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C5: Adaptive hybrid multiscale simulations of soft matter fluids

The aim of this project is to develop a new hybrid multiscale method for complex fluids, which aims at bridging the gap between continuum models and particle based simulations. The scheme couples on-the-fly a modern numerical scheme for partial differential equations, the discontinuous Galerkin method (DG) on adaptive meshes, with multiparticle collision (MPC) dynamics. This truly multi-level adaptive DG-MPC method will allow us to investigate large scale dynamics of colloid-polymer mixtures on massively parallel computing environments.


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);
doi:10.1016/j.cpc.2017.10.016

Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
G. Bispen, M. Lukacova-Medvidova, L. Yelash
J. Comput. Phys. 335, 222-248 (2017);
doi:10.1016/j.jcp.2017.01.020

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
Found. Comput. Math., 1-28 (2017);
doi:10.1007/s10208-017-9351-2

We study convergence of a mixed finite element–finite volume numerical scheme for the isentropic Navier–Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measurevalued solutions of the limit system. In particular, using the recently established weak– strong uniqueness principle in the class of dissipative measure-valued solutions we show that the numerical solutions converge strongly to a strong solutions of the limit system as long as the latter exists.

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);
URL: http://congress.cimne.com/coupled2017/frontal/default.asp

We present a new reduced-order hybrid multiscale method to simulate complex fluids. The method combines the continuum and molecular descriptions. We follow the framework of the heterogeneous multi-scale method (HMM) that makes use of the scale separation into macro- and micro-levels. On the macro-level, the governing equations of the incompressible flow are the continuity and momentum equations. The equations are solved using a high-order accurate discontinuous Galerkin Finite Element Method (dG) and implemented in the BoSSS code. The missing information on the macro-level is represented by the unknown stress tensor evaluated by means of the molecular dynamics (MD) simulations on the micro-level. We shear the microscopic system by applying Lees-Edwards boundary conditions and either an isokinetic or Lowe-Andersen thermostat. The data obtained from the MD simulations underlie large stochastic errors that can be controlled by means of the least-square approximation. In order to reduce a large number of computationally expensive MD runs, we apply the reduced order approach. Numerical experiments confirm the robustness of our newly developed hybrid MD-dG method.

Analysis and numerical solution of the Peterlin viscoelastic model (PhD Thesis)
Mizerova Hana
JGU (2015);
URL: http://ubm.opus.hbz-nrw.de/volltexte/2015/4231/

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

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);
doi:10.1140/epjst/e2012-01641-0

The aim of the present paper is to report on our recent results for GPU accelerated simulations of compressible flows. For numerical simulation the adaptive discontinuous Galerkin method with the multidimensional bicharacteristic based evolution Galerkin operator has been used. For time discretization we have applied the explicit third order Runge-Kutta method. Evaluation of the genuinely multidimensional evolution operator has been accelerated using the GPU implementation. We have obtained a speedup up to 30 (in comparison to a single CPU core) for the calculation of the evolution Galerkin operator on a typical discretization mesh consisting of 16384 mesh cells.

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