Search results for "Boundary value problem"
showing 10 items of 551 documents
A new technique for observationally derived boundary conditions for space weather
2018
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 647214). D.H.M. would like to thank STFC and the Leverhulme Trust for their financial support. ARY was supported by STFC consortium grant ST/N000781/1 to the universities of Dundee and Durham. Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficie…
Implementation of pressure reduction valves in a dynamic water distribution numerical model to control the inequality in water supply
2013
The analysis of water distribution networks has to take into account the variability of users' water demand and the variability of network boundary conditions. In complex systems, e.g. those characterized by the presence of local private tanks and intermittent distribution, this variability suggests the use of dynamic models that are able to evaluate the rapid variability of pressures and flows in the network. The dynamic behavior of the network also affects the performance of valves that are used for controlling the network. Pressure reduction valves (PRVs) are used for controlling pressure and reducing leakages. Highly variable demands can produce significant fluctuation of the PRV set po…
Trial Methods for Nonlinear Bernoulli Problem
1997
In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.
Phase separation versus wetting: A mean field theory for symmetrical polymer mixtures confined between selectively attractive walls
1996
Partially compatible symmetrical (N A # N B = N) binary mixtures of linear flexible polymers (A, B) are considered in the presence of two equivalent walls a distance D apart, assuming that both walls preferentially adsorb the same component. Using a Flory-Huggins type mean field approach analogous to previous work studying wetting phenomena in the semi-infinite version of this model, where D → ∞, it is shown that a single phase transition occurs in this thin film geometry, namely a phase separation between an A-rich and a B-rich phase (both phases include the bulk of the film). The coexistence curve is shifted to smaller values of the inverse Flory-Huggins parameter x -1 with decreasing D, …
Analysis of the Characteristics in the Meudon Constrained Evolution Scheme
2007
A first analysis of the characteristics associated with the evolving modes in the constraint evolution scheme proposed by the Meudon group in 2004 is presented. The system is written in a first-order hyperbolic form and a so-called generalized Dirac gauge is considered. Applications to inner boundary conditions in an excised approach to black hole evolutions are discussed.
Wave propagation in 1D elastic solids in presence of long-range central interactions
2011
Abstract In this paper wave propagation in non-local elastic solids is examined in the framework of the mechanically based non-local elasticity theory established by the author in previous papers. It is shown that such a model coincides with the well-known Kroner–Eringen integral model of non-local elasticity in unbounded domains. The appeal of the proposed model is that the mechanical boundary conditions may easily be imposed because the applied pressure at the boundaries of the solid must be equilibrated by the Cauchy stress. In fact, the long-range forces between different volume elements are modelled, in the body domain, as central body forces applied to the interacting elements. It is …
Variational Aspects of the Physically-Based Approach to 3D Non-Local Continuum Mechanics
2010
This paper deals with the generalization to three-dimensional elasticity of the physically-based approach to non-local mechanics, recently proposed by the authors in one-dimensional case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range central forces exerted by non-adjacent elements. Specifically, the long-range forces are modeled as central body forces depending on the relative displacements between the centroids of the volume elements, measured along the line connecting the centroids. Furthermore, the long-range forces are assumed to be proportional to a proper, material-dependent, distance-decay…
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory
2009
In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments. At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization procedure suggested by the underlying mechanical model itself…
Mechanically-based approach to non-local elasticity: Variational principles
2010
Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…
Stress gradient versus strain gradient constitutive models within elasticity
2014
Abstract A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Helling…