Structure of the self-gravitating accretion discs in the presence of outflow

2020 ◽  
Vol 496 (1) ◽  
pp. 434-441
Author(s):  
Hanifeh Ghanbarnejad ◽  
Maryam Ghasemnezhad
Keyword(s):  
Cooling Rate ◽  
Time Scale ◽  
Energy Equation ◽  
Numerical Solutions ◽  
The Self ◽  
Accretion Discs ◽  
Lower Latitude ◽  
Dynamical Time ◽  
Free Constant ◽  
Basic Equations

ABSTRACT Numerical simulations of self-gravitating accretion discs have shown that the evolution of such systems depends strongly on the rate at which it cools. In this work, we study the vertical structure of the self-gravitating accretion discs and also investigate the effect of the cooling rate on the latitudinal structure of such accretion discs. In the spherical coordinates, we write the hydrodynamics equations and simplify the basic equations based on the assumptions of axisymmetric and steady state. We use the self-similar method for solving the equations in the radial direction and we find proper boundary conditions. We find inflow–outflow solutions by considering the meridional component of the velocity field. In order to formulate the cooling term in energy equation, we introduce the new parameter β as a free constant that is the cooling time-scale in units of the dynamical time-scale. Our numerical solutions show that the thickness of the disc decreases with smaller β (or increasing the cooling term in energy equation) and it makes the disc colder and outflows form in the regions with lower latitude. So by increasing the cooling rate in the disc, the regions which belong to inflow decrease.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals The calculation of building cooling under emergency conditions to ensure their heating reliability

Vestnik MGSU ◽  
2019 ◽  
pp. 496-501 ◽  
Author(s):  
Oleg D. Samarin
Keyword(s):  
Cooling Rate ◽  
Heat Supply ◽  
Structural Characteristics ◽  
Initial Period ◽  
Residential Building ◽  
Climatic Conditions ◽  
Time Interval ◽  
Basic Equations ◽  
Building Cooling ◽  
Air Exchange

Introduction. Continuation of research in the area of premise cooling rate calculation with the aim of obtaining dependencies, which are sufficiently accurate and take into account the most of the factors essential for the problem, but at the same time having an engineering form, is still relevant. The purpose of the study is the search for a dependence of the temperature in the building premises on time in the initial period after heat supply shutdown at emergency mode. Exponential nature of this dependence is considered as a scientific hypothesis. Materials and methods. The basic equations connecting the most important components of a heat flow in a cooling room under condition of the termination of heat supply from heating devices are used and analysed in the study. A numerical model of non-stationary thermal regime of the ventilated room is implemented on the base of the solution of a differential equations system of heat conduction and heat transfer on the surfaces of the room. Results. An analytical expression is obtained for the room cooling rate when the heat supply is disconnected, which has the form of an exponential function of square root of time since the accident. The cooling time before the condensation on the inner surface of the enclosure is determined by the example of a currently existing residential building under climatic conditions of Moscow, accounting the structural characteristics of the building and normalized fresh-air flow rate. Conclusions. It is shown that the building cooling in the initial period is influenced mainly by the ratio of the heat flux associated with unorganized air exchange and the heat loss to the environment through “light” enclosure. It was found that the decrease of natural air exchange in the building cooling process leads to a certain slowdown in the decrease of temperature, but it is not decisive. It is understood that the use of airtight light opening fillers, for example, in plastic casement, under normal conditions aggravating the sanitary and hygienic situation in the premises, under emergency conditions increases the available time interval for the restoration of heat supply.

scholarly journals A general-purpose time-step criterion for simulations with gravity

2020 ◽  
Vol 495 (4) ◽  
pp. 4306-4313 ◽  
Author(s):  
Michael Y Grudić ◽  
Philip F Hopkins
Keyword(s):  
Time Scale ◽  
General Purpose ◽  
Gravitational Acceleration ◽  
Time Step ◽  
Simulation Code ◽  
Time Stepping ◽  
Dynamical Time ◽  
Adaptive Time Step ◽  
Order Of Magnitude ◽  
True Time

