Search results for "Boundary value problem"
showing 10 items of 551 documents
Thermoconvective instabilities in an inclined porous channel heated from below
2011
Abstract The thermoconvective instability in an inclined rectangular channel filled with a fluid saturated porous medium and heated from below with a uniform flux is investigated. A stationary parallel buoyant flow with a linear temperature change in the transverse direction is considered. The linear stability to transverse and longitudinal roll disturbances of this basic state is examined. The thermoconvective instability onset of transverse rolls occurs when the Darcy–Rayleigh number exceeds a critical value, that increases with the inclination angle. The critical Darcy–Rayleigh number is discontinuous at the inclination angle 23.4749° above the horizontal. It is shown that, when the incl…
Resonant Tunneling in 2D-Waveguides with Several Resonators
2021
In this chapter, we consider a two-dimensional waveguide that coincides with a strip having \(n+1\) narrows of small diameter \(\varepsilon \). All narrows are of the same shape and are spaced from each other by equal distances. Parts of the waveguide between two neighboring narrows play the role of resonators. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation in the waveguide. Near a simple eigenvalue of the closed resonator there are n resonant peaks of height close to 1. We let \(\varepsilon \rightarrow 0\) and obtain asymptotic formulas for the resonant energies and for the widths of the resonant peaks at their half-height. Th…
Convergence of Boobnov-Galerkin Method Exemplified
2004
In this Note, Boobnov–Galerkin’s method is proved to converge to an exact solution for an applied mechanics problem. We address in detail the interrelation of Boobnov–Galerkin method and the exact solution in the beam deflection problems. Namely, we show the coincidence of these two methods for clamped–clamped boundary conditions, using an alternative set of functions proposed by Filonenko-Borodich.12 Received 25 February 2003; accepted for publication 13 March 2004. Copyright c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to th…
Implicit-explicit and explicit projection schemes for the unsteady incompressible Navier–Stokes equations using a high-order dG method
2017
Abstract A modified version of the projection scheme [19] is proposed, which does not show a lower limit for the time step in contrast to the limits of stability observed numerically for some projection type schemes. An advantage of the proposed scheme is that the right-hand side of the Poisson equation for the pressure is independent of the time step. An explicit version of the current scheme is also provided besides the implicit-explicit one. For the implicit-explicit version, we retain divergence of the viscous terms on the right-hand side of the Poisson equation in order to achieve a higher accuracy for low Reynolds number flows. In this way, we also ensure that the Poisson equation wit…
Localized forms of the LBB condition and a posteriori estimates for incompressible media problems
2018
Abstract The inf–sup (or LBB) condition plays a crucial role in analysis of viscous flow problems and other problems related to incompressible media. In this paper, we deduce localized forms of this condition that contain a collection of local constants associated with subdomains instead of one global constant for the whole domain. Localized forms of the LBB inequality imply estimates of the distance to the set of divergence free fields. We use them and deduce fully computable bounds of the distance between approximate and exact solutions of boundary value problems arising in the theory of viscous incompressible fluids. The estimates are valid for approximations, which satisfy the incompres…
Inflow/outflow pressure boundary conditions for smoothed particle hydrodynamics simulations of incompressible flows
2017
Abstract Open Boundary treatment is a well-known issue in the Smoothed Particle Hydrodynamics (SPH) method, mainly when the truly Incompressible (ISPH) approach is employed. In the paper a novel method is proposed to set pressure boundary conditions in the computational domain inlets and outlets, without requiring the velocity profile assignment. The new technique allows to treat in the same way inflow and outflow sections, effectively dealing with the release of new particles at inlets and the deactivation of the ones leaving the domain through the outlets. Several 3D numerical tests, both in the laminar and turbulent regimes, are carried out to validate the proposed numerical scheme consi…
Infinitely many solutions for a mixed boundary value problem
2010
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions
2019
In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
Explicit closed form solutions of boundary value problems for systems of difference equations
1990
In this paper boundary value problems for systems of difference equations of the type , where A j ∈ C p×p and bn y j+n ∈ C p , for 0≤j≤k − 1, are studied from an algebraic point of view. Existence conditions and closed form solutions are given in terms of co-solutions of the algebraic matrix equation .
Simplified Model to Predict Runoff Generation Time for Well-Drained and Vegetated Soils
2016
The study of generation process of subsurface stormflow, typical of well-drained and high permeable soils, can be theoretically carried out by applying the continuity and the motion equations with the appropriate boundary conditions. However, difficulties and uncertainness on determining soil hydraulic properties and soil physics heterogeneities let this way not always feasible. In a different way, processes dynamic can be derived by the local scale through a coarse graining procedure, allowing to preserve medium motion character, while hydraulic fluctuation of the motion are lost. Following an approach as this, in this paper a simplified model to predict the runoff generation time, the so-…