Mathias J. Krause

• PD Dr. rer. nat.
• Head at Karlsruhe Institute of Technology

Efficient solid–liquid separation is crucial in industries like mining, but traditional chamber filter presses depend heavily on manual monitoring, leading to inefficiencies, downtime, and resource wastage. This paper introduces a machine learning-powered digital twin framework to improve the operational flexibility and predictive control of a trad...

This release contains a plethora of new models, features and usability improvements, not to forget 40+ new example cases. The addition of a wall model for fixed and moving walls usable together with a new platform-transparent fluid structure interaction module, physically parameterized multi-phase models and examples and a completely revamped code...

We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link between the method's parameters and physical properties-such as phase densities, interface thickness, and surface t...

Lattice-Boltzmann methods are established mesoscopic numerical schemes for fluid flow, that recover the evolution of macroscopic quantities (viz., velocity and pressure fields) evolving under macroscopic target equations. The approximated target equations for fluid flows are typically parabolic and include a (weak) compressibility term. A number of...

We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equation (PDE) system. The incompressible Navier--Stokes equations (NSE) are used as a paragon. Based upon the hydrodynamic limit of the Bhatnagar-Gross-Krook (BGK) Boltzmann eq...

Efficient solid-liquid separation is crucial in industries like mining, but traditional chamber filter presses depend heavily on manual monitoring, leading to inefficiencies, downtime, and resource wastage. This paper introduces a machine learning-powered digital twin framework to improve operational flexibility and predictive control. A key challe...

Digital twin (DT) technology is increasingly used in urban planning, leveraging real-time data integration for environmental monitoring. This paper presents an urban-focused DT that combines computational fluid dynamics simulations with live meteorological data to analyze pollution dispersion. Addressing the health impacts of pollutants like partic...

In this series of studies, we establish homogenized lattice Boltzmann methods (HLBM) for simulating fluid flow through porous media. Our contributions in part I are twofold. First, we assemble the targeted partial differential equation system by formally unifying the governing equations for nonstationary fluid flow in porous media. A matrix of regu...

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multicomponent flows are considered. Despite the laminar streaming regime (e.g., Re = 186), there exist secondary flow microstructures. For this setup, accurate predictions of those s...

This work studies mathematical foundations for optimal boundary control of mixers which mix two fluid phases. Existence of optima is proved and the influence of common objective functionals is discussed.

The homogenized lattice Boltzmann method (HLBM) has emerged as a flexible computational framework for studying particulate flows, providing a monolithic approach to modeling pure fluid flows and flows through porous media, including moving solid and porous particles, within a unified framework. This paper presents a thorough review of HLBM, elucida...

We analyze the spectral properties of entropic stabilizers for lattice Boltzmann methods (LBM) with multi-relaxation collision akin to Karlin–Bösch–Chikatamarla (KBC) models. In combination with a standard second-order truncated Maxwellian equilibrium and the reduced 𝐷3𝑄19 velocity set, the method is used to numerically approximate artificial decay...

This paper series considers the process of hydro-electrochemical saturation in nano-scale porous media. In this Part II, the simulation model from Part I is applied to phosphate saturation reaction in a resolved nano-porous geometry, whereby the sensitivities of the saturation product with respect to different parameters in distinct pore shapes are...

This is the first in a two paper series investigating the process of hydro-electrochemical saturation in nano-scale porous media. In Part I, a novel sensitivity assessing simulation model is developed and validated for consistency using the open-source software library OpenLB. The present work described a reactive Navier-Stokes-Poisson-Nernst-Planc...

Fruit preparations are used in various forms in the food industry. For example, they are used as an ingredient in dairy products such as yogurt with added fruit. The dispersed fruit pieces can be described as soft particles with viscoelastic material behavior. The continuous phase is represented by fluids with complex flow behavior depending on the...

We analyze the spectral properties of entropic stabilizers for lattice Boltzmann methods (LBM) with multi-relaxation collision akin to Karlin–Bösch–Chikatamarla (KBC) models. In combination with a standard second-order truncated Maxwellian equilibrium and the reduced D3Q19 velocity set, the method is used to numerically approximate artificial decay...

