Vasili Baranau1 1. Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany Corresponding author: Vasili Baranau, [email protected] Abstract: We propose a universal approach in the framework of the lattice Boltzmann method (LBM) to modeling constant velocity constraints and constant temperature constraints on curved walls, which doesn’t depend ...

A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimizatio...

In this paper we propose a preconditioned lattice Boltzmann (LB) method for steady incompressible flows. For steady flows, the macroscopic equations derived from this LB model are equivalent to those from the standard LB model, but with an improved eigenvalue system. The proposed model can be viewed as an explicit solver for preconditioned compressible Navier-Stokes equations. Linear stability ...

We propose a spectral method that discretizes the Boltzmann collision operator and satisfies a discrete version of the H-theorem. The method is obtained by modifying the existing Fourier spectral method to match a classical form of the discrete velocity method. It preserves the positivity of the solution on the Fourier collocation points and as a result satisfies the H-theorem. The fast algorit...

We present a physically-based, yet fast and simple method to simulate gaseous phenomena. In our approach, the incompressible Navier-Stokes (NS) equations governing fluid motion have been modeled in a novel way to achieve a realistic animation. We introduce the Lattice Boltzmann Model (LBM) which simulates the microscopic movement of fluid particles by linear and local rules on a grid of cells, ...

Lattice Boltzmann Method (LBM) is a novel numerical method for flows simulations. Compared with classic methods of Finite Difference Method, Finite Volume Method and Finite Element Method, LBM has numerous advantages, including inherent parallelization and simplicity of boundary condition treatment. The LBM usually has a constraint of incompressible fluid (Mach number less than 0.4). A variant ...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

The relation between the Lattice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of Navier–Stokes equations for incompressible fluid flow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compress...

The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to simulate anisotropic advection-diffusion processes. The governing differential equations of advective-diffusive systems are known to satisfy maximum principles, comparison principles, the non-negative constraint, and t...