A Combined Variational and Multi-Grid Approach for Fluid Dynamics Simulation

Ophir, Dan; Yahalom, Asher; Pinhasi, Gad A.; Kopylenko, Michael

doi:10.2514/6.2006-695

Cited by 10 publications

(20 citation statements)

References 4 publications

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“…We have also given a formula for the flow helicity in terms of our variational variables and have shown that our variable do not entail trivial helicity and that not only global helicity is conserved but also helicity per unit of vortex flux. The variational principles can clearly be used to obtain new flows using both numerical and analytical techniques and to study their stability as was done with other variational methods in Yahalom (2011), Ophir et al (2012), Yahalom (2013), Arnold (1965a), Arnold (1965b), Katz et al (1993) and Yahalom et al (1994). The reduction in the number of dynamical variables should facilitate such calculations.…”

Section: Resultsmentioning

confidence: 97%

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Variational principles for topological barotropic fluid dynamics

Yahalom

Lynden-Bell

2014

Geophysical & Astrophysical Fluid Dynamics

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Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested (vortex line foliation) with the topology of cylinders, toroids or a combination of both, we show how a Clebsch representation of the flow velocity can be introduced. This is then used to reduce the number of functions to be varied in the variational principles for such flows. We introduce a three function variational formalism for steady and non-steady barotropic flows.

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Section: Resultsmentioning

confidence: 97%

“…Other variational principles were put to use by the authors (Yahalom 2011, Ophir et al 2012 and it is anticipated that the present formalism will enhance possible applications of the variational method.…”

Section: Introductionmentioning

confidence: 99%

Variational principles for topological barotropic fluid dynamics

Yahalom

Lynden-Bell

2014

Geophysical & Astrophysical Fluid Dynamics

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“…As for designing efficient numerical schemes for integrating the equations of fluid dynamics and magnetohydrodynamics one may follow the approach described in Yahalom (2003), Yahalom & Pinhasi (2003), Ophir et al. (2005), Yahalom et al. (2005).…”

Section: Resultsmentioning

confidence: 99%

“…1988; Vladimirov, Moffatt & Ilin 1996, 1997, 1999) and for designing efficient numerical schemes for integrating the equations of fluid dynamics and magnetohydrodynamics (Yahalom 2003; Yahalom & Pinhasi 2003; Ophir et al. 2005; Yahalom, Kopylenko & Pinhasi 2005). Another possible application is connected to obtaining new analytic solutions in terms of the variational variables (Yahalom 2013 b ).…”

Section: Introductionmentioning

confidence: 99%

Simplified variational principles for non-barotropic magnetohydrodynamics

Yahalom

2016

J. Plasma Phys.

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“…It can be easily shown that provided that B is in the form given in equation (17), and equation (18) is satisfied, then both equation (1) and equation (2) are satisfied. Since according to equation (16) both ∇ × B and B are parallel it follows that equation (16) can be written as:…”

Section: Sakurai's Variational Principle Of Force-free Magnetohydrodymentioning

confidence: 99%

Simplified variational principles for barotropic magnetohydrodynamics

2008

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Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of six independent functions for non-stationary barotropic flows and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field B the velocity field v and the density ρ.The equations obtained for non-stationary barotropic magnetohydrodynamics resemble the equations of Frenkel, Levich & Stilman [1]. The connection between the Hamiltonian formalism introduced in [1] and the present Lagrangian formalism (with Eulerian variables) will be discussed.Finally the relations between barotropic magnetohydrodynamics topological constants and the functions of the present formalism will be elucidated.

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A Combined Variational and Multi-Grid Approach for Fluid Dynamics Simulation

Cited by 10 publications

References 4 publications

Variational principles for topological barotropic fluid dynamics

Variational principles for topological barotropic fluid dynamics

Simplified variational principles for non-barotropic magnetohydrodynamics

Simplified variational principles for barotropic magnetohydrodynamics

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