The large-scale structure of the Universe in the frame of the model equation of non-linear diffusion

Гурбатов, С. Н.; Саичев, А. И.; Shandarin, Sergei F.

doi:10.1093/mnras/236.2.385

Cited by 253 publications

(322 citation statements)

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“…Finally, in the case of the transformation Λ being dynamical, i.e., in which functions a(t) and ω(t) are no longer free parameters but instead are uniquely determined by global distributions of density, pressure, etc., it may be possible to achieve invariance of fluid equations for a broader class of transformations than the one discussed above (see also [21]). Moreover, certain systems may admit asymptotic invariance of the equations.…”

Section: Equation Invariance and Conservative Formulationmentioning

confidence: 99%

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

Poludnenko

Khokhlov

2007

Journal of Computational Physics

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We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame motion is adjusted to minimize local fluid velocities. Such approach allows to accommodate very efficiently large degrees of change in the flow extent. Moreover, by excluding the contribution of the bulk flow to the total energy the method eliminates the high Mach number problem in the flows of interest. An important practical advantage of the method is that it can be easily implemented with virtually any implicit or explicit Eulerian hydrodynamic scheme and adaptive mesh refinement (AMR) strategy.We also consider in detail equation invariance and existence of conservative formulation of equations for special classes of expanding/contracting reference frames. Special emphasis is placed on extensive numerical testing of the method for a variety of reference frame motions, which are representative of the realistic applications of the method. We study accuracy, conservativity, and convergence properties of the method both in problems which are not its optimal applications as well as in systems in which the use of this method is maximally beneficial. Such detailed investigation of the numerical solution behavior is used to define the requirements that need to be considered in devising problem-specific fluid motion feedback mechanisms.

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Section: Equation Invariance and Conservative Formulationmentioning

confidence: 99%

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

Poludnenko

Khokhlov

2007

Journal of Computational Physics

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“…The density field then becomes singular and the Zeldovich approximation approximation breaks down. There are extensions to the Zeldovich approximation that overcome this problem; for example, the adhesion approximation (Gurbatov et al 1989). This method, together with other methods of its ilk, share some of the attractive features of the wave-mechanical approximation we now describe.…”

Section: The Zeldovich Approximationmentioning

confidence: 99%

“…It is also plays a similar role to the viscosity parameter that appears in the adhesion approximation and which transforms the Euler equation into the Burgers equation. This is due to the fact that the Madelung transformation we employ here is mathematically related to the Hopf-Cole transformation needed to solve the Burgers equation; see Gurbatov et al (1989) for a further discussion of this point. For the behaviour of our fluid to be entirely classical, we require ν to be as small as possible in which case we intuitively expect the quantum pressure term to be negligible.…”

Section: The Wave-mechanical Approachmentioning

confidence: 99%

Gravitational instability via the Schrödinger equation

Short¹,

Coles²

2006

J. Cosmol. Astropart. Phys.

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Abstract. We study an approach to the formation of large-scale structure in the universe based on the description of a self-gravitating fluid in terms of a Schrödinger equation coupled to the usual Poisson equation. This approach has a number of promising features, but also some peculiarities. In this exploratory paper we discuss the behaviour of perturbations of the Schrödinger-Poisson system in simple one-dimensional configurations and compare the results with more conventional approaches: linear perturbation theory of the fluid equations and the Zeldovich approximation. The results demonstrate that our approach furnishes a useful addition to the repertoire of analytical techniques available for the description of cosmological perturbations, but that there are a number of subtleties to be faced when this method is applied in practice. In particular, care must be taken in choosing appropriate values for the effective Planck constant in the theory.PACS numbers: 95.35.+d, 98.65.Dx, Submitted to: J. Cosmol. Astropart. Phys.

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“…On the other hand, replacing P by a term of the form µ∇ 2 x φ leads to Burgers' equation [25] for the case of an irrotational velocity field; this is the defining equation of the adhesion model (e.g. [7]). The term µ∇ 2 x φ prevents the formation of multi-stream regions and regularizes the density singularities predicted by the Zeldovich approximation.…”

Section: The Free-particle Approximationmentioning

confidence: 99%

Wave mechanics and the adhesion approximation

Short

Coles

2006

J. Cosmol. Astropart. Phys.

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Abstract. The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrödinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrödinger equation can be reduced to the exactly solvable free-particle Schrödinger equation. The free-particle Schrödinger equation forms the basis of a new approximation scheme -the free-particle approximation -that is capable of evolving cosmological density perturbations into the quasi-linear regime. The free-particle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a non-linear term known as the quantum pressure. Simple one-dimensional tests of the free-particle method have yielded encouraging results. In this paper we comprehensively test the free-particle approximation in a more cosmologically relevant scenario by appealing to an N -body simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the free-particle approximation comprehensively out-performs both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales. PACS numbers: 95.35.+d, 98.65.Dx, Submitted to: J. Cosmol. Astropart. Phys.

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The large-scale structure of the Universe in the frame of the model equation of non-linear diffusion

Cited by 253 publications

References 0 publications

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

Gravitational instability via the Schrödinger equation

Wave mechanics and the adhesion approximation

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