scholarly journals Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

2006 ◽  
Vol 113 (1) ◽  
pp. 133-217 ◽  
Author(s):  
Vincent Acary ◽  
Bernard Brogliato ◽  
Daniel Goeleven
Keyword(s):  
Numerical Simulation ◽  
Mathematical Formulation ◽  
Higher Order ◽  
Sweeping Process ◽  
Moreau’S Sweeping Process

scholarly journals Non-autonomous higher-order Moreau's sweeping process: Well-posedness, stability and Zeno trajectories

2018 ◽  
Vol 29 (5) ◽  
pp. 941-968 ◽  
Author(s):  
BERNARD BROGLIATO
Keyword(s):  
Dynamical Systems ◽  
Differential Algebraic Equations ◽  
Higher Order ◽  
Well Posedness ◽  
Sweeping Process ◽  
Algebraic Equations ◽  
Unilateral Constraints ◽  
Uniqueness Of Solutions ◽  
Autonomous Case ◽  
Moreau’S Sweeping Process

In this article, we study the higher-order Moreau's sweeping process introduced in [1], in the case where an exogenous time-varying functionu(·) is present in both the linear dynamics and in the unilateral constraints. First, we show that the well-posedness results (existence and uniqueness of solutions) obtained in [1] for the autonomous case, extend to the non-autonomous case whenu(·) is smooth and piece-wise analytic, after a suitable state transformation is done. Stability issues are discussed. The complexity of such non-smooth non-autonomous dynamical systems is illustrated in a particular case named the higher-order bouncing ball, where trajectories with accumulations of jumps are exhibited. Examples from mechanics and circuits illustrate some of the results. The link with complementarity dynamical systems and with switching differential-algebraic equations is made.

A Parallel HOFD Scheme for Direct Numerical Simulation of Turbulent Magnetically Driven Flows

2001 ◽  
Author(s):  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Parallel Machines ◽  
Higher Order ◽  
Electrically Conducting ◽  
Wide Range ◽  
Order Scheme ◽  
Higher Order Scheme

Abstract Turbulent magnetically flows occur in a wide range of material processing systems involving electrically conducting melts. This paper presents a parallel higher order scheme for the direct numerical simulation of turbulent magnetically driven flows in induction channels. The numerical method is based on the higher order finite difference algorithm, which enjoys the spectral accuracy while minimizing the computational intensity. This, coupled with the parallel computing strategy, provides a very useful means to simulate turbulent flows. The higher order finite difference formulation of magnetically driven flow problems is described in this paper. The details of the parallel algorithm and its implementation for the simulations on parallel machines are discussed. The accuracy and numerical performance of the higher order finite difference scheme are assessed in comparison with the spectral method. The examples of turbulent magnetically driven flows in induction channels and pressure gradient driven flows in regular channels are given, and the computed results are compared with experimental measurements wherever possible.

NUMERICAL SIMULATION OF COMBUSTION OF THE COMPOSITE SOLID PROPELLANT CONTAINING BIDISPERSED BORON POWDER

2021 ◽  
pp. 131-139
Author(s):  
V.A. Poryazov ◽  
◽  
K.M. Moiseeva ◽  
A.Yu. Krainov ◽  
◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Burning Rate ◽  
Solid Propellant ◽  
Mathematical Formulation ◽  
Solid Propellants ◽  
Boron Powder ◽  
Composite Solid Propellant ◽  
Composite Solid Propellants ◽  
Composite Solid ◽  
Propellant Surface

A problem of combustion of the composite solid propellants containing various powders of metals and non-metals is relevant in terms of studying the effect of various compositions of powders on the linear rate of propellant combustion. One of the lines of research is to determine the effect of the addition of a boron powder on the burning rate of a composite solid propellant. This work presents the results of numerical simulation of combustion of the composite solid propellant containing bidispersed boron powder. Physical and mathematical formulation of the problem is based on the approaches of the mechanics of two-phase reactive media. To determine the linear burning rate, the Hermance model of combustion of composite solid propellants is used, based on the assumption that the burning rate is determined by mass fluxes of the components outgoing from the propellant surface. The solution is performed numerically using the breakdown of an arbitrary discontinuity algorithm. The dependences of the linear burning rate of the composite solid propellant on the dispersion of the boron particles and gas pressure above the propellant surface are obtained. It is shown that the burning rate of the composite solid propellant with bidispersed boron powder changes in contrast to that of the composite solid propellant with monodispersed powder. This fact proves that the powder dispersion should be taken into account when solving the problems of combustion of the composite solid propellants containing reactive particles.

A Semi-Discrete Approach for the Numerical Simulation of Freestanding Blocks

2016 ◽  
pp. 416-439
Author(s):  
Fernando Peña
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Numerical Modeling ◽  
Discrete Model ◽  
Mathematical Formulation ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Discrete Approach ◽  
Rocking Motion

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

CHAOTIC SECURE COMMUNICATION BASED ON THE CONCEPT OF EQUIVALENT CONTROL

2006 ◽  
Vol 16 (02) ◽  
pp. 419-425 ◽  
Author(s):  
MAO-YIN CHEN ◽  
DONG-HUA ZHOU ◽  
YUN SHANG
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Secure Communication ◽  
Sliding Mode ◽  
Higher Order ◽  
Order System ◽  
Augmented System ◽  
Response System ◽  
Equivalent Control ◽  
Chaotic Secure Communication

This Letter considers the problem of chaotic secure communication in the drive-response framework. The drive system can be augmented into a higher order system, and then a sliding mode observer based response system can be constructed to synchronize this augmented system. If they satisfy certain conditions, the hidden message can be recovered directly by the concept of equivalent control. Theoretical analysis and numerical simulation verify the effectiveness of the proposed method.

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