No-slip boundary condition is a widely used boundary treatment method when dealing with free surface flows (Monaghan, 1994; Morris et al., 1997).
In this paper we propose a new consistent boundary treatment for this method, which is such that continuous integration-by-parts identities (including boundary contributions) are mimicked in a discrete sense.
The BDIM predictions are compared to analytic, experimental and previous numerical results confirming the properties, efficiency and efficacy of this new boundary treatment for Cartesian grid methods.
On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region.
Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.
The subsonic/supersonic composition of the outflow boundary requires a dual boundary treatment for well-posedness.
In this paper, we present a kind of second-order curved boundary treatments for the lattice Boltzmann method solving two-dimensional convection diffusion equations with general nonlinear Robin boundary conditions.
Therefore, this boundary method could be considered as a competitive alternative for boundary treatment in LBM simulations, especially for particulate and porous flows with large fluid solid interfacial areas.
In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces.
Boundary treatments for both types of numerical methods, and the resulting self-energy Σ for the NEGF formulism, representing the dissipative effects of device contacts on the transport, are derived using auxiliary Green's functions for the exterior of the quantum devices.
