Encontrados 10 documentos, a visualizar página 1 de 1
Numerical approximation for the fractional diffusion equation via splines
Sousa, ErcíliaA 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 approximatio...
Finite difference approximations for a fractional advection diffusion problem
Sousa, ErcíliaThe 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 th...
Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a ...
Araújo, Adérito; Sousa, Ercília; Albuquerque, AntónioWe 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 t...
Insights on a sign-preserving numerical method for the advection-diffusion equa...
Sousa, ErcíliaIn 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 pr...
High-order methods and numerical boundary conditions
Sousa, ErcíliaIn 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 ther...
On the edge of stability analysis
Sousa, ErcíliaThe 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 an...
Stability Analysis of Difference Methods for Parabolic Initial Value Problems
Sousa, ErcíliaAbstract 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 a...
Effect of boundary vorticity discretisation on explicit stream-function vortici...
Sousa, Ercília; Sobey, IanThe 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 linkin...
Application of the advection-dispersion equation to characterize the hydrodynam...
Albuquerque, António; Araújo, Adérito; Sousa, ErcíliaThe 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,...
The controversial stability analysis
Sousa, ErcíliaIn 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 o...
| Financiadores do RCAAP | |||||||
|
|
|
|
|
|
||