Effect of Artificial Viscosity on the Expansion of Dis-Continuities in a Rotating Interplanetary Medium with Material Pressure

The solution of equations by seeking quasi-similar solution, in which the viscosity coefficient is taken to be at most a function of time but independent of space co-ordinates. an attempt is made to account for the material strength by including Newtonian- Viscosity term. In the present paper the characteristic method (Chester, Witham) is applied to obtain expressions of the density, the pressure, the particle velocity just behind the shock propagating in a rotating atmosphere. The effect of cariolis force is taken into account. Since the velocity effect has a tendency to smoothen out such discontinuities, the artificial viscosity coefficient suggested by Rithchmyer and Von Newmann is introduced. The problem is discussed for two different cases (i) for weak shocks and (ii) for strong shocks respectively.

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The High Pressure Rheology of Mixtures

Journal of Tribology ◽

10.1115/1.1760552 ◽

2004 ◽

Vol 126 (4) ◽

pp. 697-702 ◽

Cited By ~ 9

Author(s):

Scott Bair

Keyword(s):

Molecular Weight ◽

High Pressure ◽

Binary Systems ◽

Viscosity Coefficient ◽

Shear Thinning ◽

Newtonian Viscosity ◽

Double Shear ◽

Ideal Mixing ◽

Viscosity Behavior ◽

Single Flow

The Newtonian mixing rules for several binary systems have been experimentally investigated. Some systems show non-ideal mixing response and for some systems the non-ideal response is pressure-dependent, yielding an opportunity for manipulation of the pressure-viscosity behavior to advantage. The mixing of differing molecular weight “straight cuts” can produce very different pressure-viscosity response. This behavior underscores the difficulty in predicting the pressure-viscosity coefficient based upon chemical structure and ambient viscosity since the molecular weight distribution is also important, but it also provides another opportunity to control the high-pressure response by blending. The first experimental observation of double shear-thinning within a single flow curve is reported. Blending then provides the capability of adjusting not only the Newtonian viscosity but also the non-Newtonian shear-thinning response as well.

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Averaging and integral manifolds

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700041812 ◽

1970 ◽

Vol 2 (2) ◽

pp. 197-222 ◽

Cited By ~ 16

Author(s):

W. A. Coppel ◽

K. J. Palmer

Keyword(s):

Autonomous System ◽

Method Of Characteristics ◽

Integral Manifold ◽

Artificial Viscosity ◽

Original Method ◽

Method Of Averaging ◽

System Of Differential Equations ◽

Viscosity Term ◽

Integral Manifolds ◽

The Individual

An integral manifold for a system of differential equations is a manifold such that any solution of the equations which has a point on it is entirely contained on it. The method of averaging establishes the existence of such a manifold for a system which is a perturbation of an autonomous system with a periodic orbit. The existence of the manifold is established here under more general hypotheses, namely for perturbations which are ‘integrally small’. The method differs from the original method of Bogolyubov and Mitropolskii and operates directly with the individual solutions. This is made possibly by the use of an appropriate norm, and is equivalent to solving the partial differential equation which occurs in work by Moser and Sacker by the method of characteristics rather than by the introduction of an artificial viscosity term. Moreover, detailed smoothness properties of the manifold are obtained. For periodic perturbations the integral manifold is a torus and these smoothness properties are just sufficient to permit the application of Denjoy's theorem.

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Spiral Shocks in Accretion Disks with SPH

International Astronomical Union Colloquium ◽

10.1017/s025292110004389x ◽

1997 ◽

Vol 163 ◽

pp. 770-770

Author(s):

James Rhys Murray

Keyword(s):

Accretion Disks ◽

Equations Of Motion ◽

Fixed Ratio ◽

Artificial Viscosity ◽

Spiral Density Waves ◽

Viscosity Term ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

Low Mass ◽

Continued Use

AbstractSmoothed Particle Hydrodynamics (SPH) is now seen as a numerical scheme well suited to the study of accretion disks. SPH simulations have been conducted of cataclysmic variable disks (Lubow 1991, Murray 1996, Armitage and Livio 1996), galactic disks (Artymowicz and Lubow 1989), and protostellar disks (Artymowicz and Lubow 1994). It is therefore important to test the technique against theory and other numerical results to obtain an estimate of the accuracy and reliability of SPH in this context. Previously SPH has been tested against standard stationary and time-dependent results of viscous thin disk theory (Murray 1996). Strictly these tests relate to disks where ‘viscous’ terms dominate pressure terms in the equations of motion.In this paper we describe tests of the code more appropriate for hot disks where pressure forces are relatively more important than viscosity. Specifically we consider the form of the spiral density waves that can be excited in a disk by a perturbing gravitational potential. Very low mass perturbing bodies excite linear spiral waves which redistribute angular momentum in the disk. For increasingly massive perturbers, the disk response becomes nonlinear and eventually shocks form. In the standard formulation of SPH, an artificial viscosity term is added to the SPH equations to improve shock capture. This is equivalent to introducing a fixed ratio of shear to bulk viscosity into the equations of motion. In Eulerian schemes, artificial viscosity has been discarded in favour of other more accurate, less dissipative schemes for resolving shocks. The continued use of artificial viscosity in SPH has become a source of ‘friction’ between numericists. The simulations described here demonstrate the scheme’s ability to resolve spiral shocks, and show that SPH is a valuable tool for probing the structure of tidally perturbed accretion disks.

