Stephan Simonis

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• Dr. rer. nat. (PhD)
• PostDoc Position at Karlsruhe Institute of Technology

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional score-based diffusion model. Through extensive numerical experimentation with a set of challenging fluid flows,...

We develop stochastic lattice Boltzmann methods (LBMs) for efficiently approximating statistical solutions to the incompressible Navier–Stokes equations (NSE) in three spatial dimensions. Entropic space-time adaptive kinetic relaxation frequencies allow for stable and consistent numerical solutions with decreasing viscosity. Single level Monte Carl...

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...

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...

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...

Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1-40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work,...

Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1-40]. It is thus known that any lattice Boltzmann scheme can be expressed in terms of a corresponding multi-step finite difference scheme on the conserved variables. In the present work,...

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...

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...

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...

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...

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...

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...

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...

Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of parti...

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...

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...

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...

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...

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 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...

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...

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...

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...

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...

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...

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 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...

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...

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)....

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....

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...