On efficient simulations of multiscale kinetic transport

Abstract

We discuss a new class of approaches for simulating multiscale kinetic problems, with particular emphasis on applications related to small-scale transport. These approaches are based on a decomposition of the kinetic description into an equilibrium part, which is described deterministically (analytically or numerically), and the remainder, which is described using a particle simulation method. We show that it is possible to derive evolution equations for the two parts from the governing kinetic equation, leading to a decomposition that is dynamically and automatically adaptive, and a multiscale method that seamlessly bridges the two descriptions without introducing any approximation . Our discussion pays particular attention to stochastic particle simulation methods that are typically used to simulate kinetic phenomena; in this context, these decomposition approaches can be thought of as control-variate variance-reduction formulations, with the nearby equilibrium serving as the control. Such formulations can provide substantial computational benefits in a broad spectrum of applications because a number of transport processes and phenomena of practical interest correspond to perturbations from nearby equilibrium distributions. In many cases, the computational cost reduction is sufficiently large to enable otherwise intractable simulations.

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales I

“…Volume 1 consists of papers by Wang & Peters [1] on turbulence; by Klimenko [2] on thermodynamics and mixing; by Volpert et al [3] on anomalous diffusion; by Sukoriansky & Galperin [4] on analytical modelling of geophysical flows; by Bershadkii [5] on data interpretation in climate modelling; by Lozovatsky & Fernando [6] on measure for stirring efficiency in natural environments; by Majda & Gershgorin [7] on non-local diffusivity in climate variations; by Frederiksen et al [8] on stochastic modelling of geophysical flows; by Shu [9] on application of high-order accurate nonlinear schemes in simulations of compressible flows; by Radtke et al [10] on hybrid atomistic-continuum dynamic simulations of multi-scale kinetic problems; and by Sofieva et al [11] on measurements of stellar scintillations for quantification of atmospheric turbulence. These papers represent the broad variety of themes of the 'Turbulent mixing and beyond' programme [12] and are concerned with the fundamental aspects of turbulence, mixing and nonequilibrium dynamics.…”

“…This is not the case for a large class of problems, and new simulation methods are needed. Radtke et al [10] consider the simulation of multi-scale kinetic problems. The approach is based on a decomposition of the kinetic description into an equilibrium part that is described analytically or numerically, and a remainder, which is described using a particle simulation method.…”

Simulation of Heat Transport in Graphene Nanoribbons Using the Ab-Initio Scattering Operator

“…This results in drastically reduced statistical uncertainty, but also the ability to automatically and adaptively concentrate the computational effort in regions where kinetic effects are important, which is of great importance in the simulation of multiscale phenomena [6,9,12].…”

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

“…18 Coupled Vlasov and two-fluid code has been recently described using GPU for Vlasov solvers in locally selected kinetic domains. 9 Porting adaptive multi-scale kinetic-fluid solvers such as UFS to heterogeneous CPU-GPU computing architectures poses several challenges associated with irregular data structures of the dynamically adapted mesh, vastly different costs of computing in fluid and kinetic cells, and dynamic balancing of both CPU and GPU loads. We use here the simplest approach where GPUs are used only for the kinetic cells whereas the fluid cells are computed on CPUs.…”

“…Multi-scale kinetic-fluid models are being developed to enable using kinetic and fluid solvers in different parts of systems to achieve maximum fidelity and efficiency. 5,6,7,8,9,10 Adaptive kinetic-fluid models apply different solvers in dynamically selected regions of physical or phase space for efficient description of multi-scale phenomena in complex systems. Appropriate solvers are selected using sensors locally detecting phase space regions where kinetic approach is required and apply fluid models in other parts of the system.…”