# Mathias J. KrauseKarlsruhe Institute of Technology | KIT · Lattice Boltzmann Resarch Group (LBRG)

Mathias J. Krause

PD Dr. rer. nat.

## About

109

Publications

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947

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Introduction

* see OpenLB: http://www.openlb.net
* see LinkedIn Profile: http://www.linkedin.com/in/mathiasjkrause
* see Lattice Boltzmann Research Group: http://www.lbrg.kit.edu

Additional affiliations

April 2013 - present

October 2006 - present

## Publications

Publications (109)

Computational fluid dynamics (CFD) are being used more and more in the industry to understand and optimize processes such as fluid flows. At the same time, tools such as augmented reality (AR) are becoming increasingly important with the realization of Industry 5.0 to make data and processes more tangible. Placing the two together paves the way for...

We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) for a given scalar, linear, d-dimensional advection-diffusion equation. Subsequently, the RS is linked to a d-dimensional discrete velocity Boltzmann model (DVBM) on the zeroth and first energy...

We carry out exploratory computing to analyze the kinetic relaxation parameters of lattice Boltzmann methods (LBM) for artificial turbulence simulations. We provide numerical indication that the tunable parameters in multiple-relaxation-time (MRT) LBM are least dissipative and most accurate with respect to spectral direct numerical simulation data,...

We extend a previous work to construct a relaxation system (RS) for a given scalar, linear, d-dimensional, parabolic partial differential equation (PDE) of order two. Subsequently, the RS is downcasted to a d-dimensional discrete velocity Boltzmann model (DVBM) on the zeroth and first energy shell. In particular, the (2d+1)x(2d+1) RS recovers a lin...

We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBE) with respect to a given partial differential equation (PDE) system. The incompressible Navier–Stokes equations (NSE) are used as paragon. Based upon the diffusion limit [L. Saint-Raymond (2003), doi: 10.1016/S0012-9593(03)0...

Wall-flow filters are a standard component in exhaust gas aftertreatment and have become indispensable in vehicles. Ash and soot particles generated during engine combustion are deposited in diesel or gasoline particulate filters. During regeneration, the soot particles are oxidized. The remaining ash particles can form different deposition pattern...

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64 (double) precision, especially on GPUs. Here we evaluate the possibility to use even FP16 and posit16 (half) precisi...

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64 (double) precision, especially on GPUs. Here we evaluate the possibility to use even FP16 and posit16 (half) precisi...

We derive a novel lattice Boltzmann scheme, which uses a pressure correction forcing term for approximating the volume averaged Navier-Stokes equations (VANSE) in up to three dimensions. With a new definition of the zeroth moment of the Lattice Boltzmann equation, spatially and temporally varying local volume fractions are taken into account. A Cha...

We establish the notion of limit consistency as a novel technique to formally prove the consistency of lattice Boltzmann equations (LBE) to a given partial differential equation (PDE) [S. Simonis, M. J. Krause (2022), Preprint in review]. For the purpose of illustration, the incompressible Navier-Stokes equations (NSE) are used as a paragon. Based...

As micromixers offer the cheap and simple mixing of fluids and suspensions, they have become a key device in microfluidics. Their mixing performance can be significantly increased by periodically varying the inlet pressure, which leads to a non-static flow and improved mixing process. In this work, a micromixer with a T-junction and a meandering ch...

Major new features include support for GPUs using CUDA, vectorized collision steps on SIMD CPUs, a new implementation of our resolved particle system as well as the possibility of simulating free surface flows and reactions.
See https://www.openlb.net/news/openlb-release-1-5-available-for-download/ for the full release notes.

Am Karlsruher Institut für Technologie (KIT) findet seit 2010 jedes Sommersemester das projektorientierte Softwarepraktikum statt. Wir bieten es gemeinschaftlich vom Institut für Angewandte und Numerische Mathematik (IANM) und dem Institut für Mechanische Verfahrenstechnik und Mechanik (MVM) an. Seit dem Frühjahr 2020 werden praktische Lehrveransta...

