Dominant Advection Research Articles

Radiation from Advection-Dominated Flows

Advection-dominated accretion flow (hereafter ADAF) is the only self-consistent solution to describe the optically thin accretion flows around compact objects. The main feature of ADAF is that the dynamics of the flow is dominated by accretion process rather than radiation process. As a result of advection domination, the luminosity of ADAFs is very low. Coupled with the existence of the event horizon, ADAF has been successfully applied to the dim accretion black holes such as central core of our Galaxy: Sgr A*. In this issue, we calculate the spectrum radiated from the optically thin ADAFs and show that the observed spectrum of Sgr A* is explained with the accretion massive black hole.

Spectrum of Optically Thin Advection‐dominated Accretion Flow around a Black Hole: Application to Sagittarius A*

The global structure of optically thin advection-dominated accretion flows composed of two-temperature plasma around black holes is calculated. We adopt the full set of basic equations, including the advective energy transport in the energy equation for the electrons. The spectra emitted by the optically thin accretion flows are also investigated. The radiation mechanisms that are taken into account are bremsstrahlung, synchrotron emission, and Comptonization. The calculation of the spectra and that of the structure of the accretion flows are made to be completely consistent by calculating the radiative cooling rate at each radius. As a result of the advection domination for the ions, the heat transport from the ions to the electrons becomes practically zero, and the radiative cooling balances with the advective heating in the energy equation of the electrons. Following up on the successful work of Narayan et al., we applied our model to the spectrum of Sgr A*. We find that the spectrum of Sgr A* is explained by the optically thin advection-dominated accretion flow around a black hole of mass MBH = 106 M☉. The parameter dependence of the spectrum and the structure of the accretion flows is also discussed.

Is the Accretion Flow in NGC 4258 Advection Dominated?

The mass of the central black hole in the active galaxy NGC 4258 (M106) has been measured to be $M=3.6\times10^7\Msun$ (Miyoshi et al. 1995). The Eddington luminosity corresponding to this mass is $L_E=4.5\times10^{45}$ erg s$^{-1}$. By contrast the X-ray luminosity of the nucleus of NGC 4258 between $2-10$ keV is $(4\pm 1)\times10^{40}~{\rm erg\,s^{-1}}$ while the optical/UV luminosity is less than $1.5\times10^{42} ~{\rm erg\,s^{-1}}$. The luminosity of NGC 4258 is therefore extremely sub-Eddington, $L\sim10^{-5}L_E$ in X-rays and $L\sim3\times10^{-4} L_E$ even if we take the maximum optical/UV luminosity. Assuming the usual accretion efficiency of 0.1 would imply accretion rates orders of magnitude lower than in Seyfert galaxies and quasars. We show that the properties of the AGN in NGC 4258 can be explained by an accretion flow in the form of a very hot, optically-thin plasma which advects most of the viscously generated thermal energy into the central black hole and radiates only a small fraction of the energy. In this case the accretion rate in Eddington units could be as high as $\sim 0.16\alpha$, where $\alpha$ is the standard viscosity parameter; and the size of the hot disk should be larger than $\sim 10$ times the Schwarzschild radius. We compare the predictions of this model with observations and discuss its application to other low luminosity AGN.

Parallel fluid dynamics computations in aerospace applications

AbstractMassively parallel finite element computations of the compressible Euler and Navier‐Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables and the streamline‐upwind/Petrov‐Galerkin (SUPG) stabilization method is used to prevent potential numerial oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large‐scale 3D problems are solved using a matrix‐free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation and the ones involving moving boundaries are solved using the deformable‐spatial‐domain/stabilized‐space‐time (DSD/SST) formulation.

Wave equation model for solving advection-diffusion equation

This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator-splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first-order advection equation, the present wave equation model solves a second-order equivalent wave equation whose solution is identical to that of the first-order advection equation. Numerical examples of 1-D and 2-D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1-D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.

Computing brine transport in porous media with an adaptive‐grid method

AbstractAn adaptive‐grid finite‐difference method is applied to a model for non‐isothermal, coupled flow and transport of brine in porous media. In the vicinity of rock salt formations the salt concentration in the fluid becomes large, giving rise to disparate scales in the salt concentrations profiles. A typical situation one encounters is that of a sharp freshwater‐saltwater interface that moves in time. In such situations adaptive‐grid methods are more effective than standard fixed‐grid methods, since they refine the space grid locally and, hence, provide for substantial reduction in the number of grid points, memory use and CPU time. The adaptive‐grid method of this paper is a static, local uniform grid refinement method. Its main feature is that it integrates on nested sequences of locally uniformly refined Cartesian space grids, which are automatically adjusted in time to follow rapid spatial transitions. Variable time steps are used to cope with rapid temporal transitions, including a fast march to possible steady‐state solutions. For time stepping, the implicit, second‐order BDF scheme is used. Two specific example problems are numerically illustrated. The main physical properties involved here are advection and dispersion and in case of dominant advection sharp freshwater‐saltwater interfaces arise.

