Sensitivity analysis of one-dimensional mixed initial-boundary value problems: Application to freely propagating premixed laminar flames

A hybrid Newton/time-integration procedure for the solution of steady, laminar, one-dimensional, premixed flames

First, we formulate the mixed initial boundary value problem in the theory of thermoelastic microstretch bodies having certain internal state variables. Then by using some approachable computing techniques and the known Gronwall's inequality we will prove that the presence of internal state variables do not influence the uniqueness of solution of the mixed problem.

This study is dedicated to a micropolar porous body, including voidage time derivative among the independent constitutive variables. We formulate a heat-flux theory in this context taking into account a new set of state variables that includes the heat-flux vector and an evolution equation for it. The mixed initial boundary value problems have the specific feature that the governing system of equations consists of hyperbolic field equations only. Consistency of the theory is supported by a result of uniqueness.

Nonstationary plane contact problem in theory of elasticity for conformal cylindrical surfaces

There are considered controlled systems with distributed parameters in one dimension. Their mathematical model is given by mixed initial boundary value problems for hyperbolic partial differential equations in two dimensions. The control is performed at the boundaries, being described by ordinary differential equations accounting for the dynamics of the controllers. Two are the standard problems for such systems, especially in the nonlinear case: well posedness in the sense of J. Hadamard (existence,uniqueness and smooth dependence on data) and stability of the steady state solutions - a control oriented property. While feedback control synthesis may be performed at the formal level, validation of the resulting closed loop model as well as stability have to be analyzed with the mathematical rigor required by the theory of partial differential equations. The present paper is focused on these topics starting from the basic model of the flexible beam, accounting for the models of the flexible manipulator arm, of the overhead crane and of the oilwell drillstring. It is shown how various approaches that are known from the fundamentals of partial differential equations can be used to obtain the necessary properties.

This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies. Our intention is to show that the presence of the microstretch does not affect the main characteristics of the mixed initial boundary value problem for thermoelastic bodies. The result regarding the uniqueness theorem is derived with no definiteness assumptions on the elastic coefficients and in the absence of the restriction that the conductivity tensor is positive definite. In the last part of the paper we establish a basic relation which leads to the reciprocal theorem and to another uniqueness result. MSC:35M30, 35Q74, 74A15, 74A60, 74M25.

A time domain method building on the concept of wave splitting is used to study direct wave propagation phenomena in weakly nonlinear media. The starting point is the linear wave equation with time-dependent coefficients. This means that the studied nonlinear medium in some sense has to be approximated with a nonstationary medium which changes while the wave passes through. For the nonstationary equation homogeneous as well as particular solutions can be obtained. Two different iterative procedures to find the nonlinear solutions are discussed. They are illustrated by two problems fetched from different research fields of current interest. In the first case, the nonlinear term is linearized using the Fréchet derivative. This leads into a truly nonstationary, mixed initial boundary value problem with a linear equation characterized by both time-dependent coefficients and source terms. In this example a semiconductor device used for switching in high-frequency applications is considered. It can be described as a coplanar waveguide loaded with distributed resonant tunnel diodes. In the other example, wave propagation in Kerr media is considered. Then Taylor expansion transforms the nonlinear equation into a linear one with nonstationary source terms. In this case the nonlinearity does not lead to time-depending coefficients in the equation. The way to obtain the solution is a nonlinear variant of the Born approximation.

A partition of energy in thermoelasticity of microstretch bodies

The Navier–Stokes equations at high Reynolds numbers can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of “energy” for the Navier–Stokes equations we are able to obtain nonlinear “energy” estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions that guarantee $L^2 $ boundedness even when the Reynolds number tends to infinity. Finally, we propose a new difference scheme for modeling the Navier–Stokes equations in multidimensions for which we are able to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation.

Progress in the development of an implicit steady state solution in the coupled code TRACE/PARCS

The present article theoretically deals with the domain of influence theorem for generalized thermoelasticity with memory-dependent derivative (MDD). A mixed initial-boundary value problem is considered in an isotropic medium in the context of three-phase-lag model (TPL). The theorem is proved with the help of a domain of dependence inequality. This theorem certifies that the pair of displacement and temperature associated with the thermoelastic problem generates no thermal signals outside a suitably defined bounded domain V ∗ ( t ) for a finite time t > 0 and the set V ∗ ( t ) is the required domain of influence of the associated thermoelastic problem.

SummaryTo improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial‐domain coupled explicit‐implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration‐based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.

A combined finite element and finite difference scheme for computer simulation of microstructure evolution and its application to pore–boundary separation during sintering

A new predictor–corrector (P–C) method for multi‐site sub‐structure pseudo‐dynamic (PSD) test is proposed. This method is a mixed time integration method in which computational components separable from experimental components are solved by implicit time integration method (Newmark β method). The experiments are performed quasi‐statically based on explicit prediction of displacement. The proposed P–C method has an important advantage as it does not require the determination of the initial stiffness values of experimental components and is thus suitable for representing elastic and inelastic systems. A parameter relating to quality of displacement prediction at boundaries nodes is introduced. This parameter is determined such that P–C method can be applicable to many practical problems. Error‐propagation characteristics of P–C method are also presented. A series of examples including linear and non‐linear soil–foundation–structure interaction problem demonstrate the performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.

Two heterogeneous algorithms for partitioned analysis of nuclear power plants considering soil-structure interaction