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
Maximal dissipation and well-posedness of the Euler system of gas dynamics
E. Feireisl, A. Jüngel, M. Lukáčová-Medvid'ová
Archive for rational mechanics and analysis 250, 53 (2026)
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Convergence of a hyperbolic thermodynamically compatible finite volume scheme for the Euler equations
Michael Dumbser, Maria Lukáčová-Medvid'ová, Andrea Thomann
Numerische Mathematik 158, 715-747 (2026)
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Hybrid multiscale method for polymer melts: Analysis and simulations
Ranajay Datta, Maria Lukáčová-Medvid'ová, Andreas Schömer, Peter Virnau
ZAMM 106, e70438 (2026)
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Solving random hyperbolic conservation laws using linear programming
Shaoshuai Chi, Michael Herty, Maria Lukáčová-Medvid'ová, Yizhou Zhou
SIAM J. Sci. Comp. 48, A1184-A1205 (2026)
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Real-Time Modeling of Skyrmion Dynamics in Arbitrary 2D Spatially Dependent Pinning Potential Landscapes
S.F. Fröhlich, T. Sparmann, M.A. Brems, J. Rothörl, F. Kammerbauer, K. Raab, K. Sachin, M. Kläui, P. Virnau
Comm. Phys. 9, 243 (2026)
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Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
Kuzmin, D., Lukáčová-Medvid'ová, M., Öffner, P.
J. Num. Math. 34, 1-20 (2026)
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Influence of topology on rheological properties of polymer ring melts
Ranajay Datta, Peter Virnau
J. Chem. Phys. 162, 094902 (2025)
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Realizing Quantitative Quasiparticle Modeling of Skyrmion Dynamics in Arbitrary Potentials
M.A. Brems, T. Sparmann, S.M. Fröhlich, L.-C. Dany, J. Rothörl, F. Kammerbauer, E.M. Jefremovas, O. Farago, M. Kläui, P. Virnau
Phys. Rev. Lett. 134, 046701 (2025)
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Convergence Analysis of the Monte Carlo Method for the Random Navier–Stokes–Fourier System
Lukáčová-Medvid'ová, M., She, B., Yuan, Y.
SIAM J. Numer. Anal. 63, no. 3, 1254–1280 (2025)
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Penalty method for the Navier–Stokes–Fourier system with Dirichlet boundary conditions: convergence and error estimates
Lukáčová-Medvid'ová, M., She, B., Yuan, Y.
Numer. Math. 157, no. 3, 1079–1132 (2025)
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What is a limit of structure-preserving numerical methods for compressible flows? Numerical mathematics and advanced applications
Lukáčová-Medvid'ová, M., She, B., Yuan, Y.
ENUMATH 2023. Vol. 1, 17–33, Lect. Notes Comput. Sci. Eng., 153, Springer, Cham (2025)
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Convergence and error estimates of a penalization finite volume method for the compressible Navier-Stokes system
Lukáčová-Medvid'ová, M., She, B., Yuan, Y.
IMA J. Numer. Anal. 45, no. 2, 1054–1101 (2025)
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Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport
Lukáčová-Medvid'ová, M., Schömer, A.
J. Differential Equations 423, 1–40 (2025)
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An implicit-explicit solver for a two-fluid single-temperature model
Lukáčová-Medvid'ová, M., Peshkov, I., and Thomann, A.
Journal of Computational Physics, 498, 112696, (2024)
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New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Chertock, A., Herty, M., Iskhakov, A. S., Janajra, S., Kurganov, A., and Lukáčová-Medvid’ová, M.
Communications on Applied Mathematics and Computation, 1-34, (2024)
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Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data
Feireisl, E., Lukáčová-Medvid’ová, M., She, B., and Yuan, Y.