ABSTRACT We describe a new adaptive time-step criterion for integrating gravitational motion, which uses the tidal tensor to estimate the local dynamical time-scale and scales the time-step proportionally. This provides a better candidate for a truly general-purpose gravitational time-step criterion than the usual prescription derived from the gravitational acceleration, which does not respect the equivalence principle, breaks down when $\boldsymbol {a}=0$, and does not obey the same dimensional scaling as the true time-scale of orbital motion. We implement the tidal time-step criterion in the simulation code gizmo, and examine controlled tests of collisionless galaxy and star cluster models, as well as galaxy merger simulations. The tidal criterion estimates the dynamical time faithfully, and generally provides a more efficient time-stepping scheme compared to an acceleration criterion. Specifically, the tidal criterion achieves order-of-magnitude smaller energy errors for the same number of force evaluations in potentials with inner profiles shallower than ρ ∝ r−1 (i.e. where $\boldsymbol {a}\rightarrow 0$), such as star clusters and cored galaxies. For a given problem these advantages must be weighed against the additional overhead of computing the tidal tensor on-the-fly, but in many cases this overhead is small.

Analysis of Heat Conduction in a Heterogeneous Material by a Multiple-Scale Averaging Method

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
James White
Keyword(s):  
Heat Conduction ◽  
Thermal Energy ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Three Dimensional ◽  
Heterogeneous Material ◽  
Multiple Scale ◽  
Computational Effort ◽  
Short Scale

In order to better manage computational requirements in the study of thermal conduction with short-scale heterogeneous materials, one is motivated to arrange the thermal energy equation into an accurate and efficient form with averaged properties. This should then allow an averaged temperature solution to be determined with a moderate computational effort. That is the topic of this paper as it describes the development using multiple-scale analysis of an averaged thermal energy equation based on Fourier heat conduction for a heterogeneous material with isotropic properties. The averaged energy equation to be reported is appropriate for a stationary or moving solid and three-dimensional heat flow. Restrictions are that the solid must display its heterogeneous properties over short spatial and time scales that allow averages of its properties to be determined. One distinction of the approach taken is that all short-scale effects, both moving and stationary, are combined into a single function during the analytical development. The result is a self-contained form of the averaged energy equation. By eliminating the need for coupling the averaged energy equation with external local problem solutions, numerical solutions are simplified and made more efficient. Also, as a result of the approach taken, nine effective averaged thermal conductivity terms are identified for three-dimensional conduction (and four effective terms for two-dimensional conduction). These conductivity terms are defined with two types of averaging for the component material conductivities over the short-scales and in terms of the relative proportions of the short-scales. Numerical results are included and discussed.

Numerical solutions for the spin-up of a stratified fluid

1982 ◽  
Vol 117 ◽  
pp. 71-90 ◽  
Author(s):  
Jae Min Hyun ◽  
William W. Fowlis ◽  
Alex Warn-Varnas
Keyword(s):  
Time Scale ◽  
Numerical Solutions ◽  
Side Wall ◽  
Stratified Fluid ◽  
Meridional Flow ◽  
Laser Doppler Velocimeter ◽  
Numerical Work ◽  
Diffusion Effects ◽  
Rate Of Decay ◽  
Flow Gradients

Numerical solutions for the impulsively started spin-up of a thermally stratified fluid in a cylinder with an insulating side wall are presented. Previous experimental and numerical work on stratified spin-up had not provided a comprehensive and accurate set of flow-field data. Further, comparisons of this work with theory showed, in general, a substantial discrepancy. The theory was scaled using the homogeneous meridional-flow spin-up time scale and thus viscous-diffusion effects were excluded from the interior. It was anticipated that these effects could only be significant on the larger viscous-diffusion time scale. However, the comparisons with theory showed a faster rate of decay for the measurements even over the shorter meridional-flow spin-up time scale. Previous workers had suggested a number of explanations but the cause of the discrepancy was still unresolved. To provide data to extend the previous work, a numerical model was used. The model was first checked against accurate experimental measurements of stratified spin-up made using a laser-Doppler velocimeter. New accurate results which cover ranges of Ekman number (5·92 × 10−4 ≤ E ≤ 7·24 × 10−4), Rossby number (0·019 ≤ ε ≤ 0·220), stratification parameter (0·0 ≤ Sa−1 ≤ 1·03), and Prandtl number (5·68 ≤ σ ≤ 7·10) are presented. These results show the radial and vertical structure of the decaying azimuthal and meridional flows. The inertial–internal gravity oscillations excited by the impulsive spin-up are clearly seen. By making use of conclusions from the previous work and the results presented in this paper, it is established that viscous diffusion in the interior is the cause of the discrepancy with theory. Stratification causes the meridional spin-up flow to be confined closer to the boundary disks. This results in non-uniform spin-up of the interior and hence flow gradients in the interior. These gradients introduce viscous diffusion into the interior sooner than anticipated by the theory. A previous suggestion that the faster decay rate is due to angular momentum being injected into the interior from an oscillation of the meridional corner-jet flow is shown to be untenable.

