deriveShearStress Subroutine

public recursive subroutine deriveShearStress(fun, varSys, elempos, time, tree, nElems, nDofs, res)

Calculate the deviatoric shear stress for Newtonian fluid (exclude pressure) (no mixtures).\n Shear Stress depends on variable: nonEquilibirium

The formula is $$\tau_{\alpha \beta}= -(1-\frac{\omega}{2}) \sum_{i} f^{neq}_{i} c_{i\alpha} c_{i\beta}$$ 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-equilibirium density.\n For more information, please refer to:\n Krueger T, Varnik F, Raabe D. Shear stress in lattice Boltzmann simulations. Physical Review E. 2009;79(4):1-14.\n Thus this variable is dependent on another variable: nonEquilibirium.

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.
integer,	intent(in)			::	elempos(:)	Position of the TreeID of the element to get the variable for in the global treeID list.
type(tem_time_type),	intent(in)			::	time	Point in time at which to evaluate the variable.
type(treelmesh_type),	intent(in)			::	tree	global treelm mesh info
integer,	intent(in)			::	nElems	Number of values to obtain for this variable (vectorized access).
integer,	intent(in)			::	nDofs	Number of degrees of freedom within an element.
real(kind=rk),	intent(out)			::	res(:)	Resulting values for the requested variable. Linearized array dimension: (n requested entries) x (nComponents of this variable) x (nDegrees of freedom) Access: (iElem-1)fun%nComponentsnDofs + (iDof-1)*fun%nComponents + iComp

Contents

Variables

fPtr scheme posNonEq nCompsNonEq iLevel iElem omega nonEq tau

Variables

Type	Visibility	Attributes		Name		Initial
type(mus_varSys_data_type),	private,	pointer	::	fPtr
type(mus_scheme_type),	private,	pointer	::	scheme
integer,	private		::	posNonEq
integer,	private		::	nCompsNonEq
integer,	private		::	iLevel
integer,	private		::	iElem
real(kind=rk),	private		::	omega
real(kind=rk),	private,	allocatable	::	nonEq(:)
real(kind=rk),	private,	allocatable	::	tau(:)