Project C5: Adaptive hybrid multiscale simulations of soft matter fluids

We develop and analyse efficient, hybrid multiscale methods that bridge the continuum-particle gap by combining a discontinuous Galerkin method for the macroscopic model with molecular dynamics. In the second funding period we have focused on the description of non-Newtonian fluids, particularly polymer melts, in sim- ple and complex geometries as well as on theoretical convergence analysis of numerical schemes taking multiscale effects into account.

Building on these results we will study the flow behaviour of polymer mixtures and develop methods to separate polymers with similar molecular masses based on differences in rheological properties (WP1). Applying a probabilistic concept of solutions, we will extend our convergence analysis to these non-Newtonian systems (WP3) and investigate effects of uncertainty with machine learning techniques (WP4). In the final funding period, we would also like to expand the scope of our project to a novel, exciting class of quasi-particles, which on a coarse-grained level can be described in terms of soft matter physics. In close collaboration with experimental colleagues at the JGU Mainz we will probe and study rheological properties of magnetic skyrmions (WP2). In summary, the main goals of the final project period are two-fold: i) investigate the applicability of our hybrid multiscale method to new exciting systems (polymer mixtures, magnetic quasi-particles) and theoretical analysis (convergence and error analysis, uncertainty quantification

On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
Abgrall, R., Lukáčová-Medvid’ová, M. and Öffner, P.
Mathematical Models and Methods in Applied Sciences, 33(01), 139-173
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Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
Lukáčová-Medvid’ová, M. and Öffner, P.
Applied Mathematics and Computation, 436, 127508
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Statistical solutions for the Navier–Stokes–Fourier system
Feireisl, E., and Lukáčová-Medvid’ová, M.
Stochastics and Partial Differential Equations: Analysis and Computations, 1-25
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Error estimates of a finite volume method for the compressible Navier–Stokes–Fourier system
Danica Basarić, Mária Lukáčová-Medviďová, Hana Mizerová, Bangwei She and Yuhuan Yuan
Math. Comp. 92 (2023), 2543-2574
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An all Mach number finite volume method for isentropic two-phase flow
Lukáčová-Medvid’ová, M., Puppo, G. and Thomann, A.
Journal of Numerical Mathematics, 31(3), 175-204
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On a Hybrid Continuum-Kinetic Model for Complex Fluids
A. Chertock, P. Degond, G. Dimarco, and Lukacova-Medvidova
Partial Di er. Equ. Appl. 3, 2022, Paper No. 63, 28 pp.
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Convergence and Error Estimates for Compressible Fluid Flows with Random Data: Monte Carlo Method
Feireisl, E., Lukacova-Medvidova, M., She, B., Yuan, Y.
Math. Mod. Meth. Appl. Sci. 32 (14), 2022, 2887-2925
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Penalization method for the Navier-Stokes-Fourier system
Danica Basarić, Eduard Feireisl, Mária Lukáčová-Medviďová, Hana Mizerová, Yuhuan Yuan
ESAIM: Mathematical Modelling and Numerical Analysis, (2022)
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Existence of Dissipative Solutions to the Compressible Navier-Stokes System with Potential Temperature Transport
M. Lukacova-Medvidova, A. Schömer
Journal of Mathematical Fluid Mechanics 24(82), (2022)
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A multi-scale method for complex flows of non-Newtonian fluids
F. Tedeschi, G.G. Giusteri, L. Yelash, M. Lukáčová-Medvid’ova
Mathematics in Engineering, (2021)
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Shear thinning in oligomer melts - molecular origins and applications
R. Datta, L. Yelash, F. Schmid, F. Kummer, M. Oberlack, M. Lukáčová-Medvid'ová, P. Virnau
Polymers 13 (16), 2806 (2021)
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Computing oscillatory solutions of the Euler system via K-convergence
Eduard Feireisl, Mária Lukáčová–Medvid’ová, Bangwei She, Yue Wang
Mathematical Models and Methods in Applied Sciences 31 (03), 537-576 (2021)
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Commensurability between Element Symmetry and the Number of Skyrmions Governing Skyrmion Diffusion in Confined Geometries
Chengkun Song, Nico Kerber, Jan Rothörl, Yuqing Ge, Klaus Raab, Boris Seng, Maarten A. Brems, Florian Dittrich, Robert M. Reeve, Jianbo Wang, Qingfang Liu, Peter Virnau, Mathias Kläui
Advanced Functional Materials 31 (19), 2010739 (2021)
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Numerical methods for compressible fluid flows
E. Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She
Springer, Modeling, Simulation and Applications, Vol.20 (2021)
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Skyrmion Lattice Phases in Thin Film Multilayer
Jakub Zázvorka, Florian Dittrich, Yuqing Ge, Nico Kerber, Klaus Raab, Thomas Winkler, Kai Litzius, Martin Veis, Peter Virnau, Mathias Kläui
Advanced Functional Materials 30 (46), 2004037 (2020)
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Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions
E. Feireisl, M. Lukáčová-Medvid’ová, H. Mizerová
Foundations of Computational Mathematics 20, 923-966 (2020)
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A finite volume scheme for the Euler system inspired by the two velocities approach
E. Feireisl, M. Lukacova-Medvidova, H. Mizerova
Numerical Mathematics 144 (89-132), (2020)
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K-convergence as a new tool in numerical analysis
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova
IMA Journal of Numerical Analysis 40, 2227–2255 (2020)
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On the convergence of a finite volume method for the Navier–Stokes–Fourier system
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She
IMA Journal of Numerical Analysis, (2020)
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Thermal skyrmion diffusion used in a reshuffler device
Jakub Zázvorka, Florian Jakobs, Daniel Heinze, Niklas Keil, Sascha Kromin, Samridh Jaiswal, Kai Litzius, Gerhard Jakob, Peter Virnau, Daniele Pinna, Karin Everschor-Sitte, Levente Rózsa, Andreas Donges, Ulrich Nowak, Mathias Kläui
Nature Nanotechnology 14 (7), 658-661 (2019)
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Convergence of a finite volume scheme for the compressible Navier-Stokes system
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova
ESAIM: Mathematical Modelling and Numerical Analysis. 53, 1957–1979 (2019)
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An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions
A. Chertock, A. Kurganov, M. Lukacova-Medvidova, S. Nur Oezcan
Kinetic and Related Models 12 (1), 195–216 (2019)
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Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions
E. Feireisl, M. Lukacova-Medvidova
Foundations of Computational Mathematics 18 , 703–730 (2018)
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Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
E. Feireisl, M. Lukacova-Medvidova, S. Necasova, A. Novotny, B. She
SIAM Multiscale Modeling and Simulation 16 (1), 150–183 (2018)
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Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats
S. Stalter, L. Yelash, N. Emamy, A. Statt, M. Hanke, M. Lukáčová-Medvid’ová, P. Virnau
Computer Physics Communications, (2017)
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Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
G. Bispen, M. Lukacova-Medvidova, L. Yelash
Journal of Computational Physics 335, 222-248 (2017)
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Reduced-order hybrid multiscale method combining the molecular dynamics and the discontinuous Galerkin method
N. Emamy, M. Lukácová-Medvid’ová, S. Stalter, P. Virnau, L. Yelash
VII International Conference on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems 2017, 1-15. (2017)
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Analysis and numerical solution of the Peterlin viscoelastic model (PhD Thesis)
Mizerova Hana
Johannes Gutenberg-Universität (2015)
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Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method
B. J. Block, M. Lukáčová-Medvid’ová, P. Virnau, L. Yelash
The European Physical Journal Special Topics 210 (1), 119-132 (2012)
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