Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 26 Nov 2022 09:57:04 GMT2022-11-26T09:57:04Z50241- Effect of boundary vorticity discretization on explicit stream-function vorticity calculationshttp://hdl.handle.net/10316/8221Title: Effect of boundary vorticity discretization on explicit stream-function vorticity calculations
Authors: Sousa, E.; Sobey, I. J.
Abstract: The numerical solution of the time-dependent Navier-Stokes equations in terms of the vorticity and a stream function is a well tested process to describe two-dimensional incompressible flows, both for fluid mixing applications and for studies in theoretical fluid mechanics. In this paper, we consider the interaction between the unsteady advection-diffusion equation for the vorticity, the Poisson equation linking vorticity and stream function and the approximation of the boundary vorticity, examining from a practical viewpoint, global iteration stability and error. Our results show that most schemes have very similar global stability constraints although there may be small stability gains from the choice of method to determine boundary vorticity. Concerning accuracy, for one model problem we observe that there were cases where the boundary vorticity discretization did not propagate to the interior, but for the usual cavity flow all the schemes tested had error close to second order. Copyright © 2005 John Wiley & Sons, Ltd.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/82212005-01-01T00:00:00Z
- Numerical approximation of a diffusive hyperbolic equationhttp://hdl.handle.net/10316/11195Title: Numerical approximation of a diffusive hyperbolic equation
Authors: Araújo, A.; Neves, C.; Sousa, E.
Abstract: In this work numerical methods for one-dimensional diffusion problems
are discussed. The differential equation considered, takes into account the variation
of the relaxation time of the mass flux and the existence of a potential field. Consequently,
according to which values of the relaxation parameter or the potential field
we assume, the equation can have properties similar to a hyperbolic equation or to
a parabolic equation. The numerical schemes consist of using an inverse Laplace
transform algorithm to remove the time-dependent terms in the governing equation
and boundary conditions. For the spatial discretisation, three different approaches
are discussed and we show their advantages and disadvantages according to which
values of the potential field and relaxation time parameters we choose.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111952009-01-01T00:00:00Z
- An alternating direction implicit method for a second-order hyperbolic diffusion equation with convectionhttp://hdl.handle.net/10316/45001Title: An alternating direction implicit method for a second-order hyperbolic diffusion equation with convection
Authors: Araújo, Adérito; Neves, Cidália; Sousa, Ercília
Abstract: A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computationally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the alternating direction method is analyzed using the energy method. Numerical results are presented to illustrate the performance in different cases.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/450012014-01-01T00:00:00Z
- Geometric Study of Surface Finishing of Selective Laser Melting Mouldshttp://hdl.handle.net/10316/44194Title: Geometric Study of Surface Finishing of Selective Laser Melting Moulds
Authors: Nhangumbe, M.; Gouveia, João; Sousa, Ercília; Belbut, M.; Mateus, A.
Abstract: Selective laser melting, which is based on the principle of material incremental manufacturing, has been recognised as a promising additive manufacturing technology. The principle of additive manufacturing lies in fabricating a part or an assembly of parts, layer by layer through a bottom to top approach. The technology is suited for creating geometrically complex components that can not possibly or feasibly be made by any other means. This technique has a weak point related to the surface finishing. Therefore, during the construction of layer by layer, there is a need to use techniques such as milling to remove material. This hybrid approach allows the fabrication of parts with internal complex structures and very good surface finishing. To plan and optimize the successive additive and subtractive phases, we need a quick tool to determine when the geometry of a piece is suitable for surface finishing by a 3 axes milling machine. This problem can be reduced to a layer by layer subproblem of approximately covering a slice of the object by circles of the diameter of the smallest drill available that can reach its depth. This reduction to the plane allows us to use a medial axis approach. The medial axis of a planar domain, defined as the set of centers of maximal circles contained in the domain, relates very closely to the notion of generalized Voronoi diagram, and has been proposed in several milling applications that involve motion planning. We propose to use it, and certain extensions of it, as a practical way of determining the best possible finishing quality at a slice. To that end we have to find which of the available construction strategies best suits our needs to determine exactly or approximately the medial axis of a polygon and its extensions.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/441942017-01-01T00:00:00Z
- Impact of mercury contamination on the population dynamics of Peringia ulvae (Gastropoda): Implications on metal transfer through the trophic webhttp://hdl.handle.net/10316/25761Title: Impact of mercury contamination on the population dynamics of Peringia ulvae (Gastropoda): Implications on metal transfer through the trophic web
Authors: Cardoso, P. G.; Sousa, E.; Matos, P.; Henriques, B.; Pereira, E.; Duarte, A. C.; Pardal, M. A.
