getNEq_acoustic Function

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

Setting the non-equilibrium part based on the acoustic scaling

The non-equilibirium part of pdf is computed from strain rate tensor by \cite Latt:2011vr $$f_i^{neq} = - \frac{t_i \rho_0}{c_{s}^2 \omega)} Q_{i\alpha\beta}:S_{\alpha\beta}$$ where $\boldsymbol{A} : \boldsymbol{B}$ is Frobenius inner product. $$\boldsymbol{A} : \boldsymbol{B} = \sum_{i,j} A_{ij}B_{ij}$$ $$Q_{i\alpha\beta} = c_{i\alpha}c_{i\beta} - c_s^2 \delta_{\alpha\beta}$$ and $S$ is the strain rate tensor $$S_{\alpha\beta} = -\frac{1}{2} ( \partial_{\alpha}u_{\beta} + \partial_{\alpha}u_{\beta} )$$

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

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