A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

This paper comprises an implementation of a fourth‐order Runge–Kutta discontinuous Galerkin (RKDG4) scheme for computing the open‐channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high‐order slope limiting procedure, and high‐order source terms approximations. A comparison of the performance of the proposed method with lower‐order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high‐order model. Copyright © 2008 John Wiley & Sons, Ltd.     

An eigenvector‐based linear reconstruction approach for time stepping in discontinuous Galerkin scheme used to solve shallow water equations

Discontinuous Galerkin (DG) methods have shown promising results for solving the two‐dimensional shallow water equations. In this paper, the classical Runge–Kutta (RK) time discretisation is replaced by the eigenvector‐based reconstruction (EVR) that allows the second‐order time accuracy to be achieved within a single time‐stepping procedure. Moreover, the EVRDG approach yields stable solutions near drying and wetting fronts, whereas the classical RKDG approach yields instabilities. The proposed EVRDG technique is compared with the original RKDG approach on various test cases with analytical solutions. The EVRDG solutions are shown to be as accurate as those obtained with the RKDG scheme. Besides, the EVRDG scheme is 1.6 times faster than the RKDG method. Simulating dambreaks involving dry beds confirms that EVRDG scheme gives correct solutions, whereas the RKDG method yields instabilities. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of a second‐order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms

The present work addresses the numerical prediction of discontinuous shallow water flows by the application of a second‐order Runge–Kutta discontinuous Galerkin scheme (RKDG2). The unsteady flow of water in a one‐dimensional approach is described by the Saint Venant's model which incorporates source terms in practical applications. Therefore, the RKDG2 scheme is reformulated with a simple way to integrate source terms. Further, an adequate boundary conditions handling, by the theory of characteristics, was overviewed to be adapted to the external points of the mesh, as well as to some points of local invalidity of the Saint Venant's model. To validate the proposed technique, steady and transient test problems (all having a reference solution) were considered and computed by means of the overall method. The results were illustrated jointly with the reference solution and the results carried out by a traditional second‐order finite volume (FV2) scheme implemented with the same techniques as the RKDG2. The proposed method has proven its practical consideration when solving discontinuous shallow water flow involving: non‐prismatic channels, various cross‐sections, smoothly varying bed topography and internal boundary conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

The chaperonin of the archaeonSulfolobus solfataricus

The chaperonin of the hyperthermophilic archaeonSulfolobus solfataricus, briefly Ssocpn, was purified by a fast and high-yield procedure. Ssocpn, a 920 kDa-complex of two different subunits, displays a potassium-dependent ATPase activity with a temperature optimum at 80°C. The ability of Ssocpn to function in vitro was investigated using different protein substrates. Ssocpn promotes correct refolding of thermophilic and mesophilic enzymes from their chemically unfolded state; moreover, Ssocpn prevents the irreversible inactivation of native proteins by suppressing their precipitation upon heating. Both the activity in assisting refolding of unfolded proteins and that in preventing heat denaturation of native proteins require the hydrolysis of ATP. The chaperone-based strategies in different technological fields are discussed, and the advantages in using archaeal chaperonins are underlined.     

Structure and properties of titanium-zinc borophosphate glasses

The structure of 50ZnO-10B₂O₃-40P₂O₅+xTiO₂ glasses prepared by slow cooling (for x=0-24 mol% TiO₂) or by quenching (for x=28-64 mol% TiO₂) was studied by Raman, ³¹P and ¹¹B MAS NMR spectroscopy. TiO₂ incorporates into the glass structure, which results in a decrease in the molar volume and an increase in the glass transition temperature. According to Raman spectra Ti atoms form distorted TiO₆ octahedra and their incorporation into the structural network results in the depolymerization of phosphate chains. ¹¹B NMR spectra of the glasses with increasing TiO₂ content show gradual changes from one symmetrical signal of B(OP)₄ units to a broad complex signal which was separated into five signals ascribed to four different types of BO₄ units and one BO₃ unit. With increasing TiO₂ content a part of boron atoms changes from tetrahedral BO₄ to trigonal BO₃ units, which is ascribed to the formation of TiO₆ units in the glass structure.     

Perturbation of Conformational Dynamics of ASCUT-1 from Ascaris lumbricoides by Temperature and Sodium Dodecyl Sulfate

ASCUT-1 is a protein found in cuticlin, the insoluble residue of the cuticles of the nematode Ascaris lumbricoides. It contains the CUT-1-like domain which is shared by members of a novel family of components of extracellular matrices. The monomeric form of ASCUT-1 contains a single tryptophan residue. An understanding of the structure-function relationship of the protein under different chemical-physical conditions is of fundamental importance for an understanding of its structure and function in cuticles. In this paper we report the effect of the temperature and sodium dodecyl sulfate on the structural stability of this protein. The structure of the protein was studied in the temperature range 25–85°C in the absence and in the presence of sodium dodecyl sulfate by frequency-domain measurements of the intrinsic fluorescence intensity and anisotropy decays. The time-resolved fluorescence data in the absence of SDS indicated that the tryptophanyl emission decays were well described by a bimodal lifetime distribution, and that the temperature increases resulted in the sharpening and in the shortening of the tryptophanyl lifetime distribution. In the presence of SDS an unimodal fluorescence lifetime distribution as well as a marked decrease in the anisotropy decay values were observed.     

An improvement of classical slope limiters for high‐order discontinuous Galerkin method

In this paper, we describe some existing slope limiters (Cockburn and Shu's slope limiter and Hoteit's slope limiter) for the two‐dimensional Runge–Kutta discontinuous Galerkin (RKDG) method on arbitrary unstructured triangular grids. We describe the strategies for detecting discontinuities and for limiting spurious oscillations near such discontinuities, when solving hyperbolic systems of conservation laws by high‐order discontinuous Galerkin methods. The disadvantage of these slope limiters is that they depend on a positive constant, which is, for specific hydraulic problems, difficult to estimate in order to eliminate oscillations near discontinuities without decreasing the high‐order accuracy of the scheme in the smooth regions. We introduce the idea of a simple modification of Cockburn and Shu's slope limiter to avoid the use of this constant number. This modification consists in: slopes are limited so that the solution at the integration points is in the range spanned by the neighboring solution averages. Numerical results are presented for a nonlinear system: the shallow water equations. Four hydraulic problems of discontinuous solutions of two‐dimensional shallow water are presented. The idealized dam break problem, the oblique hydraulic jump problem, flow in a channel with concave bed and the dam break problem in a converging–diverging channel are solved by using the different slope limiters. Numerical comparisons on unstructured meshes show a superior accuracy with the modified slope limiter. Moreover, it does not require the choice of any constant number for the limiter condition. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonequilibrium simulations of filled polymer networks: searching for the origins of reinforcement and nonlinearity

We present nonequilibrium dissipative particle dynamics (DPD) simulations of cross-linked elastomers containing solid filler particles at 30% volume fraction. We study systematically the effect of the morphology (dispersed or aggregated particles) and of the effective particle-particle interactions. In addition, we have experimented by replacing the standard harmonic DPD bonds with other potential functions, conceived to deal with the finite extensibility of the polymer chains and the possibility of a slow equilibrium between strongly and weakly adsorbed chains at the rubber-filler interface. The simulation results shed some light on the basic mechanisms of rubber reinforcement, including the nonlinearity and history dependence commonly known as "Payne effect" and "Mullins effect."