Related papers: Lattice Boltzmann for linear elastodynamics: perio…
We propose an experimentally relevant scheme to create stable solitons in a three-dimensional Bose-Einstein condensate confined by a one-dimensional optical lattice, using temporal modulation of the scattering length (through ac magnetic…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order…
It is well known that there are two integral steps of streaming and collision in the lattice Boltzmann method (LBM). This concept has been changed by the author's recently proposed macroscopic lattice Boltzmann method (MacLAB) to solve the…
Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We…
We present a lattice-based numerical method to describe the non equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
It is proposed a dimensional Lattice Boltzmann Method (LBM) of wide application for simulating fluid flow and heat transfer problems. The proposed LBM consists in the numerical solution of the discrete lattice Boltzmann equation (LBE) using…
The implementation of the kinetic diffuse boundary condition with the characteristic streaming-collision mechanism is studied for the high-order lattice Boltzmann (LB) models. The obtained formulation is also tested and validated…
Modeling and simulation of multiphase flows in complex geomerties are challenging due to the complexity in describing the interface topology changes among different phases and the difficulty in implementing the boundary conditions on the…
We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in…
An elegant and uniform relaxation-rate formula is presented for the entropic lattice Boltzmann method (ELBM). The formula not only guarantees the discrete time H-theorem at numerical level but also gives full consideration to the…
The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which…
We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol…
We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is…
One of the limitations of the Lattice Boltzmann Method in simulating inertial flows is the coupling of the discretization of space to the velocity discretization. It requires an increase of the size of computational lattices in order to…
A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng equations for the evolution of the velocity and tensor order-parameter…
In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum…
In a seminal paper Ginzburg and Adler analyzed the bounce-back boundary conditions for the lattice Boltzmann scheme and showed that it could be made exact to second order for the Poiseuille flow if some expressions depending upon the…