The MC1R protein is a receptor found in melanocytes that plays a role in melanin synthesis. Mutations in this protein can impact hair color, skin tone, tanning ability, and increase the risk of skin cancer. The MC1R protein is activated by the alpha‐melanocyte‐stimulating hormone (α‐MSH). Previous studies have shown that mutations affect the intera...

OpenLB is a generic implementation of lattice Boltzmann methods (LBM) that is shared with the open source community under the terms of the GPLv2 license. Since the first release in 2007, the code continues to be improved and extended, resulting in fifteen releases and counting. The OpenLB framework is written in C++ and covers the full scope of sim...

A promising approach to quantify reaction rate parameters is to formulate and solve inverse problems by minimizing the deviation between simulation and measurement. One major challenge may become the non-uniqueness of the recovered parameters due to the ill-posed problem formulation, which requires sophisticated approaches such as regularization. T...

This research focuses on the improvement of porosity distribution within the electrode of an all‐vanadium redox flow battery (VRFB) and on optimizing novel cell designs. A half‐cell model, coupled with topology and shape optimization framework, is introduced. The multiobjective functional in both cases aims to minimize pressure drop while maximizin...

The present annual report documents the parallelization benefits of Lattice-Boltzmann particulate multiphase flow simulations realized in the open source software library OpenLB and performed on the HoreKa supercomputer. For this purpose, the parallel efficiency and total performance of test cases utilizing vectorization on CPUs as well as GPUs is...

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multi-component flows are considered. Despite the laminar streaming regime (e.g. Re = 186), there exist secondary flow micro-structures. For this setup, accurate predictions of that s...

The OpenLB project provides a C++ package for the implementation of lattice Boltzmann methods (LBM) that is general enough to address a vast range of tansport problems, e.g. in computational fluid dynamics. The source code is publicly available and constructed in a well readable, modular way. This enables for a fast implementation of both academic...

The present state of research in computational fluid dynamics (CFD) is marked by an ongoing process of refining numerical methods and algorithms with the goal of achieving accurate modeling and analysis of fluid flow and heat transfer phenomena. Remarkable progress has been achieved in the domains of turbulence modeling, parallel computing, and mes...

Efficient modeling and simulation of uncertainties in computational fluid dynamics (CFD) remains a crucial challenge. In this paper, we present the first stochastic Galerkin (SG) lattice Boltzmann method (LBM) built upon the generalized polynomial chaos (gPC). The proposed method offers an efficient and accurate approach that depicts the propagatio...

Lattice Boltzmann Methods (LBM) are particularly suited to highly parallel computational fluid dynamics simulations both on SIMD CPUs and GPUs. While heterogeneous systems combining CPUs and GPUs are ubiquitous in high performance computation (HPC), the computationally dominant collide-and-stream loop commonly only utilizes either CPUs or GPUs homo...

The pervasive presence of plastic in the environment has reached a concerning scale, being identified in many ecosystems. Bioremediation is the cheapest and most eco-friendly alternative to remove this polymer from affected areas. Recent work described that a novel cold-active esterase enzyme extracted from the bacteria Kaistella jeonii could promi...

The present state of research in Computational Fluid Dynamics (CFD) is marked by an ongoing process of refining numerical methods and algorithms with the goal of achieving accurate modeling and analysis of fluid flow and heat transfer phenomena. Remarkable progress has been achieved in the domains of turbulence modeling, parallel computing, and mes...

We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equation (PDE) system. The incompressible Navier--Stokes equations (NSE) are used as paragon. Based upon the hydrodynamic limit of the Bhatnagar--Gross--Krook (BGK) Boltzmann eq...

In this series of studies, we establish homogenized lattice Boltzmann methods (HLBM) for simulating fluid flow through porous media. Our contributions in part I are twofold. First, we assemble the targeted partial differential equation system by formally unifying the governing equations for nonstationary fluid flow in porous media. A matrix of regu...

A promising approach to quantify reaction rate parameters is to formulate and solve inverse problems by minimizing the deviation between simulation and measurement. One major challenge may become the non-uniqueness of the recovered parameters due to the ill-posed problem formulation, which requires sophisticated approaches such as regularization. T...

Fruchtzubereitungen werden in der Lebensmittelindustrie in verschiedenen Formen verwendet. So werden sie zum Beispiel als Zutat in Molkereiprodukten wie Joghurt mit Fruchtzusatz genutzt. Die wertgebende Komponente der Fruchtzubereitungen stellen dabei die dispergierten Fruchtstücke dar, welche als weiche Partikel mit viskoelastischem Materialverhal...

