On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

Finite element solution of Navier Stokes equations adapted to a priori error estimates

The paper is based on qualitative properties of the solution of the Navier-Stokes equations for incompressible fluid, and on properties of their finite element solution. In problems with corner-like singularities (e.g. on the well-known L-shaped domain) usually some adaptive strategy is used. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results.

Solution oriented partnerships - A new business model for integrating global-production efficiencies with sustainability

A business model for integrating global-production efficiencies with sustainability is discussed. Two trends that emulate some of the aspects of the wealthy are the increasing willingness of many to pay extra for customization such as clothes, of kitchens and the increasing acceptance of purchasing a service as a product substitute. Two final trends that are also based in the attitudes of people is an increased awareness of the value of local culture and an increased concern with issues of sustainability. The results show that the goal congruence between for-profit and not-for-profit organizations puts emphasis on value and belief of the organization.

Interfacial recognition of human prostate-specific antigen by immobilized monoclonal antibody: effects of solution conditions and surface chemistry.

The specific recognition between monoclonal antibody (anti-human prostate-specific antigen, anti-hPSA) and its antigen (human prostate-specific antigen, hPSA) has promising applications in prostate cancer diagnostics and other biosensor applications. However, because of steric constraints associated with interfacial packing and molecular orientations, the binding efficiency is often very low. In this study, spectroscopic ellipsometry and neutron reflection have been used to investigate how solution pH, salt concentration and surface chemistry affect antibody adsorption and subsequent antigen binding. The adsorbed amount of antibody was found to vary with pH and the maximum adsorption occurred between pH 5 and 6, close to the isoelectric point of the antibody. By contrast, the highest antigen binding efficiency occurred close to the neutral pH. Increasing the ionic strength reduced antibody adsorbed amount at the silica-water interface but had little effect on antigen binding. Further studies of antibody adsorption on hydrophobic C8 (octyltrimethoxysilane) surface and chemical attachment of antibody on (3-mercaptopropyl)trimethoxysilane/4-maleimidobutyric acid N-hydroxysuccinimide ester-modified surface have also been undertaken. It was found that on all surfaces studied, the antibody predominantly adopted the 'flat on' orientation, and antigen-binding capabilities were comparable. The results indicate that antibody immobilization via appropriate physical adsorption can replace elaborate interfacial molecular engineering involving complex covalent attachments.