An advective mixed-layer model for heat and moisture incorporating an analytic expression for moisture entrainment

A slab mixed-layer model with zero-order entrainment for both temperature and humidity is developed in order to examine the relative magnitude of advective and turbulence flux convergence effects. The model formulation provides an analytic function for the ratio of surface-layer to entrainment-layer humidity flux. Model results are compared with measured mixed-layer properties over one day at a coastal location. It is concluded that the model is highly successful at simulating the mixed-layer depth, and mean mixed-layer humidity. It is suggested that a first-order model may be more appropriate for the latter half of the day when the mixed-layer depth is decreasing due to the dominance of advection over vertical turbulence flux convergence.

The shearless turbulence mixing layer

The interaction of two energy-containing turbulence scales is studied in the absence of mean shear. The flow, a turbulence mixing layer, is formed in decaying grid turbulence in which there are two distinct scales, one on either side of the stream. This is achieved using a composite grid with a larger mesh spacing on one side of the grid than the other. The solidity of the grid, and thus the mean velocity, is kept constant across the entire flow. Since there is no mean shear there is no turbulence production and thus spreading is caused solely by the fluctuating pressure and velocity fields. Two different types of grids were used: a parallel bar grid and a perforated plate. The mesh spacing ratio was varied from 3.3:1 to 8.9:1 for the bar grid, producing a turbulence lengthscale ratio of 2.4:1 and 4.3:1 for two different experiments. For the perforated plate the mesh ratio was 3:1 producing a turbulence lengthscale ratio of 2.2:1. Cross-stream profiles of the velocity variance and spectra indicate that for the large lengthscale ratio (4.3:1) experiment, a single scale dominates the flow while for the smaller lengthscale ratio experiments, the energetics are controlled by both lengthscales on either side of the flow. In all cases the mixing layer is strongly intermittent and the transverse velocity fluctuations have large skewness. The downstream data of the second, third and fourth moments for all experiments collapse well using a single composite lengthscale. The component turbulent energy budgets show the importance of the triple moment transport and pressure terms within the layer and the dominance of advection and dissipation on the outer edge. It is also shown that the bar grids tend toward self-similarity with downstream distance. The perforated plate could not be measured to the same downstream extent and did not reach self-similarity within its measurement range. In other respects the two types of grids yielded qualitatively similar results. Finally, we emphasize the distinction between intermittent turbulent penetration and turbulent diffusion and show that both play an important role in the spreading of the mixing layer.

A new numerical approach for the advective‐diffusive transport equation

AbstractA new numerical solution procedure is presented for the one‐dimensional, transient advective‐diffusive transport equation. The new method applies Herrera's algebraic theory of numerical methods to the spatial derivatives to produce a semi‐discrete approximation. The semi‐discrete system is then solved by standard time marching algorithms. The algebraic theory, which involves careful choice of test functions in a weak form statement of the problem, leads to a numerical approximation that inherently accommodates different degrees of advection domination. Algorithms are presented that provide either nodal values of the unknown function or nodal values of both the function and its spatial derivative. Numerical solution of several test problems demonstrates the behavior of the method.

A theoretical evaluation of the influence of mechanical variables on the concentration of oxygen in a corrosion fatigue crack

The oxygen concentration in a corrosion fatigue crack has been evaluated theoretically assuming that oxygen was consumed by cathodic reduction on the walls of the crack and mass transport occurred by diffusion and advection (forced convection) with the latter resulting from the sinusoidal variation of the displacement of the crack walls. Using parameters relevant to a compact tension specimen the time-dependent distribution of the oxygen concentration in the crack was calculated as a function of ΔK (the range of the stress intensity factor), R-value (minimum load/maximum load), frequency, crack length and electrode potential (within the constraint of no significant potential drop in the crack). The influence of advection was to enhance significantly the mass transport of oxygen in the crack compared to “diffusion-only” even at low frequencies and low values of ΔK. Regions in the crack were identified in which advection dominance or diffusion dominance of the mass transport of oxygen occurred.

Dispersion of active pollutants in a shallow sea

Shallow coastal seas are the "priviledged" places for the dumping of wastes of all kinds: sewage, mud re leases, and chemical refuses are typical examples. In most cases, the shallow coastal seas are therefore very polluted. This paper describes a digital simu lation of the diffusion and transportation of pollu tants released in the shallow sea bordering Belgium. The model of course has much wider application. The principal new development in this paper is the method of integration of equations which describe such systems. The equations of the model have dominant advection terms, mixed derivatives, and nonlinear interaction terms, and are solved by a special predictor- corrector scheme consisting of three distinct steps. The mixed derivative is separated into second deri vatives along the grid axes and an auxiliary axis. The first two steps (implicit and locally one-dimen sional) form the predictor. The third one is the corrector, and it yields a consistent discrete approximation of the time derivative. The accuracy is 0(τ2 + τh + h2). A stability condition is derived and some problems in implementing the method are discussed. The paper concludes by presenting the results of a simulation of pollutant dumping in the North Sea near Ostend.

A Predictor-Corrector Method for the Numerical Simulation of Sea Pollution

The behaviour of pollutants in the sea is described by parabolic equations with dominant advection terms, mixed derivatives and non-linear interaction terms; these equations are solved by a special predictor-corrector scheme, consisting of 3 distinct steps. The mixed derivative is split up into second derivatives along the grid axes and an auxiliary axis. The 2 first steps (implicit and locally one dimensional) form the predictor. The third one is the corrector and yields a consistent discrete approximation of the time derivative. The accuracy is O(τ2+τh+h2) and a stability condition is derived.