Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method

This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.     

Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

Richtmyer-Meshkov Experiments on the Omega Laser

Observations of the interstellar medium reveal a dynamic realm permeated by shocks. These shocks are generated on a large range of scales by galactic rotation, supernovae, stellar winds, and other processes. Whenever a shock encounters a density interface, Richtmyer-Meshkov instabilities may develop. Perturbations along the interface grow, leading to structure formation and material mixing. An understanding of the evolution of Richtmyer-Meshkov instabilities is essential for understanding galactic structure, molecular cloud morphology, and the early stages of star formation. An ongoing experimental campaign studies Richtmyer-Meshkov mixing in a convergent, compressible, miscible plasma at the Omega laser facility. Cylindrical targets, consisting of a low density foam core and an aluminum shell covered by an epoxy ablator, are directly driven by fifty laser beams. The aluminum shell is machined to produce different perturbation spectra. Surface types include unperturbed (smooth), single-mode sinusoids, multi-mode (rough), and multi-mode with particular modes accentuated (specified-rough). Experimental results are compared to theory and numerical simulations.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave.
Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.     

Laser Interferometer Space Antenna double black holes: dynamics in gaseous nuclear discs

We study the inspiral of double black holes, with masses in the Laser Interferometer Space Antenna ( LISA ) window of detectability, orbiting inside a massive circumnuclear, rotationally supported gaseous disc. Using high-resolution smoothed particle hydrodynamics simulations, we follow the black hole dynamics in the early phase when gas-dynamical friction acts on the black holes individually, and continue our simulation until they form a close binary. We find that in the early sinking the black holes lose memory of their initial orbital eccentricity if they corotate with the gaseous disc. As a consequence, the massive black holes bind forming a binary with a low eccentricity, consistent with zero within our numerical resolution limit. The cause of circularization resides in the rotation present in the gaseous background where dynamical friction operates. Circularization may hinder gravitational waves from taking over and leading the binary to coalescence. In the case of counter-rotating orbits, the initial eccentricity (if present) does not decrease, and the black holes may bind forming an eccentric binary. When dynamical friction has subsided, for equal mass black holes and regardless their initial eccentricity, angular momentum loss, driven by the gravitational torque exerted on the binary by surrounding gas, is nevertheless observable down to the smallest scale probed (≃1 pc). In the case of unequal masses, dynamical friction remains efficient down to our resolution limit, and there is no sign of formation of any ellipsoidal gas distribution that may further harden the binary. During inspiral, gravitational capture of gas by the black holes occurs mainly along circular orbits; eccentric orbits imply high relative velocities and weak gravitational focusing. Thus, the active galactic nucleus activity may be excited during the black hole pairing process and double active nuclei may form when circularization is completed, on distance scales of tens of parsecs.