Fluid simulation: combined Lagrangian and multi-grid approach

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

doi:10.1680/eacm.2012.165.1.3

Cited by 4 publications

(2 citation statements)

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“…The theory can also be used to study the evolution of waves with respect to a given MHD configuration, such approach was used by Webb et al (2005) by introducing a Lagrangian variational principle in which the waves are described by displacements from the background MHD configuration. As for designing efficient numerical schemes for integrating the equations of fluid dynamics and MHD, one may follow the approach described in Zhou et al (2014), , Yahalom & Pinhasi (2003), Yahalom et al (2005) and Ophir et al (2012).…”

Section: Resultsmentioning

confidence: 99%

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

Yahalom

Qin

2020

J. Fluid Mech.

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Section: Resultsmentioning

confidence: 99%

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

Yahalom

Qin

2020

J. Fluid Mech.

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“…The first paper, by Ophir et al (2012), presents a hybrid Lagrangian multi-grid method for flow simulation. The variational principle is invoked to obtain the flow field directly from the Lagrangian for steady, irrotational, compressible flow.…”

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confidence: 99%

Editorial

Borthwick¹

2012

Proceedings of the Institution of Civil Engineers - Engineering

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Computer models enable solutions to be obtained for immensely complicated problems in mechanics. As a result, present-day engineers are able to tackle problems well beyond the range of past generations. Examples include the non-linear analysis of complex structures, the simulation of feedback processes in natural systems, the invention of high-tech instruments for biomedical applications, and the exploration of new areas of applied science such as microfluidics. Computers are also used to interpret measured data, to calculate analytical solutions, to postprocess results, etc. Given the ready availability of advanced software, engineers must develop an awareness of the risks posed by error, uncertainty, and model limitations. In particular, it is the professional responsibility of civil engineers to undertake computational analysis and design in a competent manner -and this includes understanding the fundamental mechanics on which computer models are based. Engineers should be able to assess the mathematical and numerical limitations of such models, carry out verification and validation tests, and be knowledgeable about the propagation of uncertainty, the effect of data scarcity, and risk. Although excellent guidelines exist, such as the book by Roache (1998), the Institution of Civil Engineers believes that it is time to review how computer models are applied in practice and how young engineers are educated in order to minimise the associated risk (see Borthwick et al., 2012).Volume 165 Issue EM1 of Engineering and Computational Mechanics contains seven full papers, covering advances in fluid mechanics, water-sediment mechanics, discrete particle interactions, elastic waves in solid materials, non-linear finite-element analyses, and the optimisation of steel structures. The papers are arranged such that they flow from fluid to solid mechanics.The first paper, by Ophir et al. (2012), presents a hybrid Lagrangian multi-grid method for flow simulation. The variational principle is invoked to obtain the flow field directly from the Lagrangian for steady, irrotational, compressible flow. The solution is obtained numerically by minimising the variational functional using finite elements on a hierarchy of grids of different resolution, using a computationally efficient multi-grid procedure. The computational model is applied to two-dimensional incompressible, inviscid flow past a cylinder, three-dimensional incompressible inviscid flow past a sphere, and flow past an arbitrary body. It is shown that the method is efficient and accurate. This paper is of fundamental interest to developers and users of CFD.Taylor et al. (2012) provide a means of separating small-scale periodic structure from larger-scale structure, the application being the separation of ripples from dunes. The methodology is based on Hermite functions, and can be applied to a wide range of physical problems including the spread of contaminants in a diffusing plume. The idea derived from the analysis of measured data on the movement and evolution of labo...

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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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Fluid simulation: combined Lagrangian and multi-grid approach

Cited by 4 publications

References 6 publications

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

Editorial

Variational principles for topological barotropic fluid dynamics

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