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

Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae

(Abridged) In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov $k^{-5/3}$ scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at relatively low resolutions, suggesting that very high effective Reynolds number can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, \ie the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where relatively high resolution $\sim 512^3$, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.Comment: 17 pages, 9 figures, matches published versio

Advanced numerical and statistical techniques to assess erosion and flood risk in coastal zones

Throughout history, coastal zones have been vulnerable to the dual risks of erosion and flooding. With climate change likely to exacerbate these risks in the coming decades, coasts are becoming an ever more critical location on which to apply hydro-morphodynamic models blended with advanced numerical and statistical techniques, to assess risk. We implement a novel depth-averaged hydro-morphodynamic model using a discontinuous Galerkin based finite element discretisation within the coastal ocean model {\em Thetis}. Our model is the first with this discretisation to simulate both bedload and suspended sediment transport, and is validated for test cases in fully wet and wet-dry domains. These test cases show our model is more accurate, efficient and robust than industry-standard models. Additionally, we use our model to implement the first fully flexible and freely available adjoint hydro-morphodynamic model framework which we then successfully use for sensitivity analysis, inversion and calibration of uncertain parameters. Furthermore, we implement the first moving mesh framework with a depth-averaged hydro-morphodynamic model, and show that mesh movement can help resolve the multi-scale issues often present in hydro-morphodynamic problems, improving their accuracy and efficiency. We present the first application of the multilevel Monte Carlo method (MLMC) and multilevel multifidelity Monte Carlo method (MLMF) to industry-standard hydro-morphodynamic models as a tool to quantify uncertainty in erosion and flood risk. We use these methods to estimate expected values and cumulative distributions of variables which are of interest to decision makers. MLMC, and more notably MLMF, significantly reduce computational cost compared to the standard Monte Carlo method whilst retaining the same level of accuracy, enabling in-depth statistical analysis of complex test cases that was previously unfeasible. The comprehensive toolkit of techniques we develop provides a crucial foundation for researchers and stakeholders seeking to assess and mitigate coastal risks in an accurate and efficient manner.Open Acces

Uncertainty quantification in a macroscopic traffic flow model calibrated on GPS data

International audienceThe objective of this paper is to analyze the inclusion of one or more random parameters into the deterministic Lighthill-Whitham-Richards traffic flow model and use a semi-intrusive approach to quantify uncertainty propagation. To verify the validity of the method, we test it against real data coming from vehicle embedded GPS systems, provided by Autoroutes Trafic