Abstract: The effects of mercury contamination on the population structure and dynamics of the gastropod Peringia
ulvae (also known as Hydrobia ulvae) and its impact on the trophic web were assessed along a
mercury gradient in Ria de Aveiro (Portugal). The gastropod was revealed to be a tolerant species to the
contaminant, since the highest densities, biomasses and growth productivity values were recorded at the
intermediate contaminated area followed by the most contaminated one and finally the least contaminated
area. P. ulvae was however negatively affected by mercury in terms of growth and life span. So, in
the most contaminated area the population was characterised mainly by the presence of juveniles and
young individuals. The intermediate contaminated area showed a greater equilibrium in terms of groups’
proportion, being the adults the dominant set. The least contaminated area presented intermediate
values. P. ulvae life spans were shortest in the most contaminated area (7e8 mo), followed by the least
contaminated area (10e11 mo) and finally, the intermediate one (11e14 mo).
P. ulvae revealed to be an important vehicle of mercury transfer from sediments to the trophic web,
incorporating approximately 15 g of Hg, annually, in the inner area of the Laranjo Bay (0.6 Km2).
Therefore, despite P. ulvae being revealed to be not a good bio-indicator of mercury contamination, since
it did not suffer profound modifications in its structure and functioning, it is a crucial element in the
mercury biomagnification processes throughout the food web.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/257612013-01-01T00:00:00Z
- Optical flow with fractional order regularization: Variational model and solution methodhttp://hdl.handle.net/10316/43831Title: Optical flow with fractional order regularization: Variational model and solution method
Authors: Bardeji, Somayeh Gh.; Figueiredo, Isabel N.; Sousa, Ercília
Abstract: An optical flow variational model is proposed for a sequence of images defined on a domain in R^2. We introduce a regularization term given by L^1 the norm of a fractional differential operator. To solve the minimization problem we apply the split Bregman method. Extensive experimental results, with performance evaluation, are presented to demonstrate the effectiveness of the new model and method and to show that our algorithm performs favorably in comparison to another existing method. We also discuss the influence of the order α of the fractional operator in the estimation of the optical flow, for 0 ≤ ∝ ≤ 2. We observe that the values of α for which the method performs better depend on the geometry and texture complexity of the image. Some extensions of our algorithm are also discussed.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/438312017-01-01T00:00:00Z
- A numerical approach to study the Kramers equation for finite geometries: boundary conditions and potential fieldshttp://hdl.handle.net/10316/44993Title: A numerical approach to study the Kramers equation for finite geometries: boundary conditions and potential fields
Authors: Araújo, Adérito; Das, Amal K.; Sousa, Ercília
Abstract: The Kramers equation for the phase-space function, which models the dynamics of an underdamped Brownian particle, is the subject of our study. Numerical solutions of this equation for natural boundaries (unconfined geometries) have been well reported in the literature. But not much has been done on the Kramers equation for finite (confining) geometries which require a set of additional constraints imposed on the phase-space function at physical boundaries. In this paper we present numerical solutions for the Kramers equation with a variety of potential fields—namely constant, linear, harmonic and periodic—in the presence of fully absorbing and fully reflecting boundary conditions (BCs). The choice of the numerical method and its implementation take into consideration the type of BCs, in order to avoid the use of ghost points or artificial conditions. We study and assess the conditions under which the numerical method converges. Various aspects of the solutions for the phase-space function are presented with figures and discussed in detail.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/449932015-01-01T00:00:00Z
- Super-diffusive Transport Processes in Porous Mediahttp://hdl.handle.net/10316/44968Title: Super-diffusive Transport Processes in Porous Media
Authors: Sousa, Ercília
Abstract: The basic assumption of models for the transport of contaminants through soil is that the movements of solute particles are characterized by the Brownian motion. However, the complexity of pore space in natural porous media makes the hypothesis of Brownian motion far too restrictive in some situations. Therefore, alternative models have been proposed. One of the models, many times encountered in hydrology, is based in fractional differential equations, which is a one-dimensional fractional advection diffusion equation where the usual second-order derivative gives place to a fractional derivative of order α, with 1 < α ≤ 2. When a fractional derivative replaces the second-order derivative in a diffusion or dispersion model, it leads to anomalous diffusion, also called super-diffusion. We derive analytical solutions for the fractional advection diffusion equation with different initial and boundary conditions. Additionally, we analyze how the fractional parameter α affects the behavior of the solutions.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449682013-01-01T00:00:00Z
