Related papers: On the relationship between the diffuse reflection…
Systems of N = 1, 2, . . . first-order hyperbolic conservation laws feature N undamped waves propagating at finite speeds. On their own hand, multi-step Finite Difference and lattice Boltzmann schemes with q = N + 1, N + 2, . . . unknowns…
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…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
Numerical analysis of unconfined flow over an obstacle has always been challenging in computational fluid dynamics due to the truncation of the computational domain while replicating the real-life flows and the application of the boundary…
Discrepancies between theory and recent qBounce data have prompted renewed scrutiny of how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity. We apply the theory of self-adjoint extensions…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…
Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for…
This paper concerns the diffusive limit of the time evolutionary Boltzmann equation in the half space $\mathbb{T}^2\times\mathbb{R}^+$ for a small Knudsen number $\varepsilon>0$. For boundary conditions in the normal direction, it involves…
The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice…
We prove the acoustic limit from the Boltzmann equation with hard sphere collisions and the Maxwell reflection boundary condition. Our construction of solutions include the interior fluid part and Knudsen-viscous coupled boundary layers.…
We consider in this paper the mathematical and numerical modelling of reflective boundary conditions (BC) associated to Boltzmann - Poisson systems, including diffusive reflection in addition to specularity, in the context of electron…
We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent…
We study overdamped stochastic dynamics confined by hard reflecting boundaries and show that the combination of boundary geometry and an anisotropic diffusion tensor generically generates directed motion. At the level of individual…
In this paper, we study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures $\theta_0$ and $\theta_1$. This problem was studied by Esposito et al [13,14] where…
This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior in the case that the initial data is close enough to a…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…