Wall-flow particulate filters are used for particulate matter removal from exhaust in aftertreatment systems of combustion engines. Inside these filters, the gas flow passes through a porous wall between oppositely arranged inlet and outlet channels. Due to continuously introduced solid material, the filters have to be regenerated resulting in a br...

In contrast to conventional dry separators, new types of wet scrubbers with innovative nozzle geometries are capable of separating submicron particles with comparatively low pressure drop. As those geometries can easily be adapted using 3D‐printing manufacturing, an applied geometry optimization can lead to a fast and cost‐efficient product develop...

We provide a first investigation of using lattice Boltzmann methods (LBM) for temporal large eddy simulation (TLES). The temporal direct deconvolution model (TDDM) is injected as a closure for the filtered discrete velocity Bhatnagar–Gross–Krook (BGK) Boltzmann equation with orthogonal multiple-relaxation-time (MRT) collision. The novel combination...

In the present paper, as part of an interdisciplinary research project (Priority Programme SPP2045), we propose a possible way to design an open access archive for particle-discrete tomographic datasets: the PARROT database (https://parrot.tu-freiberg.de). This archive is the result of a pilot study in the field of particle technology and three use...

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory-intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64 (double) precision, especially on GPUs. Here, we evaluate the possibility to use even FP16 and Posit16 (half) precis...

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling.
The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM.
The stability sets are defined via the spectral radius of linearized amplification ma...

Lattice Boltzmann methods (LBM) are well suited to highly parallel computational fluid dynamics (CFD) simulations due to their separability into a perfectly parallel collision step and a propagation step that only communicates within a local neighborhood. The implementation of the propagation step provides constraints for the maximum possible bandw...

The design and optimization of photobioreactors (PBR) can benefit from the development of robust and yet quantitatively accurate computational models, that incorporate the complex interplay of fundamental phenomena. At a minimum, the simulation model requires at least three submodels for hydrodynamic, light supply and biomass kinetics as pointed ou...

With its roots in kinetic theory, the lattice Boltzmann method (LBM) cannot only be used to solve complex fluid flows but also radiative transport in volume. The present work derives a novel Fresnel boundary scheme for radiative transport LBM, based on Fresnel's equation, which depicts the partly reflected radiation on surfaces. Driven from a bound...

A flexible framework for shape optimisation is presented for incompressible Newtonian fluids using lattice Boltzmann methods. It is proposed to solve optimisation problems using line search methods, with design sensitivities obtained through forward propagation automatic differentiation. The underlying fluid flow problems are modelled by homogenise...

This paper investigates a promising new approach of magnetic chromatography to improve particle fractionation in industrial-scale production. To understand the still challenging multidimensional separation mechanism, we develop a novel method to simulate magnetic nanoparticles’ behavior in a magnetized chromatographic column based on a lattice Bolt...

In this paper, we use a fluid-structure interaction (FSI) approach to simulate a Coriolis mass flowmeter (CMF). The fluid dynamics is calculated by the open-source framework OpenLB, based on the lattice Boltzmann method (LBM). For the structural dynamics we employ the open-source software Elmer, an implementation of the finite element method (FEM)....

Traditional Lattice–Boltzmann modelling of advection-diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice–Boltzmann Navier–Stokes solver is coupled to a Lattice–Bol...

A detailed knowledge of the influence of a particle’s shape on its settling behavior is useful for the prediction and design of separation processes. Models in the available literature usually fit a given function to experimental data. In this work, a constructive and data-driven approach is presented to obtain new drag correlations. To date, the o...

Reactive particulate systems are of prime importance in varieties of practical applications in process engineering. As an example this study considers extraction of phosphorous from waste water by calcium silicate hydrate particles in the P-RoC c process. For such systems modeling has a large potential to help to optimize process conditions e.g. pa...

