Diffusion analogy and shock capturing for solving aerodynamic equations

Improving the resolution of the shock is one of the most important subjects in computational aerodynamics. In this paper the behaviour of the solutions near the shock is discussed and the reason of the oscillation production is investigated heuristically. According to the differential approximation of the difference scheme the so-called diffusion analogy equation and the diffusion analogy coefficient are defined. Four methods for improving the resolution of the shock are presented using the concept of diffusion analogy.

Diffusion sliding rate in the binary gaseous mixture

radiation incident upon a test cell filled with gaseous SF6 has

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Surface-Bound Selectin-Ligand Binding Is Regulated By Carrier Diffusion

Two-dimensional (2D) kinetics of receptor-ligand interactions governs cell adhesion in many biological processes. While the dissociation kinetics of receptor-ligand bond is extensively investigated, the association kinetics has much less been quantified. Recently receptor-ligand interactions between two surfaces were investigated using a thermal fluctuation assay upon biomembrane force probe technique (Chen et al. in Biophys J 94:694-701, 2008). The regulating factors on association kinetics, however, are not well characterized. Here we developed an alternative thermal fluctuation assay using optical trap technique, which enables to visualize consecutive binding-unbinding transition and to quantify the impact of microbead diffusion on receptor-ligand binding. Three selectin constructs (sLs, sPs, and PLE) and their ligand P-selectin glycoprotein ligand 1 were used to conduct the measurements. It was indicated that bond formation was reduced by enhancing the diffusivity of selectin-coupled carrier, suggesting that carrier diffusion is crucial to determine receptor-ligand binding. It was also found that 2D forward rate predicted upon first-order kinetics was in the order of sPs > sLs > PLE and bond formation was history-dependent. These results further the understandings in regulating association kinetics of surface-bound receptor-ligand interactions.

A Trabecular Bone Explant Model of Osteocyte–Osteoblast Co-Culture for Bone Mechanobiology

The osteocyte network is recognized as the major mechanical sensor in the bone remodeling process, and osteocyte-osteoblast communication acts as an important mediator in the coordination of bone formation and turnover. In this study, we developed a novel 3D trabecular bone explant co-culture model that allows live osteocytes situated in their native extracellular matrix environment to be interconnected with seeded osteoblasts on the bone surface. Using a low-level medium perfusion system, the viability of in situ osteocytes in bone explants was maintained for up to 4 weeks, and functional gap junction intercellular communication (GJIC) was successfully established between osteocytes and seeded primary osteoblasts. Using this novel co-culture model, the effects of dynamic deformational loading, GJIC, and prostaglandin E-2 (PGE(2)) release on functional bone adaptation were further investigated. The results showed that dynamical deformational loading can significantly increase the PGE(2) release by bone cells, bone formation, and the apparent elastic modulus of bone explants. However, the inhibition of gap junctions or the PGE(2) pathway dramatically attenuated the effects of mechanical loading. This 3D trabecular bone explant co-culture model has great potential to fill in the critical gap in knowledge regarding the role of osteocytes as a mechano-sensor and how osteocytes transmit signals to regulate osteoblasts function and skeletal integrity as reflected in its mechanical properties.

The effect of diffusion and overhangs/vacancies on the microstructure of zig-zag thin film

Basing on some growth models of thin film, we have investigated the growth mechanism of glancing angle deposition (GLAD) film. The simulation verifies that the overhangs/vacancies also contribute to the columnar growth as well as the self-shadowing effect for GLAD thin film. Besides, we have studied the effect of the deposition rate, surface and bulk diffusions on the microstructure of thin film using the time-dependent Monte Carlo method. The results show that the surface and bulk diffusions can significantly enhance the packing density of thin film in GLAD growth, and the increase of the deposition rate induce the moderate decrease of the packing density. (c) 2006 Elsevier B.V. All rights reserved.