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C5: Adaptive Hybrid-Multiskalen-Simulationen von Flüssigkeiten aus weicher Materie

In diesem Projekt entwickeln wir eine neuartige hybride Multiskalenmethode für komplexe Flüssigkeiten, die teilchenbasierte Simulationen mit Kontinuumsmodellen verknüpft. Unser Ansatz zielt darauf die sogenannte „discontinuous Garlekin method“ (DG) zur Lösung von partiellen Differentialgleichungen auf einem adaptiven Gitter mit „multiparticle collision dynamics“ (MPC) zu koppeln. Diese Kombination wird es uns ermöglichen, großskalige Untersuchungen zu Dynamik und Fließeigenschaften von Kolloid-Polymer-Mischungen auf Supercomputern durchzuführen.


Analysis and numerical solution of the Peterlin viscoelastic model (Doktorarbeit)
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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