This paper is about the construction of a BGK Navier–Stokes (BGK-NS) solver in the discontinuous Galerkin (DG) framework. Since in the DG formulation the conservative variables and their slopes can be updated simultaneously, the flow evolution in each element involves only the flow variables in the nearest neighboring cells. Instead of using the semidiscrete approach in the Runge–Kutta disconti...

Gas-kinetic BGK scheme with symmetric limited positive (SLIP) method, which was developed by Xu and Jameson, is modified and extended to three-dimensional compressible flows for the first time. BGK scheme is an approximate Riemann solver that uses collisional Boltzmann equation as the governing equation for flow evolutions. To demonstrate the robustness and accuracy of the scheme, it is applied...

In this work a new class of numerical methods for the BGK model of kinetic equations is introduced. The schemes proposed are implicit with respect to the distribution function, while the macroscopic moments are evolved explicitly. In this fashion, the stability condition on the time step coincides with a macroscopic CFL, evaluated using estimated values for the macroscopic velocity and sound sp...

We introduce a general framework for kinetic BGK models. We assume to be given a system of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK models that lead to this system in the hydrodynamic limit, and that are compatible with the whole family of entropies. This is obtained by a new characterization of maxwellians as entropy minimizers, that can take int...

Over the last decades, the development of high dimensional large-scale imaging devices increases the demand of fast and accurate image processing techniques. Due to its intrinsic advantages which allows to handle complex shapes and topological changes, the level set method (LSM) is an promising technique but is computational expensive. As a fast alternative approach for solving the level set eq...

In this article, we perform a numerical stability and convergence analysis of the constrained runs initialization scheme for a lattice Boltzmann model. Gear and Kevrekidis developed this scheme in the context of coarse-grained equation-free computing. Given the macroscopic initial fields, we study the mapping of these variables to the higher-dimensional space of lattice Boltzmann variables. The...

Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. Phys. Conf. Ser., 1035 (2018), 012005] to overcome drawbacks of the Anderson--Witting Marle model. In this paper, we prove unique existence asymptotic behavior classical solutions when initial data is sufficiently close global equilibrium.

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. The model is derivable from a continuous-time Boltzmann-BGK equation in the presence of an intercomponent...

<p style='text-indent:20px;'>In this paper, we address the Cauchy problem for relativistic BGK model proposed by Anderson and Witting massless particles in Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive explicit form of Jüttner distribution FLRW spacetime, together with a set nonlinear relations that leads to conservation laws particle number, momentum, energy both ...