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Robust Schemes Based on the Method of Lines for Shock Capturing

Zeitschrift für Naturforschung A ◽

10.1515/zna-2014-0140 ◽

2015 ◽

Vol 70 (1) ◽

pp. 47-58 ◽

Cited By ~ 1

Author(s):

Mohamed M. Mousa

Keyword(s):

Method Of Lines ◽

Strong Shock ◽

Artificial Viscosity ◽

Shock Capturing ◽

Test Problems ◽

Hyperbolic Conservation ◽

Hyperbolic Conservation Law ◽

Viscosity Term ◽

The Method Of Lines ◽

Strong Shock Waves

AbstractIn this paper, the solution of nonlinear hyperbolic conservation law problems containing strong shock waves is presented using the method of lines. A difficulty with the method of lines, as with many other classical shock-capturing methods, is the threat of unphysical numerical oscillations, which can be avoided by adding an artificial viscosity term. Two schemes of the method of lines for solving the described problems have been proposed. Extensive numerical examples in both scalar and system test problems demonstrate the efficiency, robustness, and ease of implementation of the proposed schemes.

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Application of artificial viscosity in establishing supercritical solutions to the transonic integral equation

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1982.0031 ◽

1982 ◽

Vol 380 (1778) ◽

pp. 77-97

Keyword(s):

Integral Equation ◽

Transonic Flow ◽

Iterative Scheme ◽

Artificial Viscosity ◽

Linear Solution ◽

Number Range ◽

Flow Equations ◽

Viscosity Term ◽

Initial Iterate ◽

Shock Fitting

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, ‘sharp-shock solutions’ have also been obtained by the implementation of a quadratic iterative scheme with the ‘artificial viscosity solution’ as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

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Theoretical Analysis and Simulation of Airflow of Super High-Speed Grinding Wheel

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.329.507 ◽

2007 ◽

Vol 329 ◽

pp. 507-510 ◽

Cited By ~ 2

Author(s):

Ya Dong Gong ◽

H. Li ◽

Guang Qi Cai

Keyword(s):

High Speed ◽

Particle Image ◽

Viscosity Coefficient ◽

Artificial Viscosity ◽

Boundary Layer Theory ◽

Grinding Wheel ◽

Continuous Analysis ◽

High Speed Grinding ◽

Airflow Field ◽

Solving Strategy

The airflow field of super-high speed grinding was analyzed in the paper and the method of computing and analyzing the distribution of the field has been brought forward by applying boundary layer theory. Adopting the method of finite element, the model of airflow field in the 3-D grinding zone has been built up by using software; the solving strategy and the boundary conditions has been defined, where artificial viscosity coefficient in the repetitive and continuous analysis and the method by applying inertia relaxation have been discussed, which helped to revolve stability. The results of simulation was given and analyzed, which can be validated with experiment by using the equipment of PIV (particle image of velocity).

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Unsteady modelling of cavitating flow with artificial viscosity

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1549 ◽

2009 ◽

Vol 224 (1) ◽

pp. 123-132 ◽

Cited By ~ 2

Author(s):

N M Nouri ◽

M Moghimi ◽

S M H Mirsaeedi

Keyword(s):

Numerical Solutions ◽

Stokes Equations ◽

Artificial Viscosity ◽

Navier Stokes ◽

Cavitating Flows ◽

Governing Equations ◽

Navier Stokes Equations ◽

Dissipation Term ◽

Viscosity Term ◽

Cavity Characteristics

In this study, a simple model for two-dimensional (2D) cavitating flows with artificial viscosity is proposed. The governing equations are the unsteady incompressible viscous Navier—Stokes equations. The proposed method includes the combination of a source and a sink of vapour through a dissipation term. The comparison between the obtained numerical results for a 2D wedge and the numerical solutions and experimental data shows that the cavity characteristics are well simulated. It can be concluded that introducing an artificial viscosity term improves both the numerical stability and the convergence rate.

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Analisis Daya Dukung Tanah Dan Bahan Pondasi Tiang Pancang Pada Pembangunan Jembatan Kab. Jombang

Jurnal Intake : Jurnal Penelitian Ilmu Teknik dan Terapan ◽

10.32492/jintake.v9i1.757 ◽

2020 ◽

Vol 9 (1) ◽

pp. 32-37

Author(s):

Ruslan Hidayat ◽

Saiful Arfaah

Keyword(s):

Carrying Capacity ◽

Pile Foundation ◽

Heavy Traffic ◽

Traffic Volume ◽

Material Strength ◽

Cone Penetrometer ◽

The Village

One of the most important factors in the structure of the pile foundation in the construction of the bridge is the carrying capacity of the soil so as not to collapse. Construction of a bridge in the village of Klitik in Jombang Regency to be built due to heavy traffic volume. The foundation plan to be used is a pile foundation with a diameter of 50 cm, the problem is what is the value of carrying capacity of soil and material. The equipment used is the Dutch Cone Penetrometer with a capacity of 2.50 tons with an Adhesion Jacket Cone. The detailed specifications of this sondir are as follows: Area conus 10 cm², piston area 10 cm², coat area 100 cm², as for the results obtained The carrying capacity of the soil is 60.00 tons for a diameter of 30 cm, 81,667 tons for a diameter of 35 cm, 106,667 tons for a diameter of 40 cm, 150,000 tons for a diameter of 50 cm for material strength of 54,00 tons for a diameter of 30 cm, 73,500 tons for a diameter of 35 cm, 96,00 tons for a diameter of 40 cm, 166,666 tons for a diameter of 50 cm

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