Related papers: Two-dimensional finite-difference lattice Boltzman…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar-Gross-Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro and…
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…
A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of non ideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for…
We present a novel lattice Boltzmann method that has a capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this new method, a liquid-vapor boiling…
We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…
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 the continuum flow regime, the Navier-Stokes equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied gas dynamics. Both equations are constructed from modeling…
We present a new 3D lattice Boltzmann (LB) algorithm based on central moments for the D3Q27 lattice using a cuboid grid, which is parameterized by two grid aspect ratios that are related to the ratios of the particle speeds with respect to…
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…
Lattice Boltzmann method (LBM) is particularly well-suited for implementation on quantum circuits owing to its simple algebraic operations and natural parallelism. However, most quantum LBMs fix $\tau$ = 1 to avoid nonlinear collision,…
In this paper, a finite volume lattice Boltzmann method (FVLBM) based on cell-center unstructured girds is presented and full studied to simulate the incompressible laminar flows, which is simple modified from the cell-vertex unstructured…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic…
Four different kinds of laminar flows between two parallel plates are investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is estimated in two cases using numerical fits of the parabolic velocity profiles and the kinetic…
In this paper, we provide the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres with small inelasticity. The hydrodynamic system that we obtain is an incompressible…
We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to…
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…