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A discrete contact model for complex arbitrary-shaped convex geometries

Particuology 2023年第9期80卷 180-191页

作者： Jan E.Marquardt Ulrich J.Römer Hermann Nirschl Mathias J.Krause Lattice Boltzmann Research Group Karlsruhe Institute of TechnologyStraße am Forum 8Karlsruhe76131Germany Institute for Mechanical Process Engineering and Mechanics Karlsruhe Institute of TechnologyStraße am Forum 8Karlsruhe76131Germany Institute of Engineering Mechanics Karlsruhe Institute of TechnologyKaiserstraße 10Karlsruhe76131Germany Institute for Applied and Numerical Mathematics Karlsruhe Institute of TechnologyEnglerstraße 2Karlsruhe76131Germany

The shape of particles has a significant influence on the behavior of suspensions,as the particle-fluid,particle-particle,and particle-wall interactions depend on ***,the simultaneous consideration of complex particle shapes and four-way coupling remains a major *** is mainly due to a lack of suitable contact *** models for complex shapes have been proposed in literature,and most limit the accuracy of the particle-fluid *** this reason,this paper presents a novel contact model for complex convex particle shapes for use with partially saturated methods,in which we propose to obtain necessary contact properties,such as the indentation depth,by a discretization of the contact *** goal of the proposed model is to enable comprehensive and accurate studies of particulate flows,especially with high volume fractions,that lead to new insights and contribute to the improvement of existing industrial *** ensure correctness and sustainability,we validate the model extensively by studying cases with and without *** the latter case,we use the homogenized lattice Boltzmann *** provided investigations show a great agreement of the proposed discrete contact model with analytical solutions and the literature.

关键词： Partially saturated cells method Homogenized lattice Boltzmann method Arbitrarily shaped particle Discrete contact model Particle-resolved simulation OpenLB

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Local time-integration for Friedrichs’ systems

arXiv

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arXiv 2025年

作者： Hochbruck, Marlis Scheifinger, Malik Institute for Applied and Numerical Mathematics Karlsruhe Institute for Technology Karlsruhe76131 Germany

In this paper, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space discretization applied to a locally refined mesh or a small region with high wave speed. This results in a stiff system of ordinary differential equations, where the stiffness is mainly caused by a small region of the spatial mesh. When using explicit time-integration schemes, the time step size is severely restricted by a few spatial elements, leading to a loss of efficiency. As a remedy, we propose and analyze a general leapfrog-based scheme which is motivated by [5]. The new, fully explicit, local time-integration method filters the stiff part of the system in such a way that its CFL condition is significantly weaker than that of the leapfrog scheme while its computational cost is only slightly larger. For this scheme, the filter function is a suitably scaled and shifted Chebyshev polynomial. While our main interest is in explicit local-time stepping schemes, the filter functions can be much more general, for instance, a certain rational function leads to the locally implicit method, proposed and analyzed in [24]. Our analysis provides sufficient conditions on the filter function to ensure full order of convergence in space and second order in time for the whole class of local time-integration *** Codes 65M12, 65M15, 65M22 Copyright © 2025, The Authors. All rights reserved.

关键词： Rational functions

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numerical study on micro-fracture mechanism of rock dynamic failureinduced by abrupt unloading under high in-situ stresses

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Theoretical & applied Mechanics Letters 2024年第6期14卷 486-495页

作者： Yuezong Yang Anye Li Zhushan Shao Kui Wu Wei Wei Wenhui Du Yujie Wang School of Science Xi’an University of Architecture and TechnologyXi’an 710055China CAEP Software Center for High Performance Numerical Simulation Institute of Applied Physics and Computational Mathematics BeijingBeijing 100088China

Rock burst is a kind of severe engineering disaster resulted from dynamic fracture process of *** macrofailure behaviors of rocks are primarily formed after experiencing the initiation,propagation,and coalescenceof *** this paper,the grain-based discretized virtual internal bond model is employed to investigatethe fracturing process of unloaded rock under high in-situ stresses from the micro-fracture *** micro-fracturing process reveals that the longitudinal stress waves induced by unloading lead to thevisible unloading *** influences of in-situ stresses,mineral grain sizes,and grain heterogeneity on rockmacro and micro fracture are ***-crack areas of tensile and shear cracks and micro-crack anglesare statistically analyzed to reveal the rock micro-fracture *** simulated results indicate thatthe combined effect of the stress state transition and the unloading effect dominates the rock unloading *** vertical and horizontal in-situ stresses determine the stress state of surrounding rock after unloading andthe unloading effect,*** the vertical stress increases,the stress level after unloading is higher,andthe shear failure characteristics become more *** the horizontal stress increases,the unloading effectincreases,leading to the intensification of tensile *** mineral grain size and grain heterogeneity alsohave nonnegligible influences on rock unloading *** micro-fracture perspective provides further insightinto the unloading failure mechanism of deep rock excavation.

