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Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Computational molecular engineering: Scalable simulation and reliable modelling Martin Horsch Laboratory of Engineering Thermodynamics, University of Kaiserslautern

  1. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Computational molecular engineering: Scalable simulation and reliable modelling Martin Horsch Laboratory of Engineering Thermodynamics, University of Kaiserslautern Tianjin, 16 th November 2015 Tianjin Center for Applied Mathematics

  2. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Computational molecular engineering To Engineering From Physics (quantitative reliability) (qualitative accuracy) • Physically realistic modelling of • No blind fitting, but parameters of intermolecular interactions effective pair potentials are adjusted to experimental data • Separate contributions due to repulsive and dispersive as well as • Physical realism facilitates reliable electrostatic interactions interpolation and extrapolation 16th November 2015 Martin Horsch 2

  3. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Force fields for molecular modelling Geometry Bond lengths and angles Dispersion and repulsion Lennard-Jones potential: Size and energy parameters Electrostatics Point polarities (charge, dipole, quadrupole): Position and magnitude 16th November 2015 Martin Horsch 3

  4. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Simulation of bulk properties with ms2 Self-diffusion coefficient Shear viscosity 20 Thermal conductivity Second virial coefficient 3.5 N2 5 3.0 O2 CO2 -1 s -1 B / cm 3 mol -1 CO2 10 2 λ / W m -1 K -1 C2H4 15 4 10 4 η s / Pa s 2.5 10 4 D ρ / mol m 10 2 λ / Wm -1 K -1 C2H6 2.0 3 10 1.5 2 1.0 5 1 0.5 0 0.0 0 T / K 20 25 30 35 5 10 15 20 25 20 22 24 26 28 30 10 -3 ρ / mol m -3 10 -3 ρ / mol m -3 10-3 ρ / mol m-3 10 -3 ρ / mol m - 3 10 -3 ρ / mol m -3 10 -3 ρ / mol m -3 ms2 is freely available for academic use – register at http://www.ms-2.de/ 16th November 2015 Martin Horsch 4

  5. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Efficient simulation of large systems Linked-cell data structure suitable for spatial domain decomposition: (non-blocking, over- lapping MPI send/ receive operations) Methods for heterogeneous or fluctuating particle distributions: l arge s ystems “ 1 ”: m olecul ar dyn amics http://www.ls1-mardyn.de/ 16th November 2015 Martin Horsch 5

  6. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Efficient simulation of large systems Memory-efficient implementation based on the linked-cell data structure: Optionally, forces acting on molecules are only stored until their cell leaves the sliding window. hyperthreaded sliding window Efficient vectorization: ● Optimization by hand, using advanced vector extensions (AVX). ● Conversion from array of structures (AoS) to structure of arrays (SoA). l arge s ystems “ 1 ”: m olecul ar dyn amics http://www.ls1-mardyn.de/ 16th November 2015 Martin Horsch 6

  7. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Large-scale MD simulation on SuperMUC Scaling of ls1 mardyn examined on up to 146 016 cores, i.e. the whole SuperMUC at the Leibniz Supercomputing Centre, Garching, in 2013. speedup (relative to 128 cores) homogeneous LJTS liquid with 4.8 billion molecules g n i l a c s g n o r t observed strong scaling s l a e d i number of cores 16th November 2015 Martin Horsch 7

  8. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Large-scale MD simulation on SuperMUC Up to N = 4 · 10 12 on SuperMUC speedup weak scaling with 31.5 million molecules per core 2013 number of cores l arge s ystems “ 1 ”: m olecul ar dyn amics http://www.ls1-mardyn.de/ 16th November 2015 Martin Horsch 8

  9. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Large-scale MD simulation on hermit homogeneous cavitation CO 2 ( T = 280 K and ρ = 17.2 mol/l), 3CLJQ 100 million interaction sites, 110 592 cores 16th November 2015 Martin Horsch 9

  10. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Molecular simulation of fluids at interfaces ● Vapour-liquid surface tension LJTS ● Nucleation and dispersed phases ● Adsorption (fluid-fluid and fluid-solid) ● Contact angle and contact line pinning local fluid density T = 0.8 ε θ pl = 90° 16th November 2015 Martin Horsch 10

