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Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauss-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauss-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor-Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor-Green vortex flows with Mach numbers Ma={0.5;1.0;1.5;2.0} on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.
This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
Low-frequency vibrational excitations in zeolite ZSM-5 and its partially crystalline derivatives
(2004)
Molecular dynamics investigation of vibrational properties of zeolite ZSM-5-based amorphous material
(2003)
GROW: A gradient-based optimization workflow for the automated development of molecular models
(2010)
Comparison Between Coarse-Graining Models for Polymer Systems: Two Mapping Schemes for Polystyrene
(2007)
Structural and Dynamical Properties of Polystyrene Determined by Coarse-Graining MD Simulations
(2007)
We present results from a detailed study of a new, optimized coarse-grained (CG) model of polystyrene (PS) and compare it with a recently published one (Harmandaris et al., Macromolecules 2006, 39, 6708). We will explain in detail, what led us to a different mapping scheme and put that into the general framework, with special emphasis on the aspect of time mapping. The new model is tested against the structural and dynamic properties of PS, resulting from atomistic simulations.
The influence of interaction details on the thermal diffusion in binary Lennard-Jones liquids
(2001)
Crystal stability limits at positive and negative pressures, and crystal-to-glass transitions
(1995)
Spinodal of liquid water
(1993)