Alice Lieu

Bio: Alice Lieu is an academic researcher from University of Southampton. The author has contributed to research in topics: Finite element method & Helmholtz free energy. The author has an hindex of 2, co-authored 4 publications receiving 40 citations.

How Heterogeneous Pore Scale Distributions of Wettability Affect Infiltration into Porous Media

Abstract: Wettability is an important parameter that significantly determines hydrology in porous media, and it especially controls the flow of water across the rhizosphere—the soil-plant interface. However, the influence of spatially heterogeneous distributions on the soil particles surfaces is scarcely known. Therefore, this study investigates the influence of spatially heterogeneous wettability distributions on infiltration into porous media. For this purpose, we utilize a two-phase flow model based on Lattice-Boltzmann to numerically simulate the infiltration in porous media with a simplified geometry and for various selected heterogeneous wettability coatings. Additionally, we simulated the rewetting of the dry rhizosphere of a sandy soil where dry hydrophobic mucilage depositions on the particle surface are represented via a locally increased contact angle. In particular, we can show that hydraulic dynamics and water repellency are determined by the specific location of wettability patterns within the pore space. When present at certain locations, tiny hydrophobic depositions can cause water repellency in an otherwise well-wettable soil. In this case, averaged, effective contact angle parameterizations such as the Cassie equation are unsuitable. At critical conditions, when the rhizosphere limits root water uptake, consideration of the specific microscale locations of exudate depositions may improve models of root water uptake.

A performance study of high-order finite elements and wave-based discontinuous Galerkin methods for a convected Helmholtz problem

Abstract: The finite element method (FEM) remains one of the most established computational method used in industry to predict acoustic wave propagation However, the use of standard FEM is in practice limited to low frequencies because it suffers from large dispersion errors when solving short wave problems (also called pollution effect) Various methods have been developed to circumvent this issue and we compare two numerical methods for convected Helmholtz problems The methods chosen for this study are the polynomial high-order FEM and the wave-based Discontinuous Galerkin Method (DGM) The polynomial method takes advantage of the superior approximation properties of the Lobatto shape functions compared to the conventional Lagrange basis The wave-based DGM is part of the physics-based methods which include a priori knowledge about the local behaviour of the solution into the numerical model Previous studies have shown that both methods can control of the pollution effect Common belief is that compared to polynomial methods, physics-based methods can provide a significant improvement in performance, at the expense of a deterioration of the conditioning However, the results presented in this paper indicate that the differences in accuracy, efficiency and conditioning between the two approaches are more nuanced than generally assumed

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Schwarz Alternating Method

Abstract: A discrete technique of the Schwarz alternating method is presented in this last chapter, to combine the Ritz-Galerkin and finite element methods. This technique is well suited for solving singularity problems in parallel, and requires a little more computation for large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, will be studied. Also a balance strategy will be proposed to couple the iteration number with the element size used in the FEM. For the crack-infinity problem of singularity the total CPU time by the technique in this chapter is much less than that by the nonconforming combination in Chapter 12.