- A hybrid numerical method for a two-dimensional second order hyperbolic equationhttp://hdl.handle.net/10316/44962Title: A hybrid numerical method for a two-dimensional second order hyperbolic equation
Authors: Araújo, Adérito; Neves, Cidália; Sousa, Ercília
Abstract: Second order hyperbolic differential equations have been used to model many problems that appear related to heat conduction, mass diffusion and fluid dynamics. In this work a numerical method is presented to solve a two dimensional second order hyperbolic equation with convection terms. A hybrid numerical method is considered which consists of applying the Laplace transform in time and a finite volume discretization in space, where the shape functions associated with the finite volume method are chosen as the combination of hyperbolic functions. We present some numerical tests to show the efficiency of the numerical method.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/449622014-01-01T00:00:00Z
- Numerical solution for a non-Fickian diffusion in a periodic potentialhttp://hdl.handle.net/10316/45003Title: Numerical solution for a non-Fickian diffusion in a periodic potential
Authors: Araújo, Adérito; Das, Amal K.; Neves, Cidália; Sousa, Ercília
Abstract: Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider
a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/450032013-01-01T00:00:00Z
- Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusionhttp://hdl.handle.net/10316/37168Title: Numerical solution of a time-space fractional Fokker Planck equation with variable force field and diffusion
Authors: Pinto, Luís; Sousa, Ercília
Abstract: We present a numerical method to solve a time-space fractional Fokker-Planck equation with a spacetime
dependent force field F(x, t), and diffusion d(x, t). When the problem being modelled includes time
dependent coefficients, the time fractional operator, that typically appears on the right hand side of the
fractional equation, should not act on those coefficients and consequently the differential equation can not be
simplified using the standard technique of transferring the time fractional operator to the left hand side of the
equation. We take this into account when deriving the numerical method. Discussions on the unconditional
stability and accuracy of the method are presented, including results that show the order of convergence
is affected by the regularity of solutions. The numerical experiments confirm that the convergence of the
method is second order in time and space for sufficiently regular solutions and they also illustrate how the
order of convergence can depend on the regularity of the solutions. In this case, the rate of convergence can
be improved by considering a non-uniform mesh.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/371682017-01-01T00:00:00Z
- An explicit high order method for fractional advection diffusion equationshttp://hdl.handle.net/10316/27768Title: An explicit high order method for fractional advection diffusion equations
Authors: Sousa, Ercília
Abstract: We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1<α≤2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We study the convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/10316/277682014-12-01T00:00:00Z
- The controversial stability analysishttp://hdl.handle.net/10316/11447Title: The controversial stability analysis
Authors: Sousa, Ercília
Abstract: In this review we present different techniques for obtaining stability limits for a finite difference scheme––the forward-time and space-centered numerical scheme applied to the convection–diffusion equation. A survey of past attempts to state stability conditions for this scheme illustrates the difficulties in stability analysis that arise as soon as a scheme becomes more complex and illuminates the concepts of necessary and sufficient conditions for stability.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10316/114472002-01-01T00:00:00Z
- Stability Analysis of Difference Methods for Parabolic Initial Value Problemshttp://hdl.handle.net/10316/7735Title: Stability Analysis of Difference Methods for Parabolic Initial Value Problems
Authors: Sousa, Ercília
Abstract: Abstract A decomposition of the numerical solution can be defined by the normal mode representation, that generalizes further the spatial eigenmode decomposition of the von Neumann analysis by taking into account the boundary conditions which are not periodic. In this paper we present some new theoretical results on normal mode analysis for a linear and parabolic initial value problem. Furthermore we suggest an algorithm for the calculation of stability regions based on the normal mode theory.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/77352006-01-01T00:00:00Z
- Development of finite difference schemes near an inflow boundaryhttp://hdl.handle.net/10316/8215Title: Development of finite difference schemes near an inflow boundary
Authors: Sousa, E.
