Applications to Inviscid and Viscous Flows

Hirsch, Charles

doi:10.1016/b978-075066594-0/50054-0

Cited by 65 publications

(101 citation statements)

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“…Our code consists of two parts, a solver of the hydrodynamic equations and of the Poisson equation. The former is based on the flux difference splitting scheme of Roe (1981), and the second-order accuracy is achieved by the monotone upwind scheme for conservation law (MUSCL) method (e.g., Hirsch 1990). We solved the Poisson equation with the five-point central finite difference scheme and the multigrid iteration (see, e.g., Press & Teukolsky 1991).…”

Section: Numerical Methods and Boundary Conditionsmentioning

confidence: 99%

Evolution of First Cores in Rotating Molecular Cores

Saigo

Tomisaka

2006

ApJ

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We investigate the effect of rotation on the star formation process quantitatively using axisymmetric numerical calculations. An adiabatic hydrostatic object (the so-called first core) forms in a contracting cloud core, after the central region becomes optically thick and continues to contract, driven by mass accretion onto it. The structure of a rotating first core is characterized by its total angular momentum J core and mass M core , both of which increase by accretion with time. We find that the first core evolves with a constant J core /M 2 core . Evolutionary paths of first cores can be classified into two types. In a slowly rotating core with J core /M 2 core < 0:015G/( ffiffi ffi 2 p c iso ), where c iso and G represent the isothermal sound speed in the molecular cloud core and the gravitational constant, respectively, the core begins ''second collapse'' after the central density exceeds the H 2 dissociation density. This is the same evolution as a standard scenario for a spherically symmetric, nonrotating core. On the other hand, a core with J core /M 2 core > 0:015G/( ffiffi ffi 2 p c iso ) stops its contraction before the central density reaches the H 2 dissociation density and does not begin the second collapse. These rapidly rotating first cores suffer from nonaxisymmetric instabilities, such as formation of massive spiral arms, deformation into a bar, or fragmentation. Although the rotating first cores have small average luminosities of L core ¼ 0:003 0:03Ṁ core /10 À5 M yr À1 À Á L , assuming a constant mass accretion rateṀ core . Their lifetimes last several thousand years or more, which is much longer than those expected for nonrotating clouds ($1000 yr). We expect that at least several percent of prestellar cores contain first cores as very low luminosity objects. Furthermore, we find a core with 0:012G/( ffiffi ffi 2 p c iso ) < J core /M 2 core < 0:015G/( ffiffi ffi 2 p c iso ) may form close binary systems with initial separation of 0.02-0.1 AU after the second collapse phase.

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Section: Numerical Methods and Boundary Conditionsmentioning

confidence: 99%

Evolution of First Cores in Rotating Molecular Cores

Saigo

Tomisaka

2006

ApJ

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“…A number of methods in the literature [29,30] use density as a primary variable rather than pressure. This practice is especially popular in the compressible flow community.…”

Section: Solution Methodsmentioning

confidence: 99%

“…A variety of limiter functions have been used in the literature, including the minmod, superbee, van Leer, and van Albada limiters [29,30]. The corresponding functional variation is shown in Fig.…”

Section: Flux Limitersmentioning

confidence: 99%

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Survey of Numerical Methods

Murthy

Minkowycz

Sparrow

et al. 2000

Handbook of Numerical Heat Transfer

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“…The method of characteristics provides a rigorous analytical framework for the implementation of boundary conditions in numerical methods [13,14]. If the flow is normal to the boundary and free of shock waves and significant viscous effects, it is governed by the one-dimensional Euler equations for isentropic flow of a calorically perfect gas.…”

Section: Characteristic Theory For Bound-ary Conditionsmentioning

confidence: 99%

Permeable and non‐reflecting boundary conditions in SPH

Lastiwka¹,

Basa²,

Quinlan³

2008

Numerical Methods in Fluids

127

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Inflow and outflow boundary conditions are essential for the application of computational fluid dynamics to many engineering scenarios. In this paper we present a new boundary condition implementation which enables the simulation of flow through permeable boundaries in the Lagrangian mesh-free method Smoothed Particle Hydrodynamics (SPH). Each permeable boundary is associated with an inflow or outflow zone outside the domain, in which particles are created or removed as required.The analytic boundary condition is applied by prescribing the appropriate variables for particles in an inflow or outflow zone, and extrapolating other variables from within the domain. Characteristic-based nonreflecting boundary conditions, described in the literature for mesh-based methods, can be implemented within this framework. Results are presented for simple one-dimensional flows, quasi-one-dimensional compressible nozzle flow, and two-dimensional flow around a cylinder at Reynolds numbers of 40 and 100, and Mach number of 0.1. These results establish the capability of SPH to model flows through open domains, opening a broad new class of applications.

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Applications to Inviscid and Viscous Flows

Cited by 65 publications

References 0 publications

Evolution of First Cores in Rotating Molecular Cores

Evolution of First Cores in Rotating Molecular Cores

Survey of Numerical Methods

Permeable and non‐reflecting boundary conditions in SPH

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