A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is i...
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A method is presented for the prediction of transonic flutter by the Euler equations on a stationary Cartesian mesh. Local grid refinement is established through a series of embedded meshes, and a gridless method is implemented for the treatment of surface boundary conditions. For steady flows, the gridless method applies surface boundary conditions using a weighted average of the flow properties within a cloud of nodes in the vicinity of the surface. The weighting is established with shape functions derived using a least-squares fitting of the surrounding nodal cloud. For unsteady calculations, a perturbation of the shape functions is incorporated to account for a fluctuating surface normal direction. The nature of the method provides for efficient and accurate solution of transient flow problems in which surface deflections are small (i.e. flutter calculations) without the need for a deforming mesh. Although small deviations in angle of attack are considered, the mean angle of attack can be large. Results indicate good agreement with available experimental data for unsteady flow, and with computational results addressing flutter of the Isogai wing model obtained using traditional moving mesh algorithms. (c) 2005 Elsevier Ltd. All rights reserved.
A straightforward procedure is developed to determine dissipation fields (e. g., exergy destruction in conduction, pumping power, Joule heating) from the linear boundary conditions applied on their associated linear d...
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A straightforward procedure is developed to determine dissipation fields (e. g., exergy destruction in conduction, pumping power, Joule heating) from the linear boundary conditions applied on their associated linear diffusion problem (e. g., heat conduction, Darcy flow, electrical flow). The mathematical tool proposed in this article takes advantage of the quadratic (nonlinear) behavior that comes with dissipative fields equations. The first objective of this article is to build a mathematical formulation expressing any dissipation field as a combination of fundamental dissipative fields resulting from decomposed boundary conditions, similarly to linear problems where fundamental solutions may be added with the superposition principle. The second objective is to demonstrate the numerical advantage of this formulation when applied to heat transfer and fluid flow optimization problems. Application of the mathematical tool proposed in this article to boundary control problems provided significant computational time reductions.
In this paper we study necessary and sufficient conditions on f and the first eigenfunctions for the 1-Laplacian, for equations of the form [GRPHICS] when q =lambda(1), lambda(1) is the first eigenvalue for the 1-Lapl...
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In this paper we study necessary and sufficient conditions on f and the first eigenfunctions for the 1-Laplacian, for equations of the form [GRPHICS] when q <= N/(N-1) and lambda >=lambda(1), lambda(1) is the first eigenvalue for the 1-Laplacian.
problems with extremely high-transport anisotropy often arise in strongly magnetized plasmas. The numerical solution of the highly anisotropic transport equations becomes quite difficult when the computational grid is...
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problems with extremely high-transport anisotropy often arise in strongly magnetized plasmas. The numerical solution of the highly anisotropic transport equations becomes quite difficult when the computational grid is not aligned with the strong transport direction, since this can cause large numerical errors. Constructing a finite-difference scheme for a strongly anisotropic diffusion equation on a misaligned grid is discussed, and quantitative assessment of the numerical error is made for a set of example problems.
The article presents the solution for boundary-valueproblems of the elasticity theory of finite-length cylinders and cones to satisfy its axisymmetrical deformation. It says that the integral transform is applied to ...
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The article presents the solution for boundary-valueproblems of the elasticity theory of finite-length cylinders and cones to satisfy its axisymmetrical deformation. It says that the integral transform is applied to get the exact solution of boundary-value problem for cylinder torsion and torsion deformation of cone. It mentions that the subsequent use of inversion formulas gives the precise solutions for cylinder and the sliding-seal condition must be fulfilled to find the solution for cone.
We derive and test an approximate expression for the Kohn-Sham eigenfunctions and total energy associated with a given exchange-correlation functional. The expression is closely related to the approximation given by B...
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We derive and test an approximate expression for the Kohn-Sham eigenfunctions and total energy associated with a given exchange-correlation functional. The expression is closely related to the approximation given by Benoit et al. (Phys Rev Lett 2001, 87, 226401) but differs by removing an overly stringent orthogonality constraint. Tests on the Li, F, Ne, and Cr atoms done in Gaussian basis sets suggest that the approach is promising, particularly as an alternative to conventional self-consistent field or to the Harris scheme (Phys Rev B 1985, 31, 1770). (C) 2004 Wiley Periodicals, Inc.
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non-trivial integrable model. (c) 2005 Elsevier B.V. All rights reserved.
We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non-trivial integrable model. (c) 2005 Elsevier B.V. All rights reserved.
The current article is the second part of a series of two papers dedicated to the two-dimensional problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the first part, some pr...
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The current article is the second part of a series of two papers dedicated to the two-dimensional problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the first part, some preliminary steps were made, namely, the problem was reduced to two-matrix Riemann-Hilbert problems. Here these problems are solved with the help of a novel method of OE-equations. Each Riemann-Hilbert problem is embedded into a family of similar problems with the same coefficient and growth condition, but with some other cuts. The family is indexed by an artificial parameter. It is proven that the dependence of the solution on this parameter can be described by a simple ordinary differential equation (ODE1). The boundary conditions for this equation are known and the inverse problem of reconstruction of the coefficient of ODE1 from the boundary conditions is formulated. This problem is called the OE-equation. The OE-equation is solved by a simple numerical algorithm.
A geometry identification problem of two-dimensional heat conduction is solved by using the least-squares collocation meshless method and the conjugate gradient method. In the least-squares collocation meshless approa...
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A geometry identification problem of two-dimensional heat conduction is solved by using the least-squares collocation meshless method and the conjugate gradient method. In the least-squares collocation meshless approach for solving the direct heat conduction problem, a number of collocation points and auxiliary points are used to discretize the problem domain, and the collocation points are taken to construct the trial function by moving least-squares approximation. Akima cubic interpolation is employed to transform the geometry boundary inverse problem to the discrete boundary point's inverse problem and approximate the unknown boundary in an inverse iterative process. In order to illustrate the performance and verify the new solution method, four typical cases are considered. The numerical results show that the least-squares collocation meshless method combined with the conjugate gradient method is accurate and stable for solving the geometry identification problem of heat conduction.
In this paper, we give a uniqueness theorem for the moving boundary of a heat problem in a composite medium. Through solving the Cauchy problem of heat equation in each subdomain, we finally find an approximation to t...
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In this paper, we give a uniqueness theorem for the moving boundary of a heat problem in a composite medium. Through solving the Cauchy problem of heat equation in each subdomain, we finally find an approximation to the moving boundary for one-dimensional heat conduction problem in a multilayer medium. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique with the generalized cross-validation choice rule for a regularization parameter. numerical experiments for five examples show that our proposed method is effective and stable.
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