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In this work, a data-based approach to gas-surface interaction modeling, which employs the recently introduced distribution element tree (DET) method, is proposed. The DET method allows efficient data-driven probability density function (PDF) estimations with the possibility of conditional and unconditional random number resampling from the constructed distributions. As part of our ongoing research on gas-surface interaction, a comprehensive molecular dynamics (MD) study was performed, where the scattering of a nitrogen molecule from a graphite surface was investigated. Our aim here is to demonstrate how the DET method can be used in combination with the obtained MD database for constructing a generalized kernel of gas-surface interaction and for generating postscattered samples directly from the MD data itself. The major benefit of this approach is that it preserves all the relevant physics contained within numerical or experimental data, without the need for new kernel developments or accommodation coefficient calibrations. A direct comparison between the proposed approach and a classical scattering kernel used in rarefied gas flow simulations was carried out in the case of molecular beam scattering of rotationally hot and cold nitrogen from a solid surface. A further comparison between the proposed method and the available experimental data was also performed. Additionally, the ability of the DET-based kernel to satisfy the reciprocity condition, which ensures energy conservation in the case of thermal equilibrium, is demonstrated. [ABSTRACT FROM AUTHOR]

This letter investigates the clustering of particles in isotropic turbulence sustained by linear and spectral forcing. The Stokes numbers range from 0.1 to 100. The time series of particles are analyzed with autocorrelation functions of the particle velocity and local fluid velocity. The spatial distributions of particles are analyzed with probability density functions of Voronoï volumes. These statistics show significant differences between the clustering of particles in linearly and spectrally forced turbulence. [ABSTRACT FROM AUTHOR]

Abstract: Different simulation methods are applicable to study turbulent mixing. When applying probability density function (PDF) methods, turbulent transport, and chemical reactions appear in closed form, which is not the case in second moment closure methods (RANS). Moreover, PDF methods provide the entire joint velocity-scalar PDF instead of a limited set of moments. In PDF methods, however, a mixing model is required to account for molecular diffusion. In joint velocity-scalar PDF methods, mixing models should also account for the joint velocity-scalar statistics, which is often under appreciated in applications. The interaction by exchange with the conditional mean (IECM) model accounts for these joint statistics, but requires velocity-conditional scalar means that are expensive to compute in spatially three dimensional settings. In this work, two alternative mixing models are presented that provide more accurate PDF predictions at reduced computational cost compared to the IECM model, since no conditional moments have to be computed. All models are tested for different mixing benchmark cases and their computational efficiencies are inspected thoroughly. The benchmark cases involve statistically homogeneous and inhomogeneous settings dealing with three streams that are characterized by two passive scalars. The inhomogeneous case clearly illustrates the importance of accounting for joint velocity-scalar statistics in the mixing model. Failure to do so leads to significant errors in the resulting scalar means, variances and other statistics. [Copyright &y& Elsevier]

The probability density function (PDF) of the local concentration of a contaminant, or tracer, is an important component of risk assessment in applications that involve flow in heterogeneous subsurface formations. In this paper, a novel joint velocity-concentration PDF method for tracer flow in highly heterogeneous porous media is introduced. The PDF formalism accounts for advective transport, pore-scale dispersion (PSD), and molecular diffusion. Low-order approximations (LOAs), which are usually obtained using a perturbation expansion, typically lead to Gaussian one-point velocity PDFs. Moreover, LOAs provide reasonable approximations for small log conductivity variances (i.e., σ Y2 < 1). For large σ Y2, however, the one-point velocity PDFs deviate significantly from the Gaussian distribution as demonstrated convincingly by several Monte Carlo (MC) simulation studies. Furthermore, the Lagrangian velocity statistics exhibit complex correlations that span a wide range of scales, including long-range correlations due to the formation of preferential flow paths. Both non-Gaussian PDFs and complex long-range correlations are accurately represented using Markovian velocity processes (MVPs) in the proposed joint PDF method. LOA methods can be generalized to some extent by presuming a certain shape for the concentration PDF (e.g., a β PDF fully characterized by the concentration mean and variance). The joint velocity-concentration PDF method proposed here does not require any closure assumptions on the shape of the marginal concentration PDF. The Eulerian joint PDF transport equation is solved numerically using a computationally efficient particle-based approach. The PDF method is validated with high-resolution MC reference data from Caroni and Fiorotto (2005) for saturated transport in velocity fields, which are stationary in space and time, for domains with σ Y2 = 0.05, 1, and 2 and Péclet numbers ranging from 100 to 10,000. PSD is modeled using constant anisotropic dispersion coefficients in both the reference MC computations and our PDF method. [ABSTRACT FROM AUTHOR]