Related papers: Lattice Boltzmann Model for Numerical Relativity
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
A new lattice Boltzmann method for simulating multiphase flows is developed theoretically. The method is adjusted such that its continuum limit is the Navier-Stokes equation, with a driving force derived from the Cahn-Hilliard free energy.…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to…
We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such…
Lattice Boltzmann method models offer a novel framework for the simulation of high Reynolds number dilute gravity currents. The numerical algorithm is well suited to acceleration via implementation on massively parallel computer…
A modified lattice Boltzmann model with multiple relaxation times (MRT) for the convection-diffusion equation (CDE) is proposed. By modifying the relaxation matrix, as well as choosing the corresponding equilibrium distribution function…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
A modified lattice Boltzmann model with a stochastic relaxation mechanism mimicking "virtual'' collisions between free-streaming particles and solid walls is introduced. This modified scheme permits to compute plane channel flows in…
We present a free energy lattice Boltzmann model capable of simulating fluid systems with an arbitrary number of immiscible components in principle. Our method is strictly reduction consistent, ensuring that absent fluid components do not…
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in…
The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model…
The high Weissenberg number problem has been a persistent challenge in the numerical simulation of viscoelastic fluid flows. This paper presents an improved lattice Boltzmann method for solving viscoelastic flow problems at high Weissenberg…
It is shown that the Lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete…
A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
The development of multiple-relaxation-time (MRT) Lattice Boltzmann method (LBM) is a significant contribution in improving the numerical behavior, revealing the math and physics mechanism and extending the application of LBM. However, some…