getNEq_diffusive Function

public function getNEq_diffusive(layout, omega, Sxx) result(nEq)

Calculate the non-equilibrium part of pdf from strain rate tensor based on the diffusive scaling

According to \cite Junk:2005cr \n The non-equilibrium part of pdf $f_i^{neq}$ is set by \n $$f_i^{neq} = -\frac{t_i}{2\kappa c_{s}^4} \nu' S^{(1)}:\Lambda = -\frac{t_i}{2\kappa c_{s}^4} \frac{\kappa c_s^2}{\omega} S^{(1)}:\Lambda = -\frac{t_i}{2 c_{s}^2} S^{(1)}:\Lambda = -\frac{t_i}{c_{s}^2} \bm S:\Lambda$$ where $\nu' = \frac{\kappa c_s^2}{\omega}$ is the viscosity, $\bm S = \frac{1}{2}S^{(1)}$ is the strain rate tensor and $$\Lambda_{i\alpha\beta} = c_{i\alpha} c_{i\beta} - \frac{1}{D}\sum_{\gamma}(c_{i\gamma}c_{i\gamma}) \delta_{\alpha\beta}$$ and $D$ is the number of dimension. \n Notice here that strain rate tensor above has to be a traceless tensor, i.e. $Tr(S) = 0$. In current implementation, the above equation is slightly modified so that the strain rate tensor is not required to be traceless anymore. In this way, $f_i^{neq}$ calculated by this routine can recover the input strain rate tensor no matter it is traceless or not.\n Specificly the $\Lambda$ in above equation is modified slightly, i.e. $$\Lambda_{i\alpha\beta} = c_{i\alpha} c_{i\beta} - c_s^2 \delta_{\alpha\beta}$$ This routine has a unit test program utest/mus_fNeq_diffusive_test

Arguments

Type	Intent	Optional	Attributes		Name
type(mus_scheme_layout_type),	intent(in)			::	layout
real(kind=rk),	intent(in)			::	omega
real(kind=rk),	intent(in)			::	Sxx(3,3)	Strain rate tensor. It is a symmetric 3x3 matrix

Return Value real(kind=rk), (layout%fStencil%QQ)