Numerical study of toroidal magnetic field on the self-gravitating protoplanetary disks

2020 ◽  
Vol 29 (09) ◽  
pp. 2050067
Author(s):  
Hanifeh Ghanbarnejad ◽  
Maryam Ghasemnezhad
Keyword(s):  
Magnetic Field ◽  
Accretion Disks ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Ohmic Heating ◽  
The Self ◽  
Toroidal Magnetic Field ◽  
Heating Process ◽  
Heating And Cooling ◽  
The Magnetic Field

In this paper, we study the self-gravitating accretion disks by considering the toroidal component of magnetic field, [Formula: see text] and wind/outflow in the flow and also investigate the effect of two parameters, [Formula: see text] and [Formula: see text] corresponding to magnetic field on the latitudinal structure of such accretion disks. The cooling of the disk is parameterized simply as, [Formula: see text] (where [Formula: see text] is the internal energy and [Formula: see text] is the cooling timescale and [Formula: see text] is a free constant) and the heating rate is decomposed into two components, magnetic field and viscosity dissipations. We have shown that when the toroidal magnetic field becomes stronger, the heating process (viscous and resistivity) and the radiative cooling rate increase. Ohmic heating is much bigger than viscous heating and cooling, so we must consider the role of the magnetic field in the energy equation. Our numerical solutions show that the thickness of the disk decreases with strong toroidal component of magnetic field. The magnetic field leads to production of the outflow in the low latitude. So, by increasing the toroidal component of the magnetic field, the regions which belong to inflow decrease and the disk is cooled.

scholarly journals End Products of Cometary Evolution: Cometary Origin of Earth-Crossing Bodies of Asteroidal Appearance

1989 ◽  
Vol 116 (1) ◽  
pp. 537-556 ◽  
Author(s):  
G.W. Wetherill
Keyword(s):  
Time Scale ◽  
Large Fraction ◽  
Volatile Component ◽  
Cometary Nucleus ◽  
Short Period ◽  
Deep Earth ◽  
Dynamical Time ◽  
Time Required ◽  
Almost All ◽  
Cometary Origin

AbstractBecause there is no necessary connection between the time required to remove the volatile component of a cometary nucleus by solar heating (physical lifetime) and the dynamical lifetime of a comet, it is possible that a comet may evolve into an observable object of asteroidal appearance. Almost all comets have dynamical lifetimes much shorter than their physical lifetimes and in these cases complete loss of volatiles will not occur. Mechanisms do exist, however, whereby a small but significant fraction of comets will have longer dynamical lifetimes, permitting them to evolve first into Jupiter-family short period comets and then into comets with relatively safe decoupled orbits interior to Jupiter’s orbit. Observed Jupiter-family objects of asteroidal appearance (e.g., 1983SA) are much more likely to be of cometary rather than asteroidal origin. “Decoupling” is facilitated by several mechanisms: perturbations by the terrestrial planets, perturbations by Jupiter and the other giant planets (including resonant perturbations) and non-gravitational orbital changes caused by the loss of gas and dust from the comet. The dynamical time scale for decoupling is probably 105–106 years and almost all decoupled comets are likely to be of asteroidal appearance. Once decoupled, the orbits of the resulting Apollo-Amor objects will evolve on a longer (107–108 year) time scale, and the orbital evidence for these objects having originally been comets rather than asteroids will nearly disappear. Statistically, however, a large fraction of the bodies in deep Earth-crossing orbits with semi-major axes ≳ 2.2 AU are likely to be cometary objects in orbits that have not yet diffused into the steady state distribution. For plausible values of the relevant parameters, estimates can be made of the number of cometary Apollo-Amor “asteroids,” the observed number of Earthcrossing active and inactive short period comets, and the production rate of short period comets. These estimates are compatible with other theoretical and observational inferences that suggest the presence of a significant population of Apollo objects that formerly were active comets.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

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