Published online by Cambridge University Press: 21 September 2009
In vortex methods the flow field is recovered at every location of the domain when one considers the collective behavior of all computational elements. The length scales of the flow quantities that are been resolved are characterized by the particle core rather than the interparticle distance. These observations, which stem from the definition itself of vortex methods and are confirmed by its numerical analysis, differentiate particle methods from schemes such as finite differences.
The essense of the method is the “communication” of information between the particles, that requires a particle overlap. As a result, a computation is bound to become inaccurate once the particles cease to overlap. Computations involving nonoverlapping finite core particles should be regarded then as modeling and not as direct numerical simulations. Excluding case-specific initial particle distributions (e.g., particles placed on concentric rings to represent an azimuthally invariant vorticity distribution) the loss of overlap (and excessive overlap) is an inherent problem of purely Lagrangian methods.
The cause of the problem is the flow strain that may cluster particles in one direction and spread them in another in the neighborhood of hyperbolic points of the flow map, resulting in nonuniform distributions. At the onset of such particle distributions no error is usually manifested in the global quantities of the flow such as the linear and the angular impulse. However, locally the vorticity field becomes distorted and spreading of the particles results in loss of naturally present vortical structures, whereas particle clustering results in the appearance of unphysical ones on the scale of the interparticle separation.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.