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Finite element approximations for the stationary large eddy simulation model

100%
Warzyński A.
Applicationes Mathematicae
|
2010
|
tom 37
|
nr 2
171-183
EN
Some approximation procedures are presented for the system of equations arising from the large eddy simulation of turbulent flows. Existence of solutions to the approximate problems is proved. Discrete solutions generate a strongly convergent subsequence whose limit is a weak solution of the original problem. To prove the convergence theorem we use Young measures and related tools. We do not limit ourselves to divergence-free functions and our results are in particular valid for finite element approximations where one usually does not use functions with divergence equal to zero.
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Well-posedness for a class of non-Newtonian fluids with general growth conditions

51%
Gwiazda P., Świerczewska-Gwiazda A., Wróblewska A., Warzyński A.
Banach Center Publications
|
2009
|
tom 86
|
nr 1
115-128
EN
The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with the help of general x-dependent convex functions. This formulation yields the existence of solutions in generalized Orlicz spaces. These considerations are motivated by e.g. electrorheological fluids, magnetorheological fluids, and shear thickening fluids.
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