The lack of interpretability of neural networks is partially why they are not adopted in a wider variety of applications. Many works focus on explaining their predictions, but few take tabular data into consideration, which led to a small adoption even though this data is of high academic and business interest. We present relevance aggregation, an...

The simulation of surface resolved particles is a valuable tool to gain more insights in the behaviour of particulate flows in engineering processes. In this work the homogenized lattice Boltzmann method as one approach for such direct numerical simulations is revisited and validated for different scenarios. Those include a 3D case of a settling sp...

The shear stress induced breaking behavior of carbon black (CB) aggregates during the manufacturing process of Li‐ion batteries is investigated via microscale discrete element method (DEM) simulations. The relevant range of shear stress is chosen according to a planetary mixer and cathode slurries with high solid content. Aggregates of different si...

Detailed numerical analyses of temperature and air velocity distributions are relevant to assess thermal comfort in a wide range of applications. Until now mainly simulations based on Reynolds-averaged Navier–Stokes equations (RANS) are used, whereby fluctuations as well as anisotropy of the turbulence are represented with insufficient precision. T...

The connection of relaxation systems (RS) and discrete velocity Boltzmann models (DVBM) was and is essential to the progress of stability as well as convergence results for lattice Boltzmann methods (LBM). In the present study we propose a formal perturbation ansatz for the construction of an RS on the basis of a given scalar one-dimensional partia...

Learning content in mathematics, such as vector geometry, is still predominantly taught in an abstract manner, as the visualization and interaction of three-dimensional problems are limited with classical forms of teaching such as blackboard lessons or exercise sheets. This research article proposes the use of augmented reality (AR) in mathematics...

Detailed numerical analyses of temperature and air velocity distributions are relevant to assess thermal comfort in a wide range of applications. Until now mainly simulations based on Reynolds-averaged Navier--Stokes equations (RANS) are used, whereby fluctuations as well as anisotropy of the turbulence are represented with insufficient precision....

The structural analysis of proteins is an essential step for understanding their biological function. However, the process of the structural determination of these molecules is expensive and time-consuming. In order to reduce these factors, computational methods might be a provocative approach, despite the complexity associated with it. Over the de...

The industrial particle sensor market lacks simple, easy to use, low cost yet robust, safe and fast response solutions. Towards development of such a sensor, for in-line use in micro channels under continuous flow conditions, this work introduces static light scattering (SLS) determination of particle diameter using a laser with an emission power o...

Best practice energy efficiency goals (EU 2030 climate & energy framework [1]) require substantial improvements in thermal insulation. Vacuum Insulation Panels (VIPs) offer considerable advantages over traditional insulation materials in terms of thermal insulation performance, with effective thermal conductivities between 0.004 and 0.008 W/(mK) [2...

The present work compares fluid–solid interface approaches for the lattice Boltzmann method (LBM) to study vortex-induced vibrations (VIV). Two classes of fluid–solid interface approaches, namely the partially saturated methods (PSM) (Noble and Torczynski (1998), Holdych (2003), Krause et al. (2017), Trunk et al. (2018)) and moving boundary methods...

The connection of discrete velocity Boltzmann models (DVBM) to relaxation systems (RS) is essential to the progress of convergence results for lattice Boltzmann methods (LBM). The present study proposes a formal perturbation ansatz for constructing an RS on the basis of a given scalar advection-diffusion equation. Subsequently, equivalence to a DVB...

Phase change materials (PCM) have become a popular choice for building thermal management due to their low cost, chemical stability and high energy density. Though, their low thermal conductivity is a limiting factor in their use. To overcome this limitation, there has been considerable interest in the application of highly conductive substrates su...

The connection of relaxation systems and discrete velocity models is essential to the progress of stability as well as convergence results for lattice Boltzmann methods. In the present study we propose a formal perturbation ansatz starting from a scalar one-dimensional target equation, which yields a relaxation system specifically constructed for i...

For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupli...

