How Consistent Can We Solve the Tensor Equations of the Dynamic Smagorinsky Model?

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How Consistent Can We Solve the Tensor Equations of the Dynamic Smagorinsky Model?
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The basic idea of the Dynamic Smagorinsky Model (DSM) is the tensor equation that relates the resolved stress terms with the respective Smagorinsky parametrizations. Although there exist for almost 30 years approaches to solve it, they include common practices which are, in my opinion, applied too uncritically. For instance, a stringent derivation of the tensor equation results in an ambiguous formulation involving a divergence operator. A second problem that may cause inconsistencies is the frequently-used extraction of the Smagorinsky parameter from the test filtering. In my presentation, I want to point out some of these issues to obtain a better understanding of the DSM. This may also lead to a reduction of mathematical inconsistencies regarding its solution.
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