Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

Kolobov, Vladimir; Arslanbekov, Robert; Аристов, В. В.; Фролова, А. А.; Zabelok, S. A.

doi:10.1016/j.jcp.2006.09.021

Cited by 238 publications

(150 citation statements)

References 54 publications

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“…Stochastic hybrid methods were developed in [10] (mass diffusion), [11] (the "train model" for momentum diffusion), and [12] (Burgers' equation). Other recent work on coupling particle and continuum methods includes [13] (DSMC and Navier-Stokes, for aerospace applications), [14] (molecular dynamics and isothermal fluctuating hydrodynamics, for polymer simulations), and [15] (an adaptive refinement approach based on a direct numerical solution of the Boltzmann transport equation and kinetic continuum schemes).…”

Section: Introductionmentioning

confidence: 99%

Algorithm Refinement for Fluctuating Hydrodynamics

Williams¹,

Bell²,

Garcia³

2008

Multiscale Model. Simul.

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This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle al-1 gorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau-Lifshitz Navier-Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently-developed solver for LLNS, based on third-order Runge-Kutta. We present numerical tests of systems in and out of equilibrium, including timedependent systems, and demonstrate dynamic adaptive refinement by the computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the non-hydrodynamic (kinetic) time scales.

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Section: Introductionmentioning

confidence: 99%

Algorithm Refinement for Fluctuating Hydrodynamics

Williams¹,

Bell²,

Garcia³

2008

Multiscale Model. Simul.

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“…The left-hand side of BKE (advection operator) is evaluated using finite volume technique; the right-hand side (collision integral) is computed using Korobov nodes in velocity space (see details in Ref. [5]). Other methods that can be used for computing collision integral are reviewed in Ref.…”

Section: Boltzmann Solvermentioning

confidence: 99%

“…The kinetic cells were activated in the regions of large local Knudsen number based on continuum-kinetic switch (see Ref. [5] for details). Static uniform velocity mesh 24x24x24 was used for the Boltzmann solver.…”

Section: Example Of Hybrid Cpu-gpu Simulations Of Rarefied-continuum mentioning

confidence: 99%

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Zabelok

Arslanbekov

Kolobov

2015

Journal of Computational Physics

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Abstract. We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells with 24x24x24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method, the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on Lattice Boltzmann Method, all using octree Cartesian mesh. Double digit speedups on single GPU and good scaling for multiGPUs have been demonstrated.

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“…Beside the difficulty in the design of effective breakdown criteria, see also the discussion in [20] and [12], another difficulty in domain decomposition algorithms is due to the need of exchanging information between the stochastic solution obtained with DSMC and the deterministic solution of the continuum solver. This can be circumvented reducing noise through averaging, as in [17], where the stochastic solution is computed with a smaller grid in space and time with respect to the macroscopic solution, and thus it is averaged over the larger macroscopic cells.…”

Section: Introductionmentioning

confidence: 99%

“…A similar approach, with different microscopic and macroscopic control volumes, but based on a relaxation technique is considered in [27] and [8]. Otherwise, the problem of struggling with the lack of smoothness of stochastic solutions can be avoided using deterministic or semi-deterministic schemes, as in [20], following the approach of [28] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

Alaia

Puppo

2012

Journal of Computational Physics

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In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used to represent the transition between fully kinetic to equilibrium flows.In this fashion, the Boltzmann solver is used only when the collision integral is non-stiff, and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities. Thus, in principle, the same mesh size and time steps can be used in the whole computation. Moreover, the time step is limited only by convective terms.Since the Boltzmann solver is applied only in wholly kinetic regimes, we use the reduced noise DSMC scheme we have proposed in Part I of the present work. This ensures a smooth exchange of information across the different domains, with a natural way to construct interface numerical fluxes. Several tests comparing our hybrid scheme with full Boltzmann DSMC computations show the good agreement between the two solutions, on a wide range of Knudsen numbers.

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Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

Cited by 238 publications

References 54 publications

Algorithm Refinement for Fluctuating Hydrodynamics

Algorithm Refinement for Fluctuating Hydrodynamics

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

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