Evaluation of Macroscopic Properties in the Direct Simulation Monte Carlo Method

Sun, Qiang; Boyd, Iain D.

doi:10.2514/1.12542

Cited by 51 publications

(35 citation statements)

References 17 publications

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“…For instance, Rader et al [21] showed that the numerical error in thermal conductivity for Fourier heat flow of hard sphere gas was about 0.040 5 (Δx/λ) 2 due to the cell size, 0.028 7 (Δt/τ) 2 due to the time step, and 0.083/N c due to the number of particles per cell, where λ is the mean free path and τ is the mean collision time. The statistical error due to a limited sample size is proportional to 1/ √ N s for flow properties such as velocity, density, and temperature [22], where N s can be enlarged using ensemble average.…”

Section: Dsmc Methodsmentioning

confidence: 99%

On the validity of the Boltzmann-BGK model through relaxation evaluation

2014

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The Boltzmann-Bhatnagar-Gross-Krook (BGK) model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo (DSMC) results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model, however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.

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Section: Dsmc Methodsmentioning

confidence: 99%

On the validity of the Boltzmann-BGK model through relaxation evaluation

2014

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“…As this progression and relaxation occurs, DSMC and NS regions are loosely coupled and interface locations are periodically updated throughout the simulation. Before the NS portions of the hybrid numerical cycle, the macroscopic state variables are set in each NS boundary cell using a subrelaxation average [33] of the molecular properties in each corresponding DSMC cell. As an example, the final steady-state interface locations for the hollow-cylinder-flare simulation are shown at the top of Fig.…”

Section: Modular Particle-continuum Numerical Methods a Problem mentioning

confidence: 99%

Hybrid Particle-Continuum Simulations of Hypersonic Flow Over a Hollow-Cylinder-Flare Geometry

2008

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A modular particle-continuum numerical method is used to simulate steady-state hypersonic flow over a hollowcylinder-flare geometry. The resulting flowfield involves a mixture of rarefied nonequilibrium flow and high-density continuum flow. The hybrid particle-continuum method loosely couples direct simulation Monte Carlo and NavierStokes methods, which operate in different regions, use different mesh densities, and are updated using differentsized time steps. Hybrid numerical results are compared with full particle and full continuum simulations as well as with experimental data. The hybrid particle-continuum simulations are demonstrated to reproduce experimental and full particle simulation results for surface and flowfield properties including velocity slip, temperature jump, thermal nonequilibrium, heating rates, and pressure distributions with high accuracy. The hybrid method, which uses particle simulation next to the surface, is also shown to predict accurate heating rates even when a highly dissipative numerical scheme is used for the continuum solver. For this particular flow, a hybrid simulation is obtained with modest computational savings over full particle simulation. NomenclatureBr cutoff = cutoff value of the continuum-breakdown parameter

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“…Note that the amount of scatter associated with a given θ value is the same as the scatter resulting from averaging over 1 θ time-steps. 21 Figure 5 shows the success of this averaging technique applied to the DSMC velocity variation. Although when using θ = 0.01 the average follows the DSMC variation with almost no lag, the scatter is far too large to use this average as a NS boundary condition.…”

Section: Reducing Scatter In Ns Boundary Conditionsmentioning

confidence: 99%

Detailed Analysis of a Hybrid CFD-DSMC Method for Hypersonic Non-Equilibrium Flows

Schwartzentruber

Boyd

2005

38th AIAA Thermophysics Conference

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A hybrid numerical scheme designed for hypersonic non-equilibrium flows is presented which solves the Navier-Stokes equations in regions of near-equilibrium and uses the direct simulation Monte Carlo method where the flow is in non-equilibrium. Detailed analysis of each stage of the hybrid cycle illustrates the difficulty in defining physically correct DSMC boundary conditions in regards to both macroscopic state, and velocity distribution. However, results also show that DSMC boundary conditions have little effect on a previously initialized interior particle domain. A sub-relaxation technique capable of determining macroscopic, hydrodynamic properties in a DSMC simulation is used to determine low-scatter boundary conditions for the NS domain. Particle and continuum domains adapt during the hybrid simulation through application of a continuum breakdown parameter based on the gradient-length Knudsen number. The hybrid code reproduces experimental results and full DSMC simulations in half the time for a large range of 1D shock waves in argon and diatomic nitrogen gas.

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Evaluation of Macroscopic Properties in the Direct Simulation Monte Carlo Method

Cited by 51 publications

References 17 publications

On the validity of the Boltzmann-BGK model through relaxation evaluation

On the validity of the Boltzmann-BGK model through relaxation evaluation

Hybrid Particle-Continuum Simulations of Hypersonic Flow Over a Hollow-Cylinder-Flare Geometry

Detailed Analysis of a Hybrid CFD-DSMC Method for Hypersonic Non-Equilibrium Flows

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