Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization of an Algerian diatomite by inverse gas chromatography: Specific and non-specific contribution and Lewis acid–base parameters

The fundamental understanding of the behavior of a solid is intimately related to the understanding of the interactions on the surface of the latter, a major challenge in particular if the material is natural and ecological. The infinite dilution-inverse gas chromatography was used to evaluate the surface thermodynamic properties of several phases (grafted and/or coated) diatomite. A series of non- or polar-solute probes were injected at temperatures of 45?°C and 90?°C. The dispersive surface free energies values of the supports decrease with increasing temperature and their active surface is amphoteric with predominantly acidic character.     

A comparative study of fluorine substituents for enhanced stability of flexible and ITO‐free high‐performance polymer solar cells

Two low‐band gap polymer series based on benzo[1,2‐b:4,5‐b′]dithiophene (BDT) and dithienylbenzothiadiazole, with different numbers of fluorine substituents on the 2,3,1‐benzothiadiazole unit, have been synthesized and explored in a comparative study of the photochemical stability and operational lifetime in flexible large area roll‐coated bulk heterojunction solar cells. The two polymer series have different side chains on the BDT unit, namely 2‐hexyldecyloxy (BDT_HDO) ( P1–P3 ) or 2‐hexyldecylthiophene (BDT_THD) ( P4–P6 ). The photochemical stability clearly shows that the stability enhances along with the number of fluorine atoms incorporated on the polymer backbone. Fabrication of the polymer solar cells based on the materials was carried out in ambient atmosphere on a roll coating/printing machine employing flexible and indium‐tin‐oxide‐free plastic substrates. Solar cells based on the P4–P6 series showed the best performance, reaching efficiencies up to 3.8% for an active area of 1 cm², due to an enhanced current compared to P1–P3 . Lifetime measurements, carried out according to international summit on OPV stability (ISOS), of encapsulated devices reveals an initial fast decay for P1–P6 in the performance followed by a much slower decay rate, still retaining 40–55% of their initial performance after 250 h of testing under ISOS‐L‐1 conditions. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 893–899     

A ghost-cell immersed boundary method for large-eddy simulations of compressible turbulent flows

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of ‘ghost cells’ that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

Homogenization of parabolic problem with nonlinear transmission condition

In this paper, we investigate the periodic homogenization of nonlinear parabolic equation arising from heat exchange in composite material problems. This problem, defined in periodical domain, is nonlinear at the interface. This nonlinearity models the heat radiation on the interface, which constitutes the transmission boundary conditions, between the two components of the material. The main challenge is, first, to show the well-posedness of the microscopic problem using the topological degree of Leray–Schauder tools. Then, we apply the two scale convergence to identify the equivalent macroscopic model using homogenization techniques. Finally, in order to confirm the efficiency of the homogenization process, we present some numerical results obtained via finite element approximation.     

Screening of key odorants and anthocyanin compounds of cv. Okuzgozu (Vitis vinifera L.) red wines with a free run and pressed pomace using GC‐MS‐Olfactometry and LC‐MS‐MS

The principal purpose of the present work is to characterize the aroma, aroma‐active, and anthocyanin profiles of Okuzgozu wines and to observe the effect of the pomace pressing technique on these parameters. A total of 58 and 59 volatile compounds were identified and quantified in free‐run juice wine (FRW) and pressed pomace wine (PW). Alcohols were found as the most dominant group among aroma compounds followed by esters and acids. However, among all these compounds, only 11 and 13 of them could be considered as key odorants in aromatic extracts of FRW and PW, respectively. According to GC‐MS‐O analysis, ethyl octanoate (fruity), phenyl ethyl acetate (fruity), and 2‐phenyl ethanol (flowery) were found as the main contributors to the overall scent of both wines. Beyond the aroma profiles, anthocyanin contents of both types of wines were also investigated, and total 14 and 15 anthocyanins were identified and quantified in FRW and PW. Malvidin‐3‐glycoside and its acetyl and coumaroyl forms were identified as the dominant anthocyanins in both wines. It is worth noting the pressing application (2.0 atm) led to an increase of some unpleasant notes in the aroma providing chemical, pharmacy, and fermented aromas in wine. On the other hand, the wines produced with pressed pomace presented higher amounts of anthocyanins.     

Application of a biological‐based nanomagnetic catalyst in the synthesis of bis‐pyrazols and pyrano[3,2‐c]pyrazoles

{Fe₃O₄@SiO₂@(CH₂)₃‐thiourea dioxide‐SO₃H/HCl}, a newly reported nanomagnetic core–shell supported solid acid catalyst, was successfully employed in the preparation of 4,4′‐(arylmethylene)bis(1H –pyrazol‐5‐ol) and pyrano[3,2‐c ]pyrazole derivatives. The presented methods are very efficient and high‐yielding. Also, the catalyst exhibited powerful potential for reusability in both types of reactions.     

Properties of ε-value functions for a two person differential game

We consider the problem of approximate minimax for the Bolza problem of optimal control. Starting from the method of dynamic programming (Bellman) we define the ?-value function to be the approximation for the value function being a solution to the Hamilton–Jacobi equation.     

Fictitious domain methods for two‐phase flow energy balance computations in nuclear components

This paper is dedicated to the numerical simulation of nuclear components (cores and steam generators) by fictitious domain methods. The fictitious domain approach consists in immersing the physical domain under study in a Cartesian domain, called the fictitious domain, and in performing the numerical resolution on this fictitious domain. The calculation times are then efficiently reduced by the use of fast solvers. In counterpart, one has to handle with an immersed boundary, generally non‐aligned with the Cartesian mesh, which can be non‐trivial. The two fictitious domain methods compared here on industrial simulations and developed by Ramière et al. deal with an approximate immersed interface directly derived from the uniform Cartesian mesh. All the usual immersed boundary conditions (Dirichlet, Robin, Neumann), possibly mixed, are handled through a unique formulation of the fictitious problem. This kind of approximation leads to first‐order methods in space that exhibit a good ratio of the precision of the approximate solution over the CPU time, which is very important for industrial simulations. After a brief recall of the fictitious domain method with spread interface (Ramière et al., CMAME 2007) and the fictitious domain method with immersed jumps (Ramière et al., JCP 2008), we will focus on the numerical results provided by these methods applied to the energy balance equation in a steam generator. The advantages and drawbacks of each method will be pointed out. Generally speaking, the two methods confirm their very good efficiency in terms of precision, convergence, and calculation time in an industrial context. Copyright © 2011 John Wiley & Sons, Ltd.