C5:Adaptive hybrid multiscale simulations of soft matter fluids
The aim of this project is to develop and analyse a novel hybrid multiscale method to simulate fluids that combines the discontinuous Galerkin (dG) method and molecular dynamics (MD). Interaction between particles and continuum variables is realized dynamically, i.e., on-the-fly. Reduced order techniques are used to control the number of computationally expensive MD simulations. In the next funding period, we plan to (i) study error control by means of a-priori feedback estimates and analyse scheme convergence. (ii) Generalize the method to describe more complex physical systems such as non-Newtonian fluids and self-propelled colloidal particles, and (iii) move from benchmark geometries to real-world geometries used in microfluidics.
A multi-scale method for complex flows of non-Newtonian fluids
Mathematics in Engineering, (2021);
Shear thinning in oligomer melts - molecular origins and applications
Polymers13 (16),2806 (2021);
doi:https://doi.org/10.3390/polym13162806
Computing oscillatory solutions of the Euler system via K-convergence
Mathematical Models and Methods in Applied Sciences31 (03),537-576 (2021);
doi:10.1142/s0218202521500123
Commensurability between Element Symmetry and the Number of Skyrmions Governing Skyrmion Diffusion in Confined Geometries
Advanced Functional Materials31 (19),2010739 (2021);
doi:10.1002/adfm.202010739
Numerical methods for compressible fluid flows
Springer,Modeling, Simulation and Applications , Vol.20 (2021);
Skyrmion Lattice Phases in Thin Film Multilayer
Advanced Functional Materials30 (46),2004037 (2020);
doi:10.1002/adfm.202004037
Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions
Found Comput Math 20,923-966 (2020);
doi:10.1007/s10208-019-09433-z
A finite volume scheme for the Euler system inspired by the two velocities approach
Num. Math. 144 (89-132), (2020);
doi:10.1007/s00211-019-01078-y
K-convergence as a new tool in numerical analysis
IMA J. Num. Anal. 40,2227–2255 (2020);
doi:10.1093/imanum/drz045
On the convergence of a finite volume method for the Navier–Stokes–Fourier system
IMA J. Num. Anal. , (2020);
C5 Project doi:10.1093/imanum/draa060
Thermal skyrmion diffusion used in a reshuffler device
Nature Nanotechnology14 (7),658-661 (2019);
doi:10.1038/s41565-019-0436-8
Convergence of a finite volume scheme for the compressible Navier-Stokes system
ESAIM: Math. Model. Num. 53,1957–1979 (2019);
doi: https://doi.org/10.1051/m2an/2019043
An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions
Kinetic and Related Models12 (1),195–216 (2019);
URL: http://aimsciences.org//article/doi/10.3934/krm.2019009 doi:10.3934/krm.2019009
Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions
Found. Comput. Math. 18 ,703–730 (2018);
doi: DOI: 10.1007/s10208-017-9351-2
Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime
SIAM Multiscale Model. Simul. 16 (1),150–183 (2018);
URL: https://epubs.siam.org/doi/10.1137/16M1094233
Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats
Computer Physics Communications, (2017);
doi:10.1016/j.cpc.2017.10.016
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
J. Comput. Phys. 335,222-248 (2017);
doi:10.1016/j.jcp.2017.01.020
Reduced-order hybrid multiscale method combining the molecular dynamics and the discontinuous Galerkin method
VII International Conference on Computational Methods for Coupled Problems in Science and Engineering, Coupled Problems 2017,1-15. (2017);
URL: http://congress.cimne.com/coupled2017/frontal/default.asp
Analysis and numerical solution of the Peterlin viscoelastic model (PhD Thesis)
JGU (2015);
URL: http://ubm.opus.hbz-nrw.de/volltexte/2015/4231/
Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method
The European Physical Journal Special Topics210 (1),119-132 (2012);
doi:10.1140/epjst/e2012-01641-0
Contact
- Prof. Dr.MariaLukáčová
- Institut für Mathematik
- Universität Mainz
- Staudingerweg 9
- D-55128Mainz
- Tel:+49 6131 39 22831
- Fax:+49 6131 39 23331
- Sekr:+49 6131 39 22270
- lukacovaLBXnvpCLf@bWrUcoOmathematik.uni-mainz.de
- http://www.mathematik.uni-mainz.de/Members/lukacova
- Dr.PeterVirnau
- Institut für Physik
- Universität Mainz
- Staudingerweg 9
- D-55128Mainz
- Tel:+49 6131 39 20493
- Fax:+49 6131 39 20496
- virnauhot-@SOZnpS.suni-mainz de
- https://www.komet1.physik.uni-mainz.de/people/peter-virnau