Combination of field and particle methods for fluid dynamics

[scienceguru2]

hello,

in numerical fluid dynamics there are field methods like finite-volume, finite-element, etc. and particle methods like Smoothed-Particle-Hydrodynamics – SPH and others. Both approaches have advantages and disadvantages depending on the application. Both, in principal completely different approaches can be combined using a Voronoi-Diagram. These Voronoi-Cells which behave like particles fill out the complete regarded space and are moving according to the physical laws (conservation of momentum and energy; see also
http://ivancic.de/cfd2k/WhatIsCFD2k.html). These particles also can interact with each other (exchange of momentum, energy, etc. ==> the Voronoi cells/particles obey the Navier-Stokes Equations). Such a Voronoi approach can combine the advantages of field and particle methods and therefore lead to better results in the numerical fluid dynamics (e.g. for turbulent flows which cannot be predicted accurately up to now).
Unfortunately I do not know any numerical method to apply it for such Voronoi-Particles in order to describe physical flows correctly. Does anybody know such a numerical method or is interested to develop such a method together with me? I am an aerospace engineer very familiar with fluid dynamics, turbulence and their physical and thermodynamic laws but sadly I am not an expert in numerical mathematics which is necessary to derive such a new approach.

thanking you in anticipation

 

[Ackbach]

hello,

in numerical fluid dynamics there are field methods like finite-volume, finite-element, etc. and particle methods like Smoothed-Particle-Hydrodynamics – SPH and others. Both approaches have advantages and disadvantages depending on the application. Both, in principal completely different approaches can be combined using a Voronoi-Diagram. These Voronoi-Cells which behave like particles fill out the complete regarded space and are moving according to the physical laws (conservation of momentum and energy; see also
http://ivancic.de/cfd2k/WhatIsCFD2k.html). These particles also can interact with each other (exchange of momentum, energy, etc. ==> the Voronoi cells/particles obey the Navier-Stokes Equations). Such a Voronoi approach can combine the advantages of field and particle methods and therefore lead to better results in the numerical fluid dynamics (e.g. for turbulent flows which cannot be predicted accurately up to now).
Unfortunately I do not know any numerical method to apply it for such Voronoi-Particles in order to describe physical flows correctly. Does anybody know such a numerical method or is interested to develop such a method together with me? I am an aerospace engineer very familiar with fluid dynamics, turbulence and their physical and thermodynamic laws but sadly I am not an expert in numerical mathematics which is necessary to derive such a new approach.

thanking you in anticipation

This sounds like a research-level mathematics question, and, as such, I would refer you to Math Overflow. It's a site much better suited to your question, I think.