could someone here please explain to me about the flux limiter and its used and implications in finite volume methods? thank you

Dear Prapanj,

Higher order spatial accuracy can be achieved in finite volume schemes using a concept referred to as "Reconstruction". Reconstruction involves gradients, and these gradients could become numerically spurious in some regions (esp. shocks and discontinuous regions), and this could lead to convergence problems. The underlying issue is that there is no monotone scheme that is more than first order accurate. The attempt for a higher order accuracy is at the expense of loss in monotonicity (and a loss in stability) ending in code blow up. To achieve a higher order monotone scheme, monotonicity needs to be enforced, which is what limiting essentially does. Limiting could be done in two ways, either limit the gradients involved in the reconstruction procedure, before computing the flux, or, compute the fluxes with the numerical gradients as they are, and then limit the flux, where they need to be. The second kind is what are referred to as flux limiters.

Hope this helps

Regards,

Ganesh

thank u that was indeed helpful. and could u guide me what materials are available for learning more on them (about the limiters themselves) and also on the methods of limiting the gradients... thank you.

Was this not used in back-to-the-future?? In this case it is used for time travel.

Dear Prapanj,

Check out the flux limiters dextion on CFD-Wiki and the references therein. You can go on to more deeper issues from thereon

Regards,

Ganesh