1,717 research outputs found
Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo
A multilevel Monte Carlo (MLMC) method for quantifying model-form
uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS)
simulations is presented. Two, high-dimensional, stochastic extensions of the
RANS equations are considered to demonstrate the applicability of the MLMC
method. The first approach is based on global perturbation of the baseline eddy
viscosity field using a lognormal random field. A more general second extension
is considered based on the work of [Xiao et al.(2017)], where the entire
Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For
two fundamental flows, we show that the MLMC method based on a hierarchy of
meshes is asymptotically faster than plain Monte Carlo. Additionally, we
demonstrate that for some flows an optimal multilevel estimator can be obtained
for which the cost scales with the same order as a single CFD solve on the
finest grid level.Comment: 40 page
Analysis of expression of aquaporins and Na+/H+ transporters in tomato colonized by arbuscular mycorrhizal fungi and affected by salt stress
Statistical approach to crystal nucleation in glass-forming liquids
In this work, methods of description of crystal nucleation by using the statistical approach are analyzed. Findings from classical nucleation theory (CNT) for the average time of formation of the first supercritical nucleus are linked with experimental data on nucleation in glass-forming liquids stemming from repetitive cooling protocols both under isothermal and isochronal conditions. It is shown that statistical methods of lifetime analysis, frequently used in medicine, public health, and social and behavioral sciences, are applicable to crystal nucleation problems in glass-forming liquids and are very useful tools for their exploration. Identifying lifetime with the time to nucleate as a random variable in homogeneous and non-homogeneous Poisson processes, solutions for the nucleation rate under steady-state conditions are presented using the hazard rate and related parameters. This approach supplies us with a more detailed description of nucleation going beyond CNT. In particular, we show that cumulative hazard estimation enables one to derive the plotting positions for visually examining distributional model assumptions. As the crystallization of glass-forming melts can involve more than one type of nucleation processes, linear dependencies of the cumulative hazard function are used to facilitate assignment of lifetimes to each nucleation mechanism
Viscoelasticity and metastability limit in supercooled liquids
A supercooled liquid is said to have a kinetic spinodal if a temperature Tsp
exists below which the liquid relaxation time exceeds the crystal nucleation
time. We revisit classical nucleation theory taking into account the
viscoelastic response of the liquid to the formation of crystal nuclei and find
that the kinetic spinodal is strongly influenced by elastic effects. We
introduce a dimensionless parameter \lambda, which is essentially the ratio
between the infinite frequency shear modulus and the enthalpy of fusion of the
crystal. In systems where \lambda is larger than a critical value \lambda_c the
metastability limit is totally suppressed, independently of the surface
tension. On the other hand, if \lambda < \lambda_c a kinetic spinodal is
present and the time needed to experimentally observe it scales as
exp[\omega/(\lambda_c-\lambda)^2], where \omega is roughly the ratio between
surface tension and enthalpy of fusion
Superluminality in the Fierz--Pauli massive gravity
We study the propagation of helicity-1 gravitons in the Fierz--Pauli massive
gravity in nearly Minkowski backgrounds. We show that, generically, there exist
backgrounds consistent with field equations, in which the propagation is
superluminal. The relevant distances are much longer than the ultraviolet
cutoff length inherent in the Fierz--Pauli gravity, so superluminality occurs
within the domain of validity of the effective low energy theory. There remains
a possibility that one may get rid of this property by imposing fine tuning
relations between the coefficients in the non-linear generalization of the
Fierz--Pauli mass term, order by order in non-linearity; however, these
relations are not protected by any obvious symmetry. Thus, among others,
superluminality is a problematic property to worry about when attempting to
construct infrared modifications of General Relativity.Comment: 11 pages, no figure
Stochastic turbulence modeling in RANS simulations via multilevel Monte Carlo
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al. (2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level
Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates
International audienceThe lack of an universal modelling approach for turbulence in Reynolds-Averaged Navier–Stokes simulations creates the need for quantifying the modelling error without additional validation data. Bayesian Model-Scenario Averaging (BMSA), which exploits the variability on model closure coefficients across several flow scenarios and multiple models, gives a stochastic, a posteriori estimate of a quantity of interest. The full BMSA requires the propagation of the posterior probability distribution of the closure coefficients through a CFD code, which makes the approach infeasible for industrial relevant flow cases. By using maximum a posteriori (MAP) estimates on the posterior distribution, we drastically reduce the computational costs. The approach is applied to turbulent flow in a pipe at Re= 44,000 over 2D periodic hills at Re=5600, and finally over a generic falcon jet test case (Industrial challenge IC-03 of the UMRIDA project)
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