Related papers: A Boltzmann scheme with physically relevant discre…
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint…
Fluid dynamic equations are valid in their respective modeling scales. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. In order to study multiscale flow evolution…
In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Through modeling…
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the…
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the…
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM…
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our…
In this work, we present a hierarchical domain decomposition method for the multi-scale Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in \cite{lev-mor-nad-1998}. This…
A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged…
Although Lattice Boltzmann Method (LBM) is relatively straightforward, it demands a well-crafted framework to handle the complex partial differential equations involved in multiphase flow simulations. For the first time to our knowledge,…
The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…
A theoretical formulation of lattice Boltzmann models on a general curvilinear coordinate system is presented. It is based on a volumetric representation so that mass and momentum are exactly conserved as in the conventional lattice…
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to…
We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two-…
In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism.…
It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the first flux reconstruction method for high-order Boltzmann…