Related papers: Generating boundary conditions for a Boussinesq sy…
We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a…
A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class…
We address the issue of point value reconstructions from cell averages in the context of third order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques known in the…
Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a…
We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\'enard…
We address the long-time behavior of the 2D Boussinesq system, which consists of the incompressible Navier-Stokes equations driven by a non-diffusive density. We construct globally persistent solutions on a smooth bounded domain, when the…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
The imposition of inhomogeneous Dirichlet (essential) boundary conditions is a fundamental challenge in the application of Galerkin-type methods based on non-interpolatory functions, i.e., functions which do not possess the Kronecker delta…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in…
In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly…
This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…
We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform…
We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. Such conditions are typical of the boundary layers…
Imposition of free slip boundary conditions in science and engineering simulations presents a challenge when the simulation domain is non-trivial. Inspired by recent progress in symbolic computation of discontinuous Galerkin finite element…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
We investigate the nonlinear stability problem for the two-dimensional Boussinesq system around the Poiseuille flow in a finite channel. The system has the characteristic of Navier-slip boundary condition for the velocity and Dirichlet…
Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task, both in developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional…
We consider the generation of samples of a mean-zero Gaussian random field with Mat\'ern covariance function. Every sample requires the solution of a differential equation with Gaussian white noise forcing, formulated on a bounded…