Detailed analysis of the lattice Boltzmann method on unstructured grids

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.Comment: 42 page

Observation of Motion Dependent Nonlinear Dispersion with Narrow Linewidth Atoms in an Optical Cavity

As an alternative to state-of-the-art laser frequency stabilisation using ultra-stable cavities, it has been proposed to exploit the non-linear effects from coupling of atoms with a narrow transition to an optical cavity. Here we have constructed such a system and observed non-linear phase shifts of a narrow optical line by strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multi-photon scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intra-cavity power we systematically study this non-linear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub 100 mHz level and superradiant laser sources involving narrow line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation with ultranarrow clock transitions.Comment: 9 pages (including 4 pages of Supplemental Information), 6 figures. Updated to correspond to the published versio

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal

Predicting distresses using deep learning of text segments in annual reports

Corporate distress models typically only employ the numerical financial variables in the firms' annual reports. We develop a model that employs the unstructured textual data in the reports as well, namely the auditors' reports and managements' statements. Our model consists of a convolutional recurrent neural network which, when concatenated with the numerical financial variables, learns a descriptive representation of the text that is suited for corporate distress prediction. We find that the unstructured data provides a statistically significant enhancement of the distress prediction performance, in particular for large firms where accurate predictions are of the utmost importance. Furthermore, we find that auditors' reports are more informative than managements' statements and that a joint model including both managements' statements and auditors' reports displays no enhancement relative to a model including only auditors' reports. Our model demonstrates a direct improvement over existing state-of-the-art models

Finite-element lattice Boltzmann simulations of contact line dynamics

The lattice Boltzmann method has become a standard technique for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.Comment: 8 page