A Study of the Stability Properties of Smooth Particle Hydrodynamics

1996 ◽  
Vol 13 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Joseph Peter Morris
Keyword(s):  
Higher Order ◽  
Smooth Particle Hydrodynamics ◽  
Detailed Report ◽  
Transverse Waves ◽  
Stability Properties ◽  
Particle Hydrodynamics ◽  
Order Spline ◽  
The Stability ◽  
Spline Interpolants

AbstractWhen using a formulation of smooth particle hydrodynamics (SPH) which conserves momentum exactly the motion of the particles is observed to be unstable to negative stress. It is also found that under normal circumstances a lattice of SPH particles is potentially unstable to transverse waves. This paper is a summary of a detailed report (Morris 1994) investigating the nature of these and other instabilities in depth. Approaches which may be used to eliminate these instabilities are suggested. It is found that the stability properties of SPH in general improve as higher-order spline interpolants, approximating a Gaussian, are used as kernels.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

2021 ◽  
Author(s):  
Kenny W. Q. Low ◽  
Chun Hean Lee ◽  
Antonio J. Gil ◽  
Jibran Haider ◽  
Javier Bonet
Keyword(s):  
Ad Hoc ◽  
Wide Spectrum ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Point Of View ◽  
Numerical Dissipation ◽  
Lagrangian Description ◽  
Smooth Particle Hydrodynamics ◽  
Particle Hydrodynamics ◽  
Sph Algorithm

AbstractThis paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure.

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

scholarly journals Formation of Prestellar Cores via Non-Isothermal Gas Fragmentation

2015 ◽  
Vol 32 ◽  
Author(s):  
S. Anathpindika
Keyword(s):  
Gravitational Instability ◽  
Gas Flows ◽  
Smooth Particle Hydrodynamics ◽  
Three Phase ◽  
Prestellar Cores ◽  
Particle Hydrodynamics ◽  
Unstable Medium ◽  
Stage Process ◽  
Isothermal Gas ◽  
Gas Accretion

AbstractSheet-like clouds are common in turbulent gas and perhaps form via collisions between turbulent gas flows. Having examined the evolution of an isothermal shocked slab in an earlier contribution, in this work we follow the evolution of a sheet-like cloud confined by (thermal) pressure and gas in it is allowed to cool. The extant purpose of this endeavour is to study the early phases of core-formation. The observed evolution of this cloud supports the conjecture that molecular clouds themselves are three-phase media (comprising viz. a stable cold and warm medium, and a third thermally unstable medium), though it appears, clouds may evolve in this manner irrespective of whether they are gravitationally bound. We report, this sheet fragments initially due to the growth of the thermal instability (TI) and some fragments are elongated, filament-like. Subsequently, relatively large fragments become gravitationally unstable and sub-fragment into smaller cores. The formation of cores appears to be a three stage process: first, growth of the TI leads to rapid fragmentation of the slab; second, relatively small fragments acquire mass via gas-accretion and/or merger and third, sufficiently massive fragments become susceptible to the gravitational instability and sub-fragment to form smaller cores. We investigate typical properties of clumps (and smaller cores) resulting from this fragmentation process. Findings of this work support the suggestion that the weak velocity field usually observed in dense clumps and smaller cores is likely seeded by the growth of dynamic instabilities. Simulations were performed using the smooth particle hydrodynamics algorithm.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

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