Article
Mathematics, Applied
Elissa Eggenweiler, Marco Discacciati, Iryna Rybak
Summary: This paper investigates fluid flows in coupled systems consisting of a free-flow region and an adjacent porous medium. Mathematical analysis of the Stokes-Darcy problem with generalised interface conditions is conducted, and the existence and uniqueness of weak solutions for the coupled problem are proven.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Zhongwei Shen
Summary: This article examines Darcy's law for an incompressible viscous fluid flowing in a porous medium. The paper establishes the O(root epsilon) convergence rate by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Hongxing Zhao
Summary: This paper investigates the flow of fluid through a thin corrugated domain saturated with porous medium, governed by the Navier-Stokes model. Asymptotic models are derived by comparing the relation between a and the size of the periodic cylinders. The homogenization technique based on the generalized Poincare inequality is used to prove the main results.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2024)
Article
Engineering, Chemical
Paula Strohbeck, Elissa Eggenweiler, Iryna Rybak
Summary: Physically consistent coupling conditions and effective parameters are crucial for accurate modeling and simulation of various applications at the fluid-porous interface. The commonly used Beavers-Joseph condition for tangential velocity is only suitable for parallel flows and its slip coefficient value is uncertain.
TRANSPORT IN POROUS MEDIA
(2023)
Article
Computer Science, Interdisciplinary Applications
Alexandre Suss, Ivan Mary, Thomas Le Garrec, Simon Marie
Summary: A hybrid numerical method that combines the lattice Boltzmann method and a compressible finite-volume Navier-Stokes solver is proposed for unsteady aerodynamic and aeroacoustic simulations. The method allows for more realistic and detailed simulations in a reasonable amount of CPU time by taking advantage of the numerical features of both methods in specific flow regions. The key challenge lies in ensuring a smooth transition of the flow variables at the coupling interface between the lattice Boltzmann method and the Navier-Stokes solver.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Fluids & Plasmas
Hong Liang, Runlong Wang, Yikun Wei, Jiangrong Xu
Summary: In this paper, an accurate interface-capturing lattice Boltzmann method is proposed based on the modified Allen-Cahn equation for modeling an immiscible multiphase flow system. The proposed method is built on the relation between the signed-distance function and the order parameter, maintaining the mass-conserved characteristic. By carefully incorporating a suitable forcing term, the target equation can be correctly recovered. Simulation results for various interface-tracking problems demonstrate that the proposed model is more numerically accurate, particularly at a small interface-thickness scale, compared to existing lattice Boltzmann models for the conservative Allen-Cahn equation.
Article
Computer Science, Interdisciplinary Applications
Pierre Lallemand, Li-Shi Luo, Manfred Krafczyk, Wen-An Yong
Summary: This review summarizes the rigorous mathematical theory behind the lattice Boltzmann equation (LBE), including the relevant properties of the Boltzmann equation, derivation of the LBE, and important LBE models. The focus is on the numerical analysis of the LBE as a solver for the nearly incompressible Navier-Stokes equations with appropriate boundary conditions, with several numerical results provided to demonstrate the efficacy of the lattice Boltzmann method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Guangzhi Du, Liyun Zuo
Summary: A two-grid method with backtracking is proposed for the mixed Stokes/Darcy system, and theoretical analysis and numerical experiments are conducted to validate the approach. Coarse mesh correction is utilized to improve error bounds for the velocity field and pressure field, with the numerical results supporting the theoretical findings.
JOURNAL OF NUMERICAL MATHEMATICS
(2021)
Article
Chemistry, Multidisciplinary
Jia Xu, TieZhu Qiao, Qing Li, GuoWei Zhang, GuiRong Hao
Summary: This study proposes an optimization method of crystal rotation to improve the quality of crystal seeding under complex convection. By calculating and analyzing the unsteady melt flow rate, internal temperature of the melt, and crystal rotation speed, the results show that this method can effectively restrain melt convection and improve the temperature distribution on the surface of the melt.
Article
Mechanics
Dejia Zhang, Aiguo Xu, Yudong Zhang, Yanbiao Gan, Yingjun Li
Summary: This paper develops Discrete Boltzmann Models (DBMs) based on the ellipsoidal statistical Bhatnagar-Gross-Krook model to study non-equilibrium high-speed compressible flows that have various applications in engineering and science. Numerical tests demonstrate the model's ability to capture flow structures and TNE effects at different orders. The study is significant for understanding the behavior of complex fluid systems and choosing an appropriate fluid model to account for desired TNE effects.
