In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfven waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results.

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In this work a Discrete Boltzmann Model for the solution of transcritical 2D shallow water flows is presented and validated. In order to provide the model with transcritical capabilities, a particular multispeed velocity set has been employed for the discretization of the Boltzmann equation. It is shown that this particular set naturally yields a simple and closed procedure to determine higher order equilibrium distribution functions needed to simulate transcritical flow.

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrodinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found.

It is shown that lattice kinetic theory based on short-lived quasiparticles proves very effective in simulating the complex dynamics of strongly interacting fluids (SIF). In particular, it is pointed out that the shear viscosity of lattice fluids is the sum of two contributions, one due to the usual interactions between particles (collision viscosity) and the other due to the interaction with the discrete lattice (propagation viscosity).

A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing a detailed inspection of various non-equilibrium observables. Based on the TNE features, we define TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium.

The goal of this article is to study numerically the mixed convection in a differentially heated lid-driven cavity with non-uniform heating of the bottom wall. The velocity field is solved by a hybrid scheme with multiple relaxation time Lattice Boltzmann (MRT-LBM) model, while the temperature field is obtained by resolution of the energy balance equation using the finite difference method (FDM). First, the model is checked and validated using data from the literature. Validation of the present results with those available in the literature shows a good agreement.

A mathematical model and the simulation of subsoil decontamination by bioventing will be presented. The bases for the model construction are the following: (1) the pollutant is considered as immobile and confined in the unsaturated zone; (2) only oxygen is injected in the subsoil by wells; (3) the bacteria acting the pollutant removal are immobile and their growth depends on oxygen and pollutant concentration.

We show that causality violation in a Kerr naked singularity spacetime is constrained by the existence of (radial) potential barriers. We extend to the class of vortical non-equatorial null geodesics confined to $$\theta $$? $$=$$= constant hyperboloids (boreal orbits) previous results concerning timelike ones (Calvani et al. in Gen Rel Gravit 9:155, 1978), showing that within this class of orbits, the causality principle is rigorously satisfied.

The accurate segmentation of the optic disc (OD) offers an important cue to extract other retinal features in an automated diagnostic system, which in turn will assist ophthalmologists to track many retinopathy conditions such as glaucoma. Research contributions regarding the OD segmentation is on the rise, since the design of a robust automated system would help prevent blindness, for instance, by diagnosing glaucoma at an early stage and a condition known as ocular hypertension.