Foundations of Computational Mathematics, 1-53, (2024)
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Skyrmion flow in periodically modulated channels
Klaus Raab, Maurice Schmitt, Maarten A. Brems, Jan Rothörl, Fabian Kammerbauer, Sachin Krishnia, Mathias Kläui, Peter Virnau
Phys. Rev. E 110, L042601 (2024)
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Growth and aging in a few phase-separating active matter system
Florian Dittrich, Jiarul Midya, Peter Virnau, Subir K. Das
Phys. Rev. E 108, 024609 (2023)
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300-Times-Increased Diffusive Skyrmion Dynamics and Effective Pinning Reduction by Periodic Field Excitation
R. Gruber, M.A. Brems, J. Rothörl, T. Sparmann, M. Schmitt, I. Kononenko, F. Kammerbauer, M.-A. Syskaki, O. Farago, P. Virnau, M. Kläui
Advanced Materials 35, 2208922 (2023)
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Local characteristic decomposition based central-upwind scheme
Alina Chertock, Shaoshuao Chu, Michael Herty, Alexander Kurganov, Maria Lukáčová-Medvid'ová
J. Comp. Phys. 473, 111718
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Constructing coarse-grained skyrmion potentials from experimental data with Iterative Boltzmann Inversion
Y. Ge, J. Rothörl, M.A. Brems, N. Kerber, R. Gruber, T. Dohi, M. Kläui, P. Virnau
Comm. Phys. 6, 30 (2023)
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Ranajay Datta, Fabian Berressem, Friederike Schmid, Arash Nikoubashman, Peter Virnau
Viscosity of flexible and semiflexible ring melts: Molecular origins and flow-induced segregation
Macromolecules 56, 7247-7255 (2023)
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Convergence of a stochastic collocation finite volume method for the compressible Navier–Stokes system.
Feireisl, E., and Lukáčová-Medviďová, M.
The Annals of Applied Probability, 33(6A), 4936-4963, (2023)
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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, (2023)
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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, (2023)
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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, (2023)
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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, (2023)
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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, (2023)
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Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
V. Kucera, M. Lukáčová-Medvid'ová, S. Nölle, J. Schütz
Numerische Mathematik 150, 79-103 (2022)
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Approximating viscosity solutions of the Euler system
E. Feireisl, M. Lukáčová-Medvid'ová, S. Scheiner, B. Whe
Mathematics of Computation 91, 2129-2164 (2022)
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Error Estimates of the Godunov Method for the Multidimensional Compressible Euler System
Maria Lukáčová-Medvid'ová, Bangwei She, Yuhuan Yuan
J. Scientific Computing 91, 71 (2022)
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On a Hybrid Continuum-Kinetic Model for Complex Fluids
A. Chertock, P. Degond, G. Dimarco, and Lukáčová-Medvid'ová
Partial Differ. Equ. Appl. 3, Paper No. 63, 28 pp. (2022)
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Convergence and Error Estimates for Compressible Fluid Flows with Random Data: Monte Carlo Method
Feireisl, E., Lukáčová-Medvid'ová, M., She, B., Yuan, Y.
Math. Mod. Meth. Appl. Sci. 32 (14), 2887-2925 (2022)
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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. Lukáčová-Medvid'ová, 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 4, 6 (2022)
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Circuits and excitations to enable Brownian token-based computing with skyrmions
Maarten A. Brems, Mathias Kläui, Peter Virnau
Appl. Phys. Lett. 119, 132405 (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. Lukáčová-Medvid'ová, 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. Lukáčová-Medvid'ová, H. Mizerova
Numerical Mathematics 144 (89-132), (2020)
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K-convergence of finite volume solutions of the Euler equations
Maria Lukáčová-Medvid'ová
Finite volues for complex applications IX, 323, 25-37 (2020)
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K-convergence as a new tool in numerical analysis
E.Feireisl, M. Lukáčová-Medvid'ová, 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. Lukáčová-Medvid'ová, 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. Lukáčová-Medvid'ová, 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. Lukáčová-Medvid'ová, 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. Lukáčová-Medvid'ová
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. Lukáčová-Medvid'ová, S. Necasova, A. Novotny, B. She
SIAM Multiscale Modeling and Simulation 16 (1), 150–183 (2018)
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Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model
Jan Giesselmann, Niklas Kolbe, Maria Lukáčová-Medvid'ová, Nikalaos Sfakianakis
Discrete and continuous dynamics systems 23, 4397-4431 (2018)
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Free-energy barriers for crystal nucleation from fluid phases
Peter Koss, Antonia Statt, Peter Virnau, Kurt Binder
Phys. Rev. E 96, 042609 (2017)
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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 224, 198-208 (2017)
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Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
G. Bispen, M. Lukáčová-Medvid'ová, 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, 15 pp. (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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