Article
Mathematics, Applied
Rui Du, Yibo Wang
Summary: In this paper, a novel LBGK model for incompressible time-fractional Navier-Stokes equations with Caputo-type fractional derivative is proposed, where the Caputo derivative is approximated to construct the model, and a numerical example is provided to demonstrate the efficiency of the model.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Xinyuan Xie, Weifeng Zhao, Ping Lin
Summary: This paper introduces a boundary scheme for Robin boundary conditions on curved boundaries in the lattice Boltzmann method, which avoids numerical instability due to zero denominators and ensures stability and accuracy. The proposed scheme is simple to implement, has first-order accuracy, and only requires information from the present point, demonstrating good stability and accuracy in numerical examples.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mechanics
Jianghong Zhang, Gang Sun, Junjie Hu, Jian Wu, Maosen Xu
Summary: The presence of internal obstacles in square cavities significantly affects the flow and motion of solid particles. The motion of neutrally buoyant circular particles in a cavity with a circular obstacle was studied, considering factors such as obstacle size, location, initial particle position, and Reynolds number. The results show that the presence of obstacles alters the flow patterns, and the motion of particles is influenced by the Reynolds number.
Article
Engineering, Multidisciplinary
Pablo G. S. Carvalho, Philippe R. B. Devloo, Sonia M. Gomes
Summary: This article introduces a new semi-hybrid-mixed finite element formulation for solving Stokes-Brinkman problems. The method uses H(div)-conforming approximate velocity fields to ensure the continuity of normal components over element interfaces and utilizes a Lagrange multiplier to enforce tangential continuity. The method is highly robust and mass-conservative, allowing for accurate simulations of incompressible flows with exact divergence-free solutions. The application of static condensation further improves computational performance.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Richard M. Hoefer
Summary: This paper studies the solution to the Navier-Stokes equations in perforated media with small particles and no-slip boundary conditions. The behavior of the solution is examined for small values of ε, which depends on the diameter of the particles and the viscosity of the fluid. The results demonstrate that when the local Reynolds number at the particles is negligible, the particles exert an approximately linear friction force on the fluid. The effective macroscopic equations obtained depend on the magnitude of the collective friction.
Article
Mathematics, Applied
Alfredo Buttari, Markus Huber, Philippe Leleux, Theo Mary, Ulrich Ruede, Barbara Wohlmuth
Summary: Extreme scale simulation requires fast and scalable algorithms such as multigrid methods. We propose solving the coarse grid system using modern, approximate sparse direct methods and demonstrate the efficiency of this method. In extreme scale computing, aggregating the coarse grid system to a subset of processors is crucial for the sparse direct solver to achieve performance.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2022)
Article
Engineering, Chemical
Aniket S. Ambekar, Christoph Schwarzmeier, Ulrich Ruede, Vivek V. Buwa
Summary: Turbulence characteristics in a packed bed of spherical particles are investigated using simulations and direct numerical simulation (DNS). The accuracy of different turbulence models is validated with DNS. The results show that the epsilon-based model has good accuracy in handling strongly wall-dominated flow, while the omega-based model under-predicts turbulence quantities at low Reynolds numbers (Re-p). Additionally, the onset of turbulence occurs between 200 <= Re-p <= 250.
Article
Computer Science, Hardware & Architecture
Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt, Leonardo Bautista-Gomez, Tommaso Benacchio, Luca Bonaventura, Hans-Joachim Bungartz, Sanjay Chatterjee, Florina M. Ciorba, Nathan DeBardeleben, Daniel Drzisga, Sebastian Eibl, Christian Engelmann, Wilfried N. Gansterer, Luc Giraud, Dominik Goddeke, Marco Heisig, Fabienne Jezequel, Nils Kohl, Xiaoye Sherry Li, Romain Lion, Miriam Mehl, Paul Mycek, Michael Obersteiner, Enrique S. Quintana-Orti, Francesco Rizzi, Ulrich Ruede, Martin Schulz, Fred Fung, Robert Speck, Linda Stals, Keita Teranishi, Samuel Thibault, Dominik Thoennes, Andreas Wagner, Barbara Wohlmuth
Summary: Based on a seminar held at Schloss Dagstuhl, this work emphasizes the challenges of large-scale supercomputing and the need to research more advanced resilience techniques. Current simple resilience techniques are inadequate for the challenges posed by exascale systems, necessitating the development of more advanced techniques. Researchers need to consider new reliability requirements and how to design algorithms and software to meet these requirements.
INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
(2022)
Article
Mathematics, Applied
Elissa Eggenweiler, Marco Discacciati, Iryna Rybak
Summary: This paper investigates fluid flows in coupled systems consisting of a free-flow region and an adjacent porous medium. Mathematical analysis of the Stokes-Darcy problem with generalised interface conditions is conducted, and the existence and uniqueness of weak solutions for the coupled problem are proven.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yali Gao, Daozhi Han, Xiaoming He, Ulrich Ruede
Summary: In this article, numerical modeling and simulation of coupled two-phase free flow and two-phase porous media flow using the phase field approach are considered. Unconditionally stable finite element methods and time stepping methods are proposed to efficiently solve the coupled model and preserve the energy law. Numerical experiments demonstrate the convergence and energy-law preserving properties of the proposed methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Martin J. Kuehn, Carola Kruse, Ulrich Ruede
Summary: This paper investigates the numerical solution of the gyrokinetic Poisson equation that arises in Tokamak fusion reactor simulations. By discretizing the equation using finite differences or finite elements on curvilinear anisotropic meshes, the approximation order can be increased. The paper also integrates the implicit extrapolation technique into a matrix-free geometric multigrid algorithm to handle the mesh anisotropy resulting from the curvilinear coordinate system and mesh grading.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mechanics
Aniket S. Ambekar, Ulrich Ruede, Vivek V. Buwa
Summary: This study investigates the dynamics of liquid spreading in a randomly packed three-dimensional bed using simulations and numerical values. Inertial force plays a significant role in promoting lateral liquid spreading at the beginning, while capillary force dominates as the inertial force diminishes. A regime map is proposed to show the relationship between different forces and the resultant liquid spreading.
Article
Computer Science, Interdisciplinary Applications
Christoph Schwarzmeier, Ulrich Ruede
Summary: The accuracy of the free-surface lattice Boltzmann method (FSLBM) depends on the boundary condition used at the free interface. This study compared four variants of the boundary condition and found that the third variant performed significantly better than the others in various numerical experiments. These experiments included standing gravity waves, dam breaks, rising gas bubbles, and droplet impacts.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Christoph Schwarzmeier, Markus Holzer, Travis Mitchell, Moritz Lehmann, Fabian Hausl, Ulrich Rude
Summary: This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen-Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows dominated by the heavy phase. Through simulations of six benchmark cases, the accuracy and performance of both models are evaluated. The results show that the PFLBM performs well in simulating flows governed by surface tension, while the FSLBM accurately predicts the shape and rise velocity of bubbles.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mechanics
Christoph Schwarzmeier, Christoph Rettinger, Samuel Kemmler, Jonas Plewinski, Francisco Nunez-Gonzalez, Harald Koestler, Ulrich Ruede, Bernhard Vowinckel
Summary: This article presents the first numerical attempt to simulate upstream-migrating antidunes with geometrically resolved particles and a liquid-gas interface, providing high-resolution data for understanding the mechanisms of antidune migration and the underlying physics.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Engineering, Chemical
Paula Strohbeck, Elissa Eggenweiler, Iryna Rybak
Summary: Physically consistent coupling conditions and effective parameters are crucial for accurate modeling and simulation of various applications at the fluid-porous interface. The commonly used Beavers-Joseph condition for tangential velocity is only suitable for parallel flows and its slip coefficient value is uncertain.
TRANSPORT IN POROUS MEDIA
(2023)
Article
Mathematics, Applied
Frederik Hennig, Markus Holzer, Ulrich Ruede
Summary: The scientific code generation package lbmpy automates the design and implementation of lattice Boltzmann method (LBM) using metaprogramming. It introduces a concise calculus for describing multiple relaxation-time LBMs and includes techniques for numerically advantageous subtraction of a constant background component. The lbmpy frontend and code generation pipeline utilize symbolic formula manipulation and object-oriented programming to implement the new LBM calculus. The generated codes have minimal arithmetic operations and are optimized through algebraic simplifications, resulting in concise and compact numerical kernels.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
