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A survey on free boundary identification of the truncated boundary in numerical BVPs on infinite intervals

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2002年第1-2期140卷 331-344页

作者： Fazio, R Univ Messina Dept Math I-98166 Messina Italy

A free boundary formulation for the numerical solution of boundary value problems on infinite intervals was proposed recently in Fazio (SIAM J. Nurner. Anal. 33 (1996) 1473). We consider here a survey on recent developments related to the free boundary identification of the truncated boundary. The goals of this survey are: to recall the reasoning for a free boundary identification of the truncated boundary, to report on a comparison of numerical results obtained for a classical test problem by three approaches available in the literature, and to propose some possible ways to extend the free boundary approach to the numerical solution of problems defined on the whole real line. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： boundary value problems -- numerical solutions INTERVAL analysis (Mathematics)

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Sharp corner functions for Mindlin plates

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 2005年第1期72卷 1-9页

作者： McGee, OG Kim, JW Georgia Inst Technol Atlanta GA 30332 USA Ohio State Univ Columbus OH 43210 USA

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called "***, "for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

关键词： EIGENFUNCTIONS boundary value problems -- numerical solutions STRAINS & stresses (Mechanics) BUCKLING (Mechanics) PLATES (Engineering)

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The effect of buoyancy on upper-branch Tollmien-Schlichting waves

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IMA JOURNAL OF APPLIED MATHEMATICS 1997年第1期58卷 19-50页

作者： Mureithi, EW Denier, JP Stott, JAK School of Mathematics University of New South Wales Sydney 2052 Australia

We investigate the effect of buoyancy on the upper-branch linear stability characteristics of an accelerating boundary-layer how. The presence of a large thermal buoyancy force significantly alters the stability structure. As the factor G (which is related to the Grashof number of the flow, and defined in Section 2) becomes large and positive, the flow structure becomes two layered and disturbances are governed by the Taylor-Goldstein equation. The resulting inviscid modes are unstable for a large component of the wavenumber spectrum, with the result that buoyancy is strongly destabilizing. Restabilization is encountered at sufficiently large wavenumbers. For G large and negative the flow structure is again two layered. Disturbances to the basic flow are now governed by the steady Taylor-Goldstein equation in the majority of the boundary layer, coupled with a viscous wall layer. The resulting eigenvalue problem is identical to that found for the corresponding case of lower-branch Tollmien-Schlichting waves, thus suggesting that the neutral curve eventually becomes closed in this limit.

关键词： BUOYANCY WAVE analysis STABILITY theory VISCOUS flow EIGENvalueS boundary value problems -- numerical solutions

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DIFFRACTION BY AN IMPEDANCE STRIP I. REDUCING DIFFRACTION PROBLEM TO RIEMANN-HILBERT problems

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QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS 2015年第3期68卷 321-339页

作者： Shanin, A. V. Korolkov, A. I. Moscow MV Lomonosov State Univ Dept Phys Moscow 119992 Russia

A two-dimensional problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current article (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced to two matrix Riemann-Hilbert problems with exponential growth of unknown functions (for the symmetrical part and for the anti-symmetrical part). For this, the Wiener-Hopf problems are formulated, they are reduced to auxiliary functional problems by applying the embedding formula, and finally the Riemann-Hilbert problems are formulated by applying Hurd's method. In the second part, the Riemann-Hilbert problems are solved by the OE-equation method.

关键词： RIEMANN-Hilbert problems RESEARCH SOUND wave scattering boundary value problems -- numerical solutions ACOUSTIC impedance WIENER-Hopf equations

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A new efficient algorithm for solving an incompressible flow on relatively fine mesh

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2005年第6期47卷 593-610页

作者： Morii, T Japan Nucl Energy Safety Org Safety Anal & Evaluat Div Nucl Power Facil Safety Anal Grp Minato Ku Tokyo 1050001 Japan

The new coupled solver SOAR (SIMPLE Optimized and Automated Relaxation factors) proposed by the author has been reformulated on a collocated grid and compared with the SIMPLE method for computing performance as the grid is refined. The functional relation between calculational time T and total grid points N has been studied through 22 calculations for a rectangular tank and can be expressed as T approximate to k x N-m. Here, the value of the exponent in has been found to range from 1.2 to 1.5 for the SOAR solver and from 2.4 to 3.0 for the SIMPLE solver, and it is clear that the SOAR method has better computing performance than the SIMPLE method as the grid is refined. For large numbers of grid points, which are increasingly required for assessment of confidence in computational fluid dynamics, this translates into significant and predictable reductions in run times and faster project turnaround.