Abstract: Numerical schemes for a convection-diffusion problem defined on the whole real line have been derived by Morton and Sobey (IMA J. Numer. Anal. 1993; 13:141-160) using the exact evolution operator through one time step. In this paper we derive new numerical schemes by using the exact evolution operator for a convection-diffusion problem defined on the half-line. We obtain a third-order method that requires the use of a numerical boundary condition which is also derived using the same evolution operator. We determine whether there are advantages from the point of view of stability and accuracy in using these new schemes, when compared with similar methods obtained for the whole line. We conclude that the third-order scheme provides gains in terms of stability and although it does not improve the practical accuracy of existing methods faraway from the inflow boundary, it does improve the accuracy next to the inflow boundary. Copyright © 2006 John Wiley & Sons, Ltd.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/82152006-01-01T00:00:00Z
- Numerical stability of unsteady stream-function vorticity calculationshttp://hdl.handle.net/10316/8226Title: Numerical stability of unsteady stream-function vorticity calculations
Authors: Sousa, E.; Sobey, I. J.
Abstract: The stability of a numerical solution of the Navier-Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection-diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection-diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection-diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection-diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/82262003-01-01T00:00:00Z
- Application of the advection-dispersion equation to characterize the hydrodynamic regime in a submerged packed bed reactorhttp://hdl.handle.net/10316/11417Title: Application of the advection-dispersion equation to characterize the hydrodynamic regime in a submerged packed bed reactor
Authors: Albuquerque, António; Araújo, Adérito; Sousa, Ercília
Abstract: The hydraulic characteristics of a laboratory submerged packed bed, filled with a volcanic
stone, pozzuolana, have been experimentally investigated through tracer tests. Sets
of essays at flow rates from 1 to 2.5 l/h in clean conditions were performed. The results
showed a considerable amount of dispersion through the filter as the hydraulic loading was
changed, indicating a multiplicity of hydrodynamic states, approaching its behavior to plug
flow. An analytical solution for the advection-dispersion equation model have been developed
for a semi-infinite system and we have considered an appropriate physical boundary
condition. A numerical simulation using finite difference schemes is done taking into account
this particular boundary condition that changes according to the flow rates. Proper
formulation of boundary conditions for analysis of column displacements experiments in
the laboratory is critically important to the interpretation of observed data, as well as for
subsequent extrapolation of the experimental results to transport problems in the field.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114172004-01-01T00:00:00Z
- Effect of boundary vorticity discretisation on explicit stream-function vorticity calculationshttp://hdl.handle.net/10316/11416Title: Effect of boundary vorticity discretisation on explicit stream-function vorticity calculations
Authors: Sousa, Ercília; Sobey, Ian
Abstract: The numerical solution of the time dependent Navier-Stokes equations in terms of the vorticity and a stream function is a well tested process to describe two-dimensional incompressible flows, both for fluid mixing applications and for studies in theoretical fluid mechanics. In this paper, we consider the interaction between the unsteady advection-diffusion equation for the vorticity, the Poisson equation linking vorticity and stream function and the approximation of the boundary vorticity, examining from a practical viewpoint, global error and iteration stability. Our results show that most schemes have very similar global stability constraints although there may be small stability gains from the choice of method to determine boundary vorticity
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114162004-01-01T00:00:00Z
- Insights on a sign-preserving numerical method for the advection-diffusion equationhttp://hdl.handle.net/10316/11266Title: Insights on a sign-preserving numerical method for the advection-diffusion equation
Authors: Sousa, Ercília
Abstract: In this paper we explore theoretically and numerically the application
of the advection transport algorithm introduced by Smolarkiewicz to the one
dimensional unsteady advection diffusion equation. The scheme consists of a sequence
of upwind iterations, where the initial iteration is the first order accurate
upwind scheme, while the subsequent iterations are designed to compensate for
the truncation error of preceding step. Two versions of the method are discussed.
One, the classical version of the method, regards the second order terms of the
truncation error and the other considers additionally the third order terms. Stability
and convergence are discussed and the theoretical considerations are illustrated
through numerical tests. The numerical tests will also indicate in which situations
is advantageous to use the numerical methods presented.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112662008-01-01T00:00:00Z
- Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a numerical solutionhttp://hdl.handle.net/10316/11259Title: Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a numerical solution
Authors: Araújo, Adérito; Sousa, Ercília; Albuquerque, António
Abstract: We present a numerical solution for the dead zone model which describes
the solute transport in a subsurface and horizontal flow constructed wetland.