关键词： Rock burst Micro-fracture Dynamic failure Unloading effect

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The Parallel Performance of SLNE Atmosphere–Ocean–Sea Ice Coupled Model

Supercomputing Frontiers and Innovations

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Supercomputing Frontiers and Innovations 2023年第3期10卷 36-60页

作者： Fadeev, Rostislav Yu. Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences Moscow Russia Hydrometeorological Research Center of Russian Federation Moscow Russia Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences Moscow Russia Moscow Institute of Physics and Technology Dolgoprudny Russia

The paper presents the first version of SLNE coupled model. SL and NE here are the first two letters from SLAV (Semi-Lagrangian, based on Absolute Vorticity equation) atmospheric model and NEMO (Nucleus for European Modelling of the Ocean) ocean model that have been coupled using OASIS3-MCT software. SLAV uses 0.9°x0.72° regular lat-lon grid with 96 vertical levels. NEMO incorporates SI3 sea ice model. Both of them use the same ORCA025 tripolar grid. Flux adjustments to correct inconsistencies at the interface between coupled atmosphere–ocean models have not been applied in SLNE. The model design and coupling particularities are described here in detail. A series of numerical experiments with SLNE model were performed to measure its parallel performance. We also investigated the scalability of SLNE model and its components in terms of simulation speed. Based on these results, an optimum configurations of SLNE were identified. It was found that the coupled model showed scaling efficiency of about 85% on 4000 computational cores of Cray XC40-LC in comparison to the SLNE configuration running on 224 cores. Simulations with lead times ranging from a few days to several years showed that there are no significant systematic errors in the coupled model. © The Author 2023. This paper is published with open access at ***

关键词： Systematic errors

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Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions

arXiv

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arXiv 2024年

作者： Dörich, Benjamin Dörner, Julian Hochbruck, Marlis Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany

In the present paper we consider linear and isotropic Maxwell equations with inhomogeneous interface conditions. We discretize the problem with the discontinuous Galerkin method in space and with the leapfrog scheme in time. An analytical setting is provided in which we show wellposedness of the problem, derive stability estimates, and exploit this in the error analysis to prove rigorous error bounds for both the spatial and full discretization. The theoretical findings are confirmed with numerical *** Codes 65M12, 65M15, 65M60 (Primary) 35Q60 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Maxwell equations

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NEURAL numerical HOMOGENIZATION BASED ON DEEP RITZ CORRECTIONS

arXiv

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arXiv 2024年

作者： Elasmi, M. Krumbiegel, F. Maier, R. Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany

numerical homogenization methods aim at providing appropriate coarse-scale approximations of solutions to (elliptic) partial differential equations that involve highly oscillatory coefficients. The localized orthogonal decomposition (LOD) method is an effective way of dealing with such coefficients, especially if they are non-periodic and non-smooth. It modifies classical finite element basis functions by suitable fine-scale corrections. In this paper, we make use of the structure of the LOD method, but we propose to calculate the corrections based on a Deep Ritz approach involving a parametrization of the coefficients to tackle temporal variations or uncertainties. numerical examples for a parabolic model problem are presented to assess the performance of the approach. Copyright © 2024, The Authors. All rights reserved.

关键词： Homogenization method

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Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations

arXiv

引用

arXiv 2024年

作者： Patwardhan, Chinmay Frank, Martin Kusch, Jonas Karlsruhe Institute of Technology Institute of Applied and Numerical Mathematics Karlsruhe Germany Norwegian University of Life Sciences Ås Norway

The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type equation called the Rosseland approximation. The main challenges for constructing numerical schemes that exhibit the correct limiting behavior are posed by the solution's high-dimensional phase space and multi-scale effects. In this work, we propose an asymptotic-preserving and rank-adaptive dynamical low-rank approximation scheme based on the macro-micro decomposition of the particle density and a modified augmented basis-update & Galerkin integrator. We show that this scheme, for linear particle emission by the material, dissipates energy over time under a step size restriction that captures the hyperbolic and parabolic CFL conditions. We demonstrate the efficacy of the proposed method in a series of numerical *** Codes 35L65, 35Q49, 65M12, 35B40 © 2024, CC BY.

