Convergence Analysis of a Fully Discrete Family of Iterated Deconvolution Methods for Turbulence Modeling with Time Relaxation

Table 1

Error and convergence rates for Leray-deconvolution with 𝐽=0 for the Taylor-Green vortex with Re=10,000, 𝛼=√ℎ, and 𝛿=√⁴ℎ. Note the convergence rate is approaching 1 as predicted by (5.21).

m (=1/h)	‖𝑢−𝑤^ℎ‖∞,0	Rate	‖∇(𝑢−𝑤^ℎ)‖2,0	Rate
20	0.038975		1.651230
40	0.024334	0.680	1.468510	0.169
60	0.017751	0.778	1.159840	0.582
80	0.013854	0.862	0.935247	0.748
100	0.011255	0.931	0.774285	0.846