This model is a system of two mass balance equations for two conceptual areas: the
main channel and the storage zone. We use finite difference schemes to determine
the numerical solution of the system and we study its convergence by presenting
properties related to the stability and accuracy of the schemes.
Concerning the experimental results, the magnitude of the longitudinal dispersion
and the extension of dead volumes is estimated for clean conditions and after a
certain operating period under organic loading conditions. The results showed a
considerable amount of longitudinal dispersion through the bed, which was very
strong near the feeding point, indicating the occurrence of mixing and significant
presence of dead zones and short-circuiting.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112592008-01-01T00:00:00Z
- Finite difference approximations for a fractional advection diffusion problemhttp://hdl.handle.net/10316/11247Title: Finite difference approximations for a fractional advection diffusion problem
Authors: Sousa, Ercília
Abstract: The use of the conventional advection diffusion equation in many physical
situations has been questioned by many investigators in recent years and alternative
diffusion models have been proposed. Fractional space derivatives are used
to model anomalous diffusion or dispersion, where a particle plume spreads at a
rate inconsistent with the classical Brownian motion model. When a fractional derivative
replaces the second derivative in a diffusion or dispersion model, it leads
to enhanced diffusion, also called superdiffusion. We consider a one dimensional
advection-diffusion model, where the usual second-order derivative gives place to a
fractional derivative of order , with 1 < ≤ 2. We derive explicit finite difference
schemes which can be seen as generalizations of already existing schemes in the
literature for the advection-diffusion equation. We present the order of accuracy of
the schemes and in order to show its convergence we prove they are stable under
certain conditions. In the end we present a test problem.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112472008-01-01T00:00:00Z
- On the edge of stability analysishttp://hdl.handle.net/10316/11302Title: On the edge of stability analysis
Authors: Sousa, Ercília
Abstract: The application of high order methods to solve problems with physical
boundary conditions in many cases implies to consider a different numerical
approximation on the discrete points near the boundary. The choice of these approximations,
called the numerical boundary conditions, influence most of the times
the stability of the numerical method.
Some theoretical analysis for stability, such as the von Neumann analysis, do
not take into account the influence of the numerical representation of the boundary
conditions on the overall stability of the scheme. The spectral analysis considers
the eigenvalues of the matrix iteration of the scheme and although they reflect
some of the influence of numerical boundary conditions on the stability, many times
eigenvalues fail to capture the transient effects in time-dependent partial differential
equations.
The Lax analysis does provide information on the influence of numerical boundary
conditions although in practical situations it is generally not easy to derive the
corresponding stability conditions. In this paper we present properties that relates
the von Neumann analysis, the spectral analysis and the Lax analysis and show
under which circumstances the von Neumann analysis together with the spectral
analysis provides sufficient conditions to achieve Lax stability.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113022007-01-01T00:00:00Z
- Numerical approximation for the fractional diffusion equation via splineshttp://hdl.handle.net/10316/11172Title: Numerical approximation for the fractional diffusion equation via splines
Authors: Sousa, Ercília
Abstract: A one dimensional fractional diffusion model is considered, where the
usual second-order derivative gives place to a fractional derivative of order , with
1 < ≤ 2. We consider the Caputo derivative as the space derivative, which is a
form of representing the fractional derivative by an integral operator. The numerical
solution is derived using Crank-Nicolson method in time combined with a spline
approximation for the Caputo derivative in space. Consistency and convergence of
the method is examined and numerical results are presented.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111722009-01-01T00:00:00Z
- High-order methods and numerical boundary conditionshttp://hdl.handle.net/10316/4599Title: High-order methods and numerical boundary conditions
Authors: Sousa, Ercília
Abstract: In this paper we present high-order difference schemes for convection diffusion problems. When we apply high-order numerical methods to problems where physical boundary conditions are not periodic there is a need to choose adequate numerical boundary conditions in order to preserve the high-order accuracy. Next to the boundary we do not usually have enough discrete points to apply the high-order scheme and therefore at these nodes we must consider different approximations, named the numerical boundary conditions.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/45992007-01-01T00:00:00Z