关键词： Phase space methods

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ROBUST FULLY DISCRETE ERROR BOUNDS FOR THE KUZNETSOV EQUATION IN THE INVISCID LIMIT

arXiv

引用

arXiv 2024年

作者： Dörich, Benjamin Nikolić, Vanja Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76149 Germany Department of Mathematics Radboud University Nijmegen6525 AJ Netherlands

The Kuznetsov equation is a classical wave model of acoustics that incorporates quadratic gradient nonlinearities. When its strong damping vanishes, it undergoes a singular behavior change, switching from a parabolic-like to a hyperbolic quasilinear evolution. In this work, we establish for the first time the optimal error bounds for its finite element approximation as well as a semi-implicit fully discrete approximation that are robust with respect to the vanishing damping parameter. The core of the new arguments lies in devising energy estimates directly for the error equation where one can more easily exploit the polynomial structure of the nonlinearities and compensate inverse estimates with smallness conditions on the error. numerical experiments are included to illustrate the theoretical *** Codes 65M12, 65M15, 35L72, 65M60 Copyright © 2024, The Authors. All rights reserved.

关键词： Damping

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Dynamic fracture with a continuum-kinematics-based peridynamic and a phase-field approach

Dynamic fracture with a continuum-kinematics-based peridynam...

引用

92nd Annual Meeting of the International Association of applied mathematics and Mechanics, GAMM 2022

作者： Friebertshäuser, Kai Thomas, Marita Tornquist, Sven Weinberg, Kerstin Wieners, Christian University of Siegen Siegen Germany Weierstrass Institute for Applied Analysis and Stochastics Berlin Germany FU Berlin Germany Institute of Applied and Numerical Mathematics KIT Karlsruhe Germany

The notion of dynamic fracture with continuum-kinematics-based peridynamics is presented in this work. A geometrically precise version of peridynamics called continuum-kinematics-based peridynamics adds surface-or volume-based interactions to the traditional peridynamic bonds, accurately capturing the finite deformation kinematics. The point families produced from the horizon of the material points are used to construct the surfaces and volumes taken into account for these non-local interactions. In continuum kinematics-based peridynamics, the traditional bond-stretch damage technique is insufficient for fracture. Due to the loss of strength in the internal force densities of the material points, it is now extended to the surface-and volume-based interactions by new failure factors. numerical examples demonstrate that the proposed approach effectively manages crack propagation, impact damage, and spontaneous crack initiation under dynamic loading circumstances with large deformations. When the results are compared to phase-field calculations, there is a remarkable agreement concerning the damage patterns. © 2023 The Authors. Proceedings in applied mathematics & Mechanics published by Wiley-VCH GmbH.

关键词： Kinematics

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A MULTISCALE APPROACH TO THE STATIONARY GINZBURG-LANDAU EQUATIONS OF SUPERCONDUCTIVITY

arXiv

引用

arXiv 2024年

作者： Döding, Christian Dörich, Benjamin Henning, Patrick Institute for Numerical Simulation University of Bonn Bonn53115 Germany Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76149 Germany Department of Mathematics Ruhr-University Bochum Bochum44801 Germany

In this work, we study the numerical approximation of minimizers of the Ginzburg–Landau free energy, a common model to describe the behavior of superconductors under magnetic fields. The unknowns are the order parameter, which characterizes the density of superconducting charge carriers, and the magnetic vector potential, which allows to deduce the magnetic field that penetrates the superconductor. Physically important and numerically challenging are especially settings which involve lattices of quantized vortices which can be formed in materials with a large Ginzburg–Landau parameter κ. In particular, κ introduces a severe mesh resolution condition for numerical approximations. In order to reduce these computational restrictions, we investigate a particular discretization which is based on mixed meshes where we apply a Lagrange finite element approach for the vector potential and a localized orthogonal decomposition (LOD) approach for the order parameter. We justify the proposed method by a rigorous a-priori error analysis (in L2 and H1) in which we keep track of the influence of κ in all error contributions. This allows us to conclude κ-dependent resolution conditions for the various meshes and which only impose moderate practical constraints compared to a conventional finite element discretization. Finally, our theoretical findings are illustrated by numerical *** Codes 65N12, 65N15 (Primary) 65N30, 35Q56 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Lagrange multipliers

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