mus_deriveStrainRate Subroutine

private recursive subroutine mus_deriveStrainRate(fun, varsys, stencil, iLevel, posInState, pdf, res, nVals)

Calculate the strain rate ( or rate of strain, or rate of deformation)

The equation is: $$\tau_{\alpha \beta}= -\frac{3\omega}{2\rho} \sum_{i} f^{neq}_{i} c_{i\alpha} c_{i\beta}$$ where $\tau_{\alpha \beta}$ is the stress in the $\beta$-direction on a face normal to the $\alpha$-axis,\n $f^{neq}_i = f_i - f^{eq}_i$ is the non-equilibrium pdf.\n For more information, please refer to: equation 45 in\n Krueger T, Varnik F, Raabe D. Shear stress in lattice Boltzmann simulations. Physical Review E. 2009;79(4):1-14.\n

For multi-level mesh, Omega on finer level needs to be adjusted in order to get the correct shearstress calculation.\n First, we defines c as the dx ratio between finer and coarse level.\n $c={ \Delta dx }_{ c }/{ \Delta dx }_{ f }$ Then the viscosity on the different levels must satisfy:\n $\frac { { \nu }_{ f } }{ { \nu }_{ c } } =c$ This constrain leads to a relationship of omega on different levels:\n ${\omega}_f = \frac {1}{ {\lambda}(\frac{1}{{\omega}_c}-0.5)+0.5 }$ For more information, please refer to:\n Manuel H, Harald K, Joerg B, Sabine R. Aeroacoustic validation of the lattice boltzmann method on non-uniform grids. ECCOMAS 2012

Arguments

Type	Intent	Optional	Attributes		Name
class(tem_varSys_op_type),	intent(in)			::	fun	description of the method to obtain the variables, here some preset values might be stored, like the space time function to use or the required variables.
type(tem_varSys_type),	intent(in)			::	varsys	the variable system to obtain the variable from.
type(tem_stencilHeader_type),	intent(in)			::	stencil	fluid stencil defintion
integer,	intent(in)			::	iLevel	current level
integer,	intent(in)			::	posInState(:)	Position of element in levelwise state array
real(kind=rk),	intent(in)			::	pdf(:)	pdf array
real(kind=rk),	intent(out)			::	res(:)	results
integer,	intent(in)			::	nVals	nVals to get