关键词： numerical grid generation (numerical analysis) FLUID dynamics boundary value problems -- numerical solutions PARTIAL differential equations -- numerical solutions numerical analysis FLUID mechanics DYNAMICS

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Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations

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CHAOS SOLITONS & FRACTALS 2015年 77卷 240-246页

作者： Shah, Kamal Khalil, Hammad Khan, Rahmat Ali Univ Malakand Dept Math Chakadara Dir L Khyber Pakhtunk Pakistan

In this article, we study a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions. We use the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii's fixed point theorem for uniqueness and existence results. As in application, we provide an example to illustrate our main results. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： COUPLED mode theory (Wave-motion) boundary value problems -- numerical solutions NONLINEAR equations FRACTIONAL differential equations DIFFERENTIAL equations -- numerical solutions

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Conformal mappings involving curvilinear quadrangles

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IMA JOURNAL OF APPLIED MATHEMATICS 1996年第2期57卷 181-191页

作者： Craster, RV Department of Theoretical Mechanics University of Nottingham Nottingham NG7 2RD UK

The conformal mapping of a curvilinear quadrangle to a half-plane is a classical problem in analysis;it occurs during the analytical solution of free-boundary problems involving groundwater flows. Apart from degenerate cases, in general, it is not known how to perform such mappings;the difficulty arises because the mapping functions are given by the solutions of a Fuchsian differential equation. For a quadrangle this Fuchsian equation involves both accessory parameters and free points that are unknown a priori;the analysis of such equations is therefore difficult, and there are usually no obvious solutions. In this paper conformal mappings involving a special class of curvilinear quadrangles are constructed, and a general approach is devised in the special cases when one (or more) vertex angle is equal to 2 pi. By implication this suggests that there are degenerate classes of Fuchsian equations involving accessory parameters and free points;these classes are discussed.

关键词： CONFORMAL mapping LINE integrals boundary value problems -- numerical solutions AUTOMORPHIC functions SET theory PARAMETER estimation

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Treatment of the inlet boundary conditions in natural-convection flows in open-ended channels

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 1999年第3期35卷 317-345页

作者： Marcondes, F Maliska, CR Univ Fed Santa Catarina Dept Mech Engn BR-88040900 Florianopolis SC Brazil Univ Fed Paraiba Dept Mech Engn BR-58109970 Campina Grande Brazil

The present work deals with the numerical solution of elliptic flows encountered in open-ended channels, The important question of applying boundary conditions for pressure and velocity for these flows is considered and a new method for the application of boundary conditions at the channel inlet is proposed. It is shown that the flow reversal at the channel outlet, which appears when nonsymmetric flow conditions are present, is strongly dependent on the entrance boundary conditions for pressure. Results for the straight channel in situations where flow reversal is present are reported for a wide range of Rayleigh numbers. solutions for L-shaped channels are also reported with the aim of demonstrating the application of the model to arbitrary channels. II is shown that for certain flow situations the use of all elliptic formulation is imperative in order to predict correctly the flow behavior in open-ended channels.

关键词： HEAT -- Convection, Natural CHANNELS (Hydraulic engineering) boundary value problems -- numerical solutions

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On the fundamental state energy for a Schrodinger operator with magnetic field in domains with corners

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ASYMPTOTIC ANALYSIS 2005年第3-4期41卷 215-258页

作者： Bonnaillie, V Univ Paris 11 CNRS UMR 8628 Dept Math F-91405 Orsay France

The superconducting properties of a sample submitted to an external magnetic field are mathematically described by the minimizers of the Ginzburg-Landau's functional. The analysis of the Hessian of the functional leads to estimate the fundamental state for the Schrodinger operator with intense magnetic field for which the superconductivity appears. So we are interested in the asymptotic behavior of the energy for the Schrodinger operator with a magnetic field. A lot of papers have been devoted to this problem, we can quote the works of Bernoff-Sternberg, Lu-Pan, Helffer-Mohamed. These papers deal with estimates of the energy in a regular domain and our goal is to establish similar results in a domain with corners. Although this problem is often mentioned in the physical literature, there are very few mathematical papers. We only know the contributions by Pan and Jadallah which deal with very particular domains like a square or a quarter plane. The physicists Brosens, Devreese, Fomin, Moshchalkov, Schweigert and Peeters propose a non optimal upper bound for the energy. Here, we present a more rigorous analysis and give an asymptotics of the smallest eigenvalue of the operator in a sector Omega(alpha) of angle alpha when alpha is closed to 0, an estimate for the eigenfunctions and we use these results to study the fundamental state in the semi-classical case.

关键词： MAGNETIC fields ELECTRIC conductivity SUPERCONDUCTIVITY boundary value problems -- numerical solutions INTEGRAL equations -- numerical solutions DIFFERENTIAL equations -- numerical solutions

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A Simple and Accurate Ghost Cell Method for the Computation of Incompressible Flows Over Immersed Bodies with Heat Transfer

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2010年第1期58卷 17-39页

作者： Pan, Dartzi Natl Cheng Kung Univ Dept Aeronaut & Astronaut Tainan 70101 Taiwan

A simple, stable, and accurate ghost cell method is developed to solve the incompressible flows over immersed bodies with heat transfer. A two-point stencil is used to build the flow reconstruction models for both Dirichlet and Neumann boundary conditions on the immersed surface. Tests show that the current scheme is second-order-accurate in all error norms for both types of boundary condition, with the only exception that under Neumann condition the order of the maximum norm of temperature error is 1.44. Various forced- and natural-convection problems for cylinders immersed in open field or in a cavity are computed and compared with published data.

关键词： HEAT transfer FLUID dynamic measurements NEUMANN problem boundary value problems -- numerical solutions DIRICHLET problem

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