Using lattice Boltzmann methods with multiple relaxation times for robust and fast incompressible turbulent flow simulations requires tuning of the kinetic parameters. We outsource the perfect parallelizability of lattice Boltzmann methods to analyze kinetic relaxation with respect to non-linear stability and consistency based on explorative comput...

Wall-flow filters are applied in the exhaust treatment of internal combustion engines for the removal of particulate matter (PM). Over time, the pressure drop inside those filters increases due to the continuously introduced solid material, which forms PM deposition layers on the filter substrate. This leads to the necessity of regenerating the fil...

An Euler–Lagrange multicomponent, non-Newtonian Lattice-Boltzmann method is applied for the first time to model a full-scale gas-mixed anaerobic digester for wastewater treatment. Rheology is modelled through a power-law model and, for the first time in gas-mixed anaerobic digestion modelling, turbulence is modelled through a Smagorinsky Large Eddy...

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...

Numerical simulations are used for the approximate prediction of situations under strictly defined conditions. They are based on mathematical models and represent interdependencies in the form of algorithms and computer programs. In everyday life, they are now ubiquitous for everyone, for example in weather forecasts or economic growth forecasts. I...

United in their motivation to better understand and describe the world, scientists from a wide range of disciplines search for new insights every day. At first glance, the approaches chosen on the way to gaining scientific knowledge seem to be very different. However, terms such as “number”, “pattern” or “model” appear in the communication of resul...

OpenLB is an object-oriented implementation of LBM. It is the first implementation of a generic platform for LBM programming, which is shared with the open source community (GPLv2). Since the first release in 2007, the code has been continuously improved and extended which is documented by thirteen releases as well as the corresponding release note...

The OpenLB project provides a C++ package for the implementation of lattice Boltzmann methods (LBM) that is general enough to address a vast range of transport problems, e.g. in computational fluid dynamics. The source code is publicly available and constructed in a well readable, modular way. This enables for a fast implementation of both academic...

Mutations that affect the proteins responsible for the nucleotide excision repair (NER) pathway can lead to diseases such as xeroderma pigmentosum, trichothiodystrophy, Cockayne syndrome, and Cerebro-oculo-facio-skeletal syndrome. Hence, understanding their molecular behavior is needed to elucidate these diseases' phenotypes and how the NER pathway...

Colorectal cancer (CRC) is one of the most common types of cancer, with many studies associating its development with changes in the gut microbiota. Recent developments in sequencing technologies and subsequent meta-analyses of gut metagenome provided a better understanding of species association to CRC tumorigenesis. Still, the importance of high-...

Rearrangement events in wall-flow filters lead to the formation of specific deposition patterns, which affect a filter’s pressure drop, its loading capacity and the separation efficiency. A universal and consistent formulation of probable causes and influence factors does not exist and appropriate calculation models that enable a quantification of...

The exhaust from combustion engines contains particulate matter (PM), which poses potential health risks to human lungs. Current emission laws place increasingly strict limitations on both PM and particle number, leading to the necessity of using wall-flow filters to separate out a significant amount of the introduced PM. As this leads to an increa...

Lattice Boltzmann methods (LBM) are well suited to highly parallel computational fluid dynamics 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 bandwidth-l...

Presentation on OpenLB's refactoring journey

We use free energy lattice Boltzmann methods to simulate shear and extensional flows of a binary fluid in two and three dimensions. To this end, two classical configurations are digitally twinned, namely a parallel-band device for binary shear flow and a four-roller apparatus for binary extensional flow. The free energy lattice Boltzmann method and...

We use free energy lattice Boltzmann methods (FRE LBM) to simulate shear and extensional flow of a binary mixture in two and three dimensions. To this end, two classical configurations are digitally twinned, namely a parallel-band device for binary shear flow and a four-roller apparatus for binary extensional flow. The FRE LBM and the test cases ar...

The design and optimization of photobioreactor(s) (PBR) benefit from the development of robust and quantitatively accurate computational fluid dynamics (CFD) models, which incorporate the complex interplay of fundamental phenomena. In the present work, we propose a comprehensive computational model for tubular photobioreactors equipped with glass s...

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...

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...

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...

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...

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...

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...