of large vortical structures, among others. Besides an order of magnitude reduction in computational costs, when compared to state-of-the-art direct numerical simulations (DNS), these methods come with the additional advantage of using static Cartesian meshes also for moving objects, which reduces the complexity of the scheme. Going beyond first-order statistics, a detailed comparison of mean and root-mean-square velocity profiles with high-order spectral element DNS simulations and experimental data shows excellent agreement, highlighting the accuracy and reliability of the method for resolved simulations. Moreover, we show that the implicit subgrid features of the entropic lattice Boltzmann method can be utilized to further reduce the grid sizes and the computational costs, providing an alternative to modern modelling approaches such as large-eddy simulations for complex flows.ISSN:0022-1120ISSN:1469-764

Exoskelett Transparenz: Vorwärtssteuerung vs. Störbeobachter

Undesired forces during human-robot interaction limit training effectiveness with rehabilitation robots. Thus, avoiding such undesired forces by improved mechanics, sensorics, kinematics, and controllers are the way to increase exoskeleton transparency. In this paper, the arm therapy exoskeleton ARMin IV+ was used to compare the differences in transparency offered by using the previous feed-forward model-based controller, with a disturbance observer in a study. Systematic analysis of velocity-dependent effects of controller transparency in single- and multi-joint scenarios performed in this study highlight the advantage of using disturbance observers for obtaining consistent transparency behavior at different velocities in single-joint and multi-joint movements. As the main result, the concept of the disturbance observer sets a new benchmark for ARMin transparency