secondMom Function

public pure function secondMom(cxcx, f, QQ) result(m)

Calculate second moments of some quantity $f$ $$M_{\alpha\beta} = \sum_{i=1}^{Q} c_{i\alpha} c_{i\beta} f_i$$ where Q is number of discrete velocity.\n The output is 1 dimentional array which has 6 componenents.\n Specifically, $$m_1 = \sum_{i=1}^{Q} c_{i1} c_{i1} f_i$$ $$m_2 = \sum_{i=1}^{Q} c_{i2} c_{i2} f_i$$ $$m_3 = \sum_{i=1}^{Q} c_{i3} c_{i3} f_i$$ $$m_4 = \sum_{i=1}^{Q} c_{i1} c_{i2} f_i$$ $$m_5 = \sum_{i=1}^{Q} c_{i2} c_{i3} f_i$$ $$m_6 = \sum_{i=1}^{Q} c_{i3} c_{i1} f_i$$ This function is used by shear stress and strain rate.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxcx(6,QQ)
real(kind=rk),	intent(in)			::	f(QQ)	quantity to which second moment is applied
integer,	intent(in)			::	QQ

Return Value real(kind=rk)(6)

Contents

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