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Wojciech Sulisz 《国际流体数值方法杂志》1987,7(4):353-370
Two-dimensional fluid flow problems expressed in terms of velocity potentials or stream functions are often summarized as boundary-value problems for the Laplace or Poisson equations, or the homogeneous or non-homogeneous biharmonic equations. Simple local co-ordinate systems have been applied to the solution of integral equations associated with these boundary-value problems. This procedure has been shown to be an efficient technique in the numerical solution of fluid flow problems. 相似文献
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The problem of block elements used to solve boundary-value problems of continuum mechanics is discussed. An example of constructing
a semibounded block element is presented. Pseudodifferential equations describing the block element parameters are derived.
The relationship between formulas and methods for calculating wave fields in block elements and layered media is found. 相似文献
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We consider a parametrized boundary-value problem containing an unknown parameter both in nonlinear ordinary differential equations and in nonlinear boundary conditions. By using a suitable change of variables, we reduce the original problem to a family of problems with linear boundary conditions plus certain nonlinear algebraic determining equations. We construct a numerical-analytic scheme suitable for studying the solutions of the transformed boundary-value problem. 相似文献
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G. V. Druzhinin 《Journal of Applied Mechanics and Technical Physics》2003,44(6):779-785
A unified method for constructing basis (eigen) functions is proposed to solve problems of mechanics of continuous media, problems of cubature and quadrature, and problems of approximation of hypersurfaces. Numerical-analytical methods are described, which allow obtaining approximate solutions of internal and external boundary-value problems of mechanics of continuous media of a certain class (both linear and nonlinear). The method is based on decomposition of the sought solutions of the considered partial differential equations into series in basis functions. An algorithm is presented for linearization of partial differential equations and reduction of nonlinear boundary-value problems, which are reduced to systems of linear algebraic equations with respect to unknown coefficients without using traditional methods of linearization. 相似文献
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An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
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V. F. Zhuravlev 《Nonlinear Oscillations》2011,13(4):558-568
We consider linear boundary-value problems for operator equations with generalized invertible operators in Banach spaces that
have bases. Using the technique of generalized inverse operators applied to generalized invertible operators in Banach spaces,
we establish conditions for the solvability of linear boundary-value problems for these operator equations and obtain formulas
for the representation of their solutions. We consider special cases of these boundary-value problems, namely, so-called n- and d-normally solvable boundary-value problems as well as normally solvable problems for Noetherian operator equations. 相似文献
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The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep
problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions
of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found
by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value
problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form
of operators in the mathematical problem formulation 相似文献
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This paper is mainly concerned with the dynamic response of an elastic foun- dation of finite height bounded to the surface of a saturated half-space.The foundation is subjected to time-harmonic vertical loadings.First,the transform solutions for the governing equations of the saturated media are obtained.Then,based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half- space is completely pervious or impervious,this dynamic mixed boundary-value problem can lead to dual integral equations,which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures.In the numerical exam- ples,the dynamic compliances,displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system.In most of the cases,the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions. 相似文献