Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations

Fast kinetic simulator for relativistic matter

Relativistic kinetic theory is ubiquitous to several fields of modern physics, finding application at large scales in systems in astrophysical contexts, all of the way down to subnuclear scales and into the realm of quark-gluon plasmas. This motivates the quest for powerful and efficient computational methods that are able to accurately study fluid dynamics in the relativistic regime as well as the transition to beyond hydrodynamics-in principle all of the way down to ballistic regimes. We present a family of relativistic lattice kinetic schemes for the efficient simulation of relativistic flows in both strongly (fluid) and weakly (rarefied gas) interacting regimes. The method can deal with both massless and massive particles, thereby encompassing ultra- and mildly relativistic regimes alike. The computational performance of the method for the simulation of relativistic flows across the aforementioned regimes is discussed in detail, along with prospects of future applications.

A variable time step self-consistent mean field DSMC model for three-dimensional environments

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.

Multiscale semi-Lagrangian lattice Boltzmann method

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets of lower and higher order are consistently and efficiently coupled, allowing us to use the higher-order model only when and where needed. This includes regions of high Mach or high Knudsen numbers. The coupling procedure of discrete velocity sets consists of either a projection of the higher-order populations onto the lower-order lattice or lifting of the lower-order populations to the higher-order velocity space. Both lifting and projection are local operations, which enable a flexible adaptive velocity set. The proposed scheme is formulated for both a static and an optimal, co-moving reference frame, in the spirit of the recently introduced Particles on Demand method. The multi-scale scheme is validated with an advection of an athermal vortex and in a jet flow setup. The performance of the proposed scheme is further investigated in the shock structure problem and a high-Knudsen-number Couette flow, typical examples of highly non-equilibrium flows in which the order of the velocity set plays a decisive role. The results demonstrate that the proposed multi-scale scheme can operate accurately, with flexibility in terms of the underlying models and with reduced computational requirements.

Discrete Boltzmann trans-scale modeling of high-speed compressible flows

We present a general framework for constructing trans-scale discrete Boltzmann models (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function that satisfies additional nonhydrodynamic kinetic moments. To characterize the thermodynamic nonequilibrium (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two measures are presented: (i) the relative TNE strength, describing the relative strength of the (N+1)th order TNE effects to the Nth order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted is best described by the relative TNE intensity and/or the discrepancy rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with 26 discrete velocities at Burnett level is formulated, verified, and validated.

Chimaera simulation of complex states of flowing matter

We discuss a unified mesoscale framework (chimaera) for the simulation of complex states of flowing matter across scales of motion. The chimaera framework can deal with each of the three macro-meso-micro levels through suitable 'mutations' of the basic mesoscale formulation. The idea is illustrated through selected simulations of complex micro- and nanoscale flows.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.