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June 28, 2009, 08:55	Smagorinsky model details	#1
lakeat Senior Member Daniel WEI (老魏) Join Date: Mar 2009 Location: Beijing, China Posts: 689 Blog Entries: 9 Rep Power: 21	Sorry, I do not understand, I saw in "Smagorinsky.H", Code: tmp<volScalarField> k(const tmp<volTensorField>& gradU) const { return (2.0ck_/ce_)sqr(delta())magSqr(dev(symm(gradU))); } As I remember: $\begin{array}{l} {\nu _{SGS}} = {\left( {{C_S}\Delta } \right)^2}\left\| {{\bf{\bar S}}} \right\| \\ K = {\left( {{C_I}\Delta } \right)^2}{\left\| {{\bf{\bar S}}} \right\|^2} \\ \left\| {{\bf{\bar S}}} \right\| = {\left( {{\bf{\bar S}}{\rm{:}}{\bf{\bar S}}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}} \\ \end{array}$ Question 1: Why using magSqr(dev(symm(gradU)))* instead of symm(gradU) && symm(gradU) to get ${{\bf{\bar S}}{\rm{:}}{\bf{\bar S}}}$ ???? Question 2: If magSqr(dev(symm(gradU))) = symm(gradU) && symm(gradU) = ${{\bf{\bar S}}{\rm{:}}{\bf{\bar S}}}$ , then $K = \frac{{2{C_K}}}{{{C_\varepsilon }}}{\Delta ^2}{\left\| {{\bf{\bar S}}} \right\|^2}$ But I saw in "Smagorinsky.C" Code: nuSgs_ = ck_delta()sqrt(k(gradU)); Which means ${\nu _{SGS}} = {C_K}\Delta \sqrt K$ Then, replace K with $K = \frac{{2{C_K}}}{{{C_\varepsilon }}}{\Delta ^2}{\left\| {{\bf{\bar S}}} \right\|^2}$ ${\nu _{SGS}} = {C_K}\Delta \sqrt K = {C_K}\Delta \sqrt {\frac{{2{C_K}}}{{{C_\varepsilon }}}{\Delta ^2}{{\left\| {{\bf{\bar S}}} \right\|}^2}} = {C_K}\sqrt {\frac{{2{C_K}}}{{{C_\varepsilon }}}} {\Delta ^2}\left\| {{\bf{\bar S}}} \right\|$ Compare with ${\nu _{SGS}} = {\left( {{C_S}\Delta } \right)^2}\left\| {{\bf{\bar S}}} \right\|$ We'll get ${\left( {{C_S}} \right)^2} = {C_K}\sqrt {\frac{{2{C_K}}}{{{C_\varepsilon }}}}$ But I heard somone said ${\left( {{C_S}} \right)^2} = {C_K}\sqrt {\frac{{{C_K}}}{{{C_\varepsilon }}}}$ So, I'm puzzled, I wonder if it was a mistake, that k should be written as Code: tmp<volScalarField> k(const tmp<volTensorField>& gradU) const { return (ck_/ce_)sqr(delta())magSqr(dev(symm(gradU))); } Thank you makaveli_lcf, maysmech, MaximeIST and 2 others like this. __________________ ~ Daniel WEI ------------- Boeing Research & Technology - China Beijing, China Email

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