  11. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Long-range correction at planar interfaces short range long range For planar interfaces: (explicit) (correction) Long-range correction from the density profile, following Janeček . cutoff radius Full evaluation of all pairwise interactions is too expensive ... ... short-range interactions are evaluated only for neighbours . 16th November 2015 Martin Horsch 11

  12. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Long-range correction at planar interfaces Two-centre LJ fluid (2CLJ) For planar interfaces: Long-range correction from the surface tension / εσ -2 density profile, following Janeček . T = 0.979 ε 1 nm Janeček-Lustig term no angle averaging no long-range correction Angle-averaging expression for multi-site models, following Lustig . cutoff radius / σ Dipole and dispersion lead to analogous long-range correction expressions. The long-range contribution of the quadrupole can be neglected. 16th November 2015 Martin Horsch 12

  13. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Surface tension at high precision Lennard-Jones fluid surface tension / εσ -2 LJ 1.23   ε T γ ( ) T = 2.94 1 −  ÷ 0 2 σ T   c temperature / ε 16th November 2015 Martin Horsch 13

  14. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Objective: Accuracy for multiple properties ethylene oxide model by Eckl et al. (2008) uncertainty of reference molecular model 16th November 2015 Martin Horsch 14

  15. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Force fields for molecular modelling temperature simulation density 2CLJQ models: [mol/l] DIPPR correlation • 2 LJ centres • Quadrupole vapour pressure (logarithmic) Fit of parameters σ , ε , L , Q to VLE data of 29 fluids by Stoll et al. No interfacial properties were Deviation: considered for the • δρ ' ≈ 1 % parameterization. • δP sat ≈ 5 % inverse temperature [1/K] 16th November 2015 Martin Horsch 15

  16. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Predictive capacity of literature models Two LJ + quadrupole (2CLJQ) Two LJ + dipole (2CLJD) Fit to bulk properties 10 to 20 % overestimation of vapour-liquid surface tension 16th November 2015 Martin Horsch 16

  17. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Massively parallel molecular modelling Two LJ + quadrupole (2CLJQ) Two LJ + dipole (2CLJD) L * = 0.4 L * = 0.2 surface tension / εσ -2 Q * = 1.41 Q * = 1.41 L * = 0.4 Q * = 0 L * = 0.4 Q * = 2 L * = 0.6 Q * = 1.41 temperature / ε ● Systematic exploration of the four-dimensional model parameter space ● Correlation of the surface tension by a critical scaling expression 16th November 2015 Martin Horsch 17

  18. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Multicriteria model optimization Pareto optimality criterion Pareto set for carbon dioxide Multicriteria optimization requires massively-parallel molecular modelling. 16th November 2015 Martin Horsch 18

  19. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Pareto sets for 2CLJQ models of real fluids criteria: ρ ', p s , γ Projections of the Pareto set on the parameter space reveal intrinsic cor- relations between different model parameters, such as ε and Q . 16th November 2015 Martin Horsch 19

  20. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Pareto sets for 2CLJQ models of real fluids criteria: ρ ', p s , γ The dimension of the parameter space is effectively reduced, facilitating an efficient multicriteria optimization by navigating on the Pareto set. 16th November 2015 Martin Horsch 20

  21. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Pareto sets for 2CLJQ models of real fluids Representation of objective and parameter spaces by patch plots : Pareto-optimal 2CLJQ models for molecular oxygen 16th November 2015 Martin Horsch 21

  22. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Fast and simple model parameterization 16th November 2015 Martin Horsch 22

  23. Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Summary The traditional art of molecular modelling An expert modelling artist designs and publishes • a single optimized model for a particular fluid, • according to his choice of criteria (often unknown to the public), • users are passive, they have to live with the artists' decision. Scientific modelling by multicriteria optimization For established model classes and multiple thermodynamic criteria, • the dependence of thermodynamic properties on the model parameters is determined and correlated, • the deviation between model properties and real fluid behaviour is characterized, and the Pareto set is published, • users can design their own tailored model with minimal effort . 16th November 2015 Martin Horsch 23

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