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Hybrid Solutions (hybrid + solution)
Selected AbstractsHybrid finite-volume finite-difference scheme for the solution of Boussinesq equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005K. S. Erduran Abstract A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams,Basforth third-order predictor and Adams,Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model ,HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd. [source] Flexible nanocrystalline-titania/polyimide hybrids with high refractive index and excellent thermal dimensional stabilityJOURNAL OF POLYMER SCIENCE (IN TWO SECTIONS), Issue 6 2010Guey-Sheng Liou Abstract In this study, a novel synthetic route was developed to prepare polyimide,nanocrystalline,titania hybrid optical films with a relatively high titania content (up to 50 wt %) and thickness (20,30 ,m) from soluble polyimides containing hydroxyl groups. Two series of newly soluble polyimides were synthesized from the hydroxy-substituted diamines with various commercial tetracarboxylic dianhydrides. The hydroxyl groups on the backbone of the polyimides could provide the organic,inorganic bonding and resulted in homogeneous hybrid solutions by controlling the mole ratio of titanium butoxide/hydroxyl group. AFM, SEM, TEM, and XRD results indicated the formation of well-dispersed nanocrystalline-titania. The flexible hybrid films could be successfully obtained and revealed relatively good surface planarity, thermal dimensional stability, tunable refractive index, and high optical transparency. A three-layer antireflection coating based on the hybrid films was prepared and showed a reflectance of less than 0.5% in the visible range indicated its potential optical applications. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1433,1440, 2010 [source] Hybrid, numerical solutions, for three-dimensional, compressible Navier-Stokes layerPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009A. NastaseArticle first published online: 5 MAR 2010 The author proposes new hybrid solutions for the three-dimensional, compressible Navier-Stokes layer (NSL) over a flying configuration (FC), which use the analytical potential solutions, of the same FC, two times, namely: to reinforce the numerical solutions by multiplying them with these analytical solutions and as outer flow (instead of the parallel flow, used by Prandtl in his boundary layer theory). These hybrid solutions fulfill the last behavior, have correct jumps along the singular lines (like subsonic leading edges, junction lines wing-fuselage, etc.), are split, accurate and rapid convergent. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||