Statistics – Computation
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..795m&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Statistics
Computation
Scientific paper
This work deals with protoplanetary system computational modeling and protoplanets forming based on modern program packages. Pictures of fields for pressure and velocity into a gravitating and rotating gas-dust cloud (around a protostar) are obtained. This work shows that evolution of rotating gas-dust cloud forms planetary bunches (or planetary embryos) in the centrally symmetric gravitational field. This work also develops an analysis of hydrodynamic flows into a rotating protoplanetary cloud [1] with usage of nonlinear dynamics methods based on the matrix decomposition in the state-space [2] and the fractal-topological methods [3]. The computer simulation of hydrodynamic flows is carried out by means of program package STAR-CD [4]. The system of differential equations in partial derivatives containing the Navier-Stokes and continuity equations in cylindrical coordinates is investigated. Let us represent velocity field as a sum of basic flow velocity V (satisfying the Navier-Stokes equation) and disturbance of velocity v' . Taking into account these simplifications we obtain the equation system relatively components of velocity disturbance v' = (u',v',w' ) . The system of partial differential equations modeling the hydrodynamic processes in the vortex flow is reduced to the system of ordinary differential equations (describing an attractor) based on the Galerkin's method. Taking into account the continuity equation the form of u' - and w' - functions is chosen. The similar attractor of this system has been obtained in [5]. Then the fractal-topological characteristics of this attractor are investigated using matrix decomposition methods [2], [3]. The obtained results of analysis are in accord with the computational simulation. References: [1] Schlichting H. Grenzschicht-Theorie. Verlag G Braun, Karlsruhe, 1970. [2] Krot A.M. Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system. Nonlinear Phenomena in Complex Systems, vol. 4, no.2, pp. 106-115, 2001. [3] Krot A.M. and Minervina H.B. Minimal attractor embedding estimation based on matrix decomposition for analysis of dynamical systems. Nonlinear Phenomena in Complex Systems, vol.5, no.2, pp.161-172, 2002. [4] Methodology for STAR-CD: Version 3.24, Computational Dynamics Limited, 2004. [5] Baldin V.A., Krot A.M. and Minervina H.B. The development of model for boundary layers past a concave wall with usage of nonlinear dynamics methods. Advances in Space Research, vol. 37, no. 3, pp. 501-506, 2006.
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