arXiv subjects

Marcus Herrmann

Publications and source records attributed to Marcus Herrmann.

5 recordsLinked to original sources

arXiv2024

Enhancing the statistical evaluation of earthquake forecasts -- An application to Italy

Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake Predictability (CSEP, Schorlemmer et al., 2018) with new statistical methods supported by mathematical theory. To demonstrate their applicability, we evaluate three short-term forecasting models that were submitted to the CSEP-Italy experiment, and two ensemble models thereof. The models produce weekly overlapping forecasts for the expected number of M4+ earthquakes in a collection of grid cells. We compare the models' forecasts using consistent scoring functions for means or expectations, which are widely used and theoretically principled tools for forecast evaluation. We further discuss and demonstrate their connection to CSEP-style earthquake likelihood model testing, and specifically suggest an improvement of the T-test. Then, using tools from isotonic regression, we investigate forecast reliability and apply score decompositions in terms of calibration and discrimination. Our results show where and how models outperform their competitors and reveal a substantial lack of calibration for various models. The proposed methods also apply to full-distribution (e.g., catalog-based) forecasts, without requiring Poisson distributions or making any other type of parametric assumption.

stat.AP↗

arXiv2024

A High-Fidelity Methodology for Particle-Resolved Direct Numerical Simulations

We present a novel computational method for direct numerical simulations of particle-laden flows with fully-resolved particles (PR-DNS). The method is based on the recently developed Volume-Filtering Immersed Boundary method [Dave et al, Journal of Computational Physics, 487:112136, 2023] derived by volume-filtering the transport equations. This approach is mathematically and physically rigorous, in contrast to other PR-DNS methods which rely on ad-hoc numerical schemes to impose no-slip boundary conditions on the surface of particles. With the present PR-DNS strategy, we show that the ratio of filter size to particle diameter acts as a parameter that controls the level of fidelity. In the limit where this ratio is very small, a well-resolved PR-DNS is obtained. Conversely, when the ratio of filter size to particle diameter is large, a classic point-particle method is obtained. The discretization of the filtered equations is discussed and compared to other PR-DNS strategies based on direct-forcing immersed boundary methods. Numerical examples with sedimenting resolved particles are discussed.

physics.flu-dyn↗

arXiv2022

The volume-filtering immersed boundary method

We present a novel framework to deal with static and moving immersed boundaries (IB). In this strategy, called Volume-Filtering Immersed Boundary (VFIB) method, transport equations are derived by filtering the Navier-Stokes equations and accounting for stresses at the solid-fluid interface. The result is that boundary conditions that normally apply on the interface are transformed into bodyforces that apply on the right-hand side of the filtered transport equations. The filter width acts as a parameter that controls the level of resolution. The IB is considered well-resolved if the filter width is much smaller than the characteristic corrugation scale of the interface. There are several innovations in this IB method. First, it sheds light on the role of the internal flow which arises when the transport equations are solved inside the IB. We show that, it is essential to separate stresses due to the external and internal fluids in order to get accurate forces and provide a method to do so. Second, we show that volumes associated with Lagrangian forcing points on the boundary depend on the local topology of the surface. We provide a method to compute these volumes using a triangle tessellation of the interface and the surface density function. Third, we provide an efficient procedure to compute the solid volume fraction, thus, enabling tagging interior/exterior cells. This volume fraction is also involved in the procedure to separate stresses due to the external fluid from the total stresses. Fourth, we show a path forward to extend the VFIB method to Large Eddy Simulations involving IBs. Lastly, we apply the VFIB in several numerical tests involving two- and three- dimensional static and moving IBs. We show greatly improved results compared to prior IB methods. Further, we test several filter kernels and show that, for well-resolved IBs, the choice of the kernel plays little role.

physics.flu-dyn↗

arXiv2021

Comparative evaluation of point process forecasts

Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules, which are statistically principled tools for the comparative evaluation of predictive performance, to the point process setting, and place both new and existing methodology in this framework. With reference to earthquake likelihood model testing, we demonstrate that extant techniques apply in much broader contexts than previously thought. In particular, the Poisson log-likelihood can be used for theoretically principled comparative forecast evaluation in terms of cell expectations. We illustrate the approach in a simulation study and in a comparative evaluation of operational earthquake forecasts for Italy.

math.ST↗

arXiv2010

Primary Atomization of a Liquid Jet in Crossflow

In this fluid dynamics video, we present a visualization of the primary atomization of a turbulent liquid jet injected into a turbulent gaseous crossflow. It is based on a detailed numerical simulation of the primary atomization region of the jet using a finite volume, balanced force, incompressible LES/DNS flow solver coupled to a Refined Level Set Grid (RLSG) solver to track the phase interface position. The visualization highlights the two distinct breakup modes of the jet: the column breakup mode of the main liquid column and the ligament breakup mode on the sides of the jet and highlights the complex evolution of the phase interface geometry.

physics.flu-dyn↗