In this paper we use a fluid-structure interaction (FSI) approach to simulate a Coriolis mass flowmeter (CMF). The fluid dynamics are calculated by the open source framework OpenLB, based on the lattice Boltzmann method (LBM). For the structural dynamics we employ the open source software Elmer, an implementation of the finite element method (FEM)....

In this paper, we compare the capabilities of two open source near-wall-modeled large eddy simulation (NWM-LES) approaches regarding prediction accuracy, computational costs and ease of use to predict complex turbulent flows relevant to internal combustion (IC) engines. The applied open source tools are the commonly used OpenFOAM, based on the fini...

We present the OpenLB package, a C++ library providing a flexible framework for lattice Boltzmann simulations. The code is publicly available and published under GNU GPLv2, which allows for adaption and implementation of additional models. The extensibility benefits from a modular code structure achieved e.g. by utilizing template meta-programming....

The development of sustainable trucks has drawn a lot of attention lately. However, the reduction of fuel consumption and emissions related to deep frozen food transports has not yet been satisfactorily considered. In this paper, a thermal Large Eddy Lattice Boltzmann Method (LES-LBM) is applied to investigate two concepts for optimized refrigerate...

The thermal properties of lightweight buildings can be efficiently improved by using phase change materials (PCMs). The heat storage capacity of the building can be extended exactly at the desired temperature level, which leads to an enormous increase in residential comfort. This is shown in the present paper using the example of a prefabricated wo...

In a previous work, the feasibility of coupling magnetic resonance imaging (MRI) measurements and computational fluid dynamics (CFD) was presented, called CFD-MRI. Using a lattice Boltzmann based topology optimisation approach, the method can be described as a Navier–Stokes filter for flow MRI measurements. The main objective of this article is the...

In this article, the adjoint lattice Boltzmann method (ALBM) for solving fluid domain identification problems for incompressible fluids, proposed by Krause et al. (2016), is improved and validated. The problem is formulated as a distributed control problem which minimises the distance between a given, e.g. from measurements like MRI, and a simulate...

Stability, consistency and accuracy of various lattice Boltzmann schemes are investigated by means of numerical experiments on decaying homogeneous isotropic turbulence (DHIT). Therefore, the Bhatnagar–Gross–Krook (BGK), the entropic lattice Boltzmann (ELB), the two-relaxation-time (TRT), the regularized lattice Boltzann (RLB) and the multiple-rela...

The numerical prediction of pressure drop within wall-bounded flow domains at high Reynolds numbers (Re) using a large-eddy simulation (LES) approach is a challenging task for industrial applications because the fluid domain is usually underresolved. A lattice Boltzmann method (LBM) with Bhatnagar, Gross and Krook (BGK) collision operator coupled w...

Lattice Boltzmann methods (LBM) are used for massively parallel computational fluid dynamics simulations since they are easily parallelizable with a perfectly parallel and local in space collision step and a streaming step that only transfers data between neighboring grid points. Current CPU hardware architectures focus on increasing parallelism th...

In this study, a thermal Large Eddy Lattice Boltzmann Method (LBM–LES) is applied to Taylor–Couette flow simulations, allowing detailed analysis of local heat transport over a wide range of Taylor numbers, including resolved transient Taylor vortices.
The challenge in thermal management of electric motors is to control the temperature in the air ga...

A novel Lattice-Boltzmann model to simulate gas mixing in anaerobic digestion is developed and described. For the first time, Euler–Lagrange multiphase, non-Newtonian and turbulence modelling are applied jontly with a novel hybrid boundary condition. The model is validated in a laboratory-scale framework and flow patterns are assessed through Parti...

Due to reduced thermal conductivity, vacuum insulation panels (VIPs) provide significant thermal insulation performance. Our novel vacuum panels operate at reduced pressure and are filled with a powder of precipitated silicic acid to further hinder convection and provide static stability against atmospheric pressure. To obtain an in depth understan...