Crystallographic Lattice Boltzmann Method

Lightweight lattice Boltzmann

A regularized version of the lattice Boltzmann method for efficient simulation of soft materials is introduced. Unlike standard approaches, this method reconstructs the distribution functions from available hydrodynamic variables (density, momentum, and pressure tensor) without storing the full set of discrete populations. This scheme shows significantly lower memory requirements and data access costs. A series of benchmark tests of relevance to soft matter, such as collisions of fluid droplets, is discussed to validate the method. The results can be of particular interest for high-performance simulations of soft matter systems on future exascale computers.

Lattice Boltzmann model for weakly compressible flows

We present an energy conserving lattice Boltzmann model based on a crystallographic lattice for simulation of weakly compressible flows. The theoretical requirements and the methodology to construct such a model are discussed. We demonstrate that the model recovers the isentropic sound speed in addition to the effects of viscous heating and heat flux dynamics. Several test cases for acoustics and thermal and thermoacoustic flows are simulated to show the accuracy of the proposed model.

General curved boundary treatment for two- and three-dimensional stationary and moving walls in flow and nonflow lattice Boltzmann simulations

The aim of this study is to introduce a general approach to implement curved boundaries in lattice Boltzmann simulations. The main idea is to determine boundary values by extrapolating macroscopic properties from some reference points inside the computational domain. The introduced approach is based on a unified extrapolation equation that can be employed for any macroscopic value (flow and nonflow properties) in arbitrary two- and three-dimensional geometries. In the case of nonflow simulations, the present treatment can easily apply Dirichlet and Neumann boundary conditions. By introducing a point cloud description of geometry, the new treatment can handle any complex geometry that is modeled by a CAD program. The application of the new treatment is also extended to moving boundaries, by developing a novel force calculation method. The proposed boundary treatment is tested against several well-established problems and the order of accuracy of solutions is evaluated. Numerical results show that the present treatment is of second-order accuracy with respect to the grid spacing in flow simulations, and it leads to a significant enhancement in nonflow simulations as well.

Essentially Entropic Lattice Boltzmann Model

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88×10^{6}.

Deciphering pore-level precipitation mechanisms

Mineral precipitation and dissolution in aqueous solutions has a significant effect on solute transport and structural properties of porous media. The understanding of the involved physical mechanisms, which cover a large range of spatial and temporal scales, plays a key role in several geochemical and industrial processes. Here, by coupling pore scale reactive transport simulations with classical nucleation theory, we demonstrate how the interplay between homogeneous and heterogeneous precipitation kinetics along with the non-linear dependence on solute concentration affects the evolution of the system. Such phenomena are usually neglected in pure macroscopic modelling. Comprehensive parametric analysis and comparison with laboratory experiments confirm that incorporation of detailed microscale physical processes in the models is compulsory. This sheds light on the inherent coupling mechanisms and bridges the gap between atomistic processes and macroscopic observations.

Entropic multirelaxation-time 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 [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)JCTPAH0021-999110.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)JFLSA70022-112010.1017/jfm.2016.448] 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 and then turbulence and deforming geometries. 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 in the transitional regime at a Reynolds number of Re=40000 and, finally, to access the model's performance for deforming geometries, 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.

Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows

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.