New Theory of Hybrid-Upwind Technique and Discrete Del Operator for Finite-Element Method

In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamline-upwind weighting function. Furthermore, we define a discrete del operator for the reduction of memory storage in the computer. As a result, we achieve simplicity of formulation and high-speed calculation of the finite-element method.     

Short Communication Finite Element Analysis of Visco-elastic Flow Under High Shear Rate Using the GSMAC-method

In the present work, we carry out a finite element analysis of visco-elastic flows for the multi-mode Giesekus model at high shear rales flow. We have already proposed a new numerical scheme suitable for the analysis of visco-elastic fluids in the previous paper. It is mainly composed of two parts: the MUSCL (Monotone Upstream-centered Scheme for Conservation Law)-TVD (Total Variation Diminishing) for the numerical analysis of the constitutive equation and the GSMAC (Generalized Simplified Maker and Cell)-FEM (Finite Element Method) for the momentum equation. We apply the new scheme for the flows through the contraction plane for the multi-mode Giesekus model that considers eight relaxation modes. It shows suitable matching with experimental data at low shear rates, and we confirm that the results are stable at high shear rates.     

Improved Method of Molecular Imprinting of Cyclodextrin on Silica-gel Surface for the Preparation of Stable Stationary HPLC Phase

By using N-(3-triethoxysilyl)propylacrylamide (TPAAm), vinyl groups were introduced onto the surface of silica-gel. On the surface of this silica-gel, β-CyD was molecularly imprinted by using a redox initiator, and the composite was used as stationary phase of high performance liquid chromatography (HPLC). The pump pressure was sufficiently low and did not increase even after continuous elution for 24 h. In order to prepare still more stable columns, a new polymerization process was developed. There, the redox initiator was first mixed with the surface-modified silica-gel and then vinylated β-CyD, crosslinker, and the template were added. This modification promoted the immobilization of β-CyD copolymer to the silica-gel, resulting in still lower pump pressure. Concurrently, the imprinting efficiency was increased in comparison with previous method where the redox initiator was directly added to the mixture of the β-CyD–template complex, crosslinker, and surface-modified silica-gel. The molecularly imprinted β-CyD column, prepared by this new method, efficiently discriminated the enantiomers of N-benzyloxycarbonyltyrosine.     

Application of the GSMAC-CIP Method to Incompressible Navier-Stokes Equations at High Reynolds Numbers

The conventional shape function for the finite-element method (FEM) is linear, and it is thus inadequate for analyzing numerically complex flows at high Reynolds numbers. In this study, we propose a new scheme, GSMAC-CIP, using the third-order shape function, which requires continuity of the value of the function and its first space derivative in the whole space and is formulated by a finite element method for the cubic interpolated pseudo-particle (CIP) method. We verified the effectiveness of this new scheme by analyzing the forced-driven convection in a square cavity at Re = 1000, 5000 and 10000. The numerical results obtained by the present scheme are compared with those of GSMAC-FEM using coarser meshes, and it is shown that the present scheme is superior to GSMAC-FEM in terms of space accuracy. Moreover, it is shown that the numerical results obtained by the present scheme using fine meshes were in precise agreement with those obtained by Ghia et al.