CFD Online Discussion Forums

gibb's (free) energy is a thermodynamic state function, and has nothing to do with numerical oscillations.

the gibb's phenomenon, on the other hand, is indeed pertinent to the oscillations. i have never explored the WWWeb to learn about gibb's phenomenon. you might try Google.

basically, the gibb's phenomenon is the presence of spurious oscillations when a function G of order higher than piecewise linear is used to approximate a function F that exhibits a discontinuity. the less the numerical damping in your scheme, the more will be amplitude of the oscillations. the higher the (polynomial) order of G, the higher will be the frequency of the oscillations, i think.

if you use a low-dissipation scheme to capture a sharp gradient (such as a boundary layer in viscous flow) with a coarse mesh, you will see oscillations, but the oscillations can be avoided by refining the mesh till you obtain a smooth approximation to the sharp gradient. however, if you use a low-dissipation scheme to capture a true discontinuity (such as a shock in invscid flow), you will get oscillations in the vicinity of the shock, and refining the mesh will not help. instead, you must increase the numerical dissipation (adjust the artificial viscosity of the scheme) to effectively lower the order of the scheme in the vicinity of the shock. this will not improve the accuracy, but it will make the solution look more natural on a plot.

you can read about the gibb's phenomenon in chapters or books on approximation of functions by fourier series. you can read about the implications of the gibb's phenomenon in numerical analysis and the need for numerical dissipation when capturing shocks in most books on CFD.