Modeling and Test of an Electropneumatic Servovalve Controlled Long Rodless Actuator

1996 ◽  
Vol 118 (3) ◽  
pp. 457-462 ◽  
Author(s):  
X. Lin ◽  
F. Spettel ◽  
S. Scavarda
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Transmission Line ◽  
Dynamic Behavior ◽  
Numerical Scheme ◽  
Distributed Parameter ◽  
One Dimensional ◽  
Flow Parameters ◽  
Characteristics Method ◽  
Cylinder Model

The usual way of modeling an electropneumatic servodrive system consists of supposing the homogeneity of the flow parameters in the cylinder. In order to study the influence of the transmission line effects on the dynamic behavior of a long pneumatic rodless cylinder, a generalized one-dimensional distributed parameter cylinder model is presented. The proposed numerical scheme combining the finite difference and the “characteristics” method enables the simulate of a long rodless cylinder by taking into account the servovalve boundary conditions and the piston movement. The simulated results are compared with experimental results.

Numerical Methods of Higher-Order Accuracy for Diffusion- Convection Equations

1968 ◽  
Vol 8 (03) ◽  
pp. 293-303 ◽  
Author(s):  
H.S. Price ◽  
J.C. Cavendish ◽  
R.S. Varga
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Variational Methods ◽  
Miscible Displacement ◽  
Two Dimensional ◽  
Order Accuracy ◽  
One Dimensional ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Diffusion Convection

Abstract A numerical formulation of high order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. Introduction The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusion-convection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation: (1) where the diffusivity is taken to be unity and c(x, t) represents a normalized concentration, i.e., c(x, t) satisfied 0 less than c(x, t) less than 1. Typical boundary conditions are given by ....................(2) Our interest in this apparently simple problem arises because accurate numerical approximations to this equation with the boundary conditions of Eq. 2 are as theoretically difficult to obtain as are accurate solutions for the general equations describing the behavior of two-dimensional miscible displacement. This is because the numerical solution for this simplified problem exhibits the two most important numerical difficulties associated with the more general problem: oscillations and undue numerical dispersion. Therefore, any solution technique that successfully solves Eq. 1, with boundary conditions of Eq. 2, would be excellent for calculating two-dimensional miscible displacement. Many authors have presented numerical methods for solving the simple diffusion-convection problem described by Eqs. 1 and 2. Peaceman and Rachford applied standard finite difference methods developed for transient heat flow problems. They observed approximate concentrations that oscillated about unity and attempted to eliminate these oscillations by "transfer of overshoot". SPEJ P. 293ˆ

scholarly journals Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
A. Navarro-Quiles ◽  
J.-V. Romero ◽  
M.-D. Roselló ◽  
M. A. Sohaly
Keyword(s):  
Stochastic Process ◽  
Standard Deviation ◽  
Finite Difference ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Sufficient Conditions ◽  
Numerical Approximations ◽  
One Dimensional ◽  
The Mean ◽  
Theoretical Results

This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 523-527 ◽  
Author(s):  
James Caldwell ◽  
Svetislav Savovic´ ◽  
Yuen-Yick Kwan
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Finite Difference Methods ◽  
Melting Process ◽  
Time Dependent ◽  
One Dimensional ◽  
Stefan Problems ◽  
Finite Difference Solution ◽  
Very High

The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However, very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.

scholarly journals Mixed problem for a one-dimensional wave equation with conjugation conditions and second-order derivatives in boundary conditions

2020 ◽  
Vol 56 (3) ◽  
pp. 287-297
Author(s):  
V. I. Korzyuk ◽  
S. N. Naumavets ◽  
V. P. Serikov
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Analytical Form ◽  
Second Order ◽  
Conjugation Conditions ◽  
One Dimensional ◽  
Characteristics Method ◽  
Half Strip ◽  
Dimensional Wave

In this paper, we consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives. Moreover, the conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied. A classical solution to this problem is found in an analytical form by the characteristics method. This solution is approved to be unique if the relevant conditions are fulfilled.

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