A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

Triangle Evolution-A Hybrid Heuristic for Global Optimization

Abstract This paper presents a hybrid heuristic{triangle evolution (TE) for global optimization. It is a real coded evolutionary algorithm. As in di®erential evolution (DE), TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is di®erent. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and e±cient for global optimization problems with continuous variables. Moreover, it requires only one (explicit) control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.

A comparative assessment of the methods of control of water hyacinth infestation with regards to fish production

Water hyacinth (Eichhornia crassipes) has been subject of three control methods since its arrival into the Nigerian freshwater lagoon system in 1984 - mechanical, chemical and biological. An assessment of these three methods seems to suggest that mechanical and chemical control methods, both of which being costly, must be applied either solely or integrated to combat the present level of considerable infestation in Nigeria. The biological control methods are advisable for slow, sustained control and can only cope with low levels of infestation. It is thus concluded that the preliminary control method should be mechanical or chemical to effectively abate the nuisance plant, followed by biological control once infestation levels have been sufficiently reduced

The effect of traditional handling, processing and storage methods on the quality of dried fish in small scale fisheries in Nigeria

Most of the fish marketed throughout Nigeria are in either smoked or dried form. The technological requirement for other forms of preservation like chilling and freezing cannot be afforded by the small scale fisher folk. Considerable quantities of fish processed for distant consumer markets are lost at handling, processing, storage and marketing stages. Significant losses occur through infestation by mites, insects, fungal infestation and fragmentation during transportation. This paper attempts to describe the effect of these losses on fish quality and suggests methods of protecting fish from agents of deterioration

A preliminary investigation into the effect of different storage methods on the keeping quality of smoked Oreochromis niloticus

The study was carried out to asses the nutritional qualities of smoked O. niloticus and to discover the best methods of storage to minimize spoilage and infestation of smoked fish. Result showed that the protein contents in A and D decreased while the protein contents of b and C increased. The lipid content increased only in A while it decreased in B-C and D. The moisture content generally increased over the period of storage and there was an increase in ash content only in C while it decreased in A, B and D. The samples packed in polythene bag suffered about 35% mould infection and a few were attached by rodents with some fouling. Samples packed in jute bag were in good condition but were slightly attached by insect. All samples packed in carton and basket were still in good state but there were insect attack in those packed in carton

Numerical methods for ill-posed, linear problems

A means of assessing the effectiveness of methods used in the numerical solution of various linear ill-posed problems is outlined. Two methods: Tikhonov' s method of regularization and the quasireversibility method of Lattès and Lions are appraised from this point of view.

In the former method, Tikhonov provides a useful means for incorporating a constraint into numerical algorithms. The analysis suggests that the approach can be generalized to embody constraints other than those employed by Tikhonov. This is effected and the general "T-method" is the result.

A T-method is used on an extended version of the backwards heat equation with spatially variable coefficients. Numerical computations based upon it are performed.

The statistical method developed by Franklin is shown to have an interpretation as a T-method. This interpretation, although somewhat loose, does explain some empirical convergence properties which are difficult to pin down via a purely statistical argument.

Diagonal forms, linear algebraic methods and Ramsey-type problems

This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.