A free boundary formulation for the numerical solution of boundaryvalueproblems on infinite intervals was proposed recently in Fazio (SIAM J. Nurner. Anal. 33 (1996) 1473). We consider here a survey on recent develo...
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A free boundary formulation for the numerical solution of boundaryvalueproblems 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.
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 bounda...
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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.
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 struc...
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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.
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, namel...
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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.
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 gr...
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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.
In this article, we study a coupled system of impulsive boundaryvalueproblems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions...
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In this article, we study a coupled system of impulsive boundaryvalueproblems 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.
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-boundaryproblems involving groundwater flows. Apart from degenerat...
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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-boundaryproblems 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.
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 a...
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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.
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 ...
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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.
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 Dir...
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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.
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