mus_derivedQuantities_module2

This module provides functions for calculating macroscopic quantities

Uses

Interfaces

public interface getEquilibrium

private pure function getEquilibrium_forElemfromState(state, elem, layout, varPos, nScalars, neigh) result(equil)

Calculate the equilibrium distribution function in all directions

The equilibrim distribution function is:\n $f^{eq}_i = w_i \rho ( 1 + \frac{\vec c_i \cdot \vec u}{c^2_s} + \frac{ {(\vec c_i \cdot \vec u)}^2}{2c^4_s} - \frac{\vec u \cdot \vec u}{2c^2_s})$ \n where $w_i$ is the weight in each direction,\n $\rho$ is the macroscopic value of density,\n $c_s$ is the speed of sound,\n $\vec c_i$ is the lattice unit velocity in each direction,\n $\vec u$ is the macroscopic value of velocity.

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem
type(mus_scheme_layout_type),	intent(in)	::	layout
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars
integer,	intent(in)	::	neigh(:)

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

public pure function getEqByDensVel(dens, vel, layout) result(equil)

Calculate the equilibrium distribution function in all directions

The equilibrium distribution function is:\n $f^{eq}_i = w_i \rho ( 1 + \frac{\vec c_i \cdot \vec u}{c^2_s} + \frac{ {(\vec c_i \cdot \vec u)}^2}{2c^4_s} - \frac{\vec u \cdot \vec u}{2c^2_s})$

where $w_i$ is the weight in each direction,\n $\rho$ is the macroscopic value of density,\n $c_s$ is the speed of sound,\n $\vec c_i$ is the lattice unit velocity in each direction,\n $\vec u$ is the macroscopic value of velocity.

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	dens
real(kind=rk),	intent(in)	::	vel(3)
type(mus_scheme_layout_type),	intent(in)	::	layout

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

private pure function getEquilibrium_forPdfSubset(subset, layout, varPos) result(equil)

Calculate the equilibrium distribution function in all directions

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(mus_scheme_layout_type),	intent(in)	::	layout
integer,	intent(in)	::	varPos(:)

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

public interface getDensity

private pure function getDensity_forElemFromState(state, elem, stencil, varPos, nScalars) result(res)

Calculate the density of a given element number with the given state vector (sum up all values)

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars

Return Value real(kind=rk)

private pure function getDensity_forPdfSubset(subset, stencil, varPos) result(res)

Calculate the density of a given subset of pdfs vector (sum up all values)

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk)

public interface getVelocity

private pure function getVelocity_forElemFromState_noForce(state, elem, stencil, varPos, nScalars) result(vel)

Calculate the velocity in all 3 directions from the element indicated (elem), reading the pdf (state information) from the state array. state array includes all the pdfs of all elements. The access to the state array has to be done via the generic access macro IDX, as we want to access post-collision values.

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem	element index, for which to calc velocity
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars

Return Value real(kind=rk), (3)

private pure function getVelocity_forPdfSubset(subset, stencil, varPos) result(vel)

Calculate the velocity in all 3 directions from a subset given, ordered according to the stencil

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk), (3)

public interface getVelocity_incomp

private pure function getVelocity_forPdfSubset_incomp(subset, stencil, varPos) result(vel)

Calculate the velocity in all 3 directions from a subset given, ordered according to the stencil

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk), (3)

Functions

public pure function getEqByDensVel(dens, vel, layout) result(equil)

Calculate the equilibrium distribution function in all directions

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	dens
real(kind=rk),	intent(in)	::	vel(3)
type(mus_scheme_layout_type),	intent(in)	::	layout

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

public pure function getShearRate(strain) result(shear)

Author: Jiaxing Qi

Calculate the Shear Rate

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	strain(:)	strain rate tensor: xx, yy, zz, xy, yz, zx

Return Value real(kind=rk)

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

Author: Jiaxing Qi

Setting the non-equilibrium part based on the acoustic scaling

Arguments

Type	Intent		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)

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

Author: Jiaxing Qi

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

Arguments

Type	Intent		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)

public pure function convPrePost(omega) result(conv)

Author: Jiaxing Qi

Conversion factor betwen the pre- and post-collision quantity for the shear stress.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	omega

Return Value real(kind=rk)

public pure function getNonEqFac_intp(omegaS, omegaT) result(fac)

Calculate the conversion factor to convert nonEq moments between fine and coarser.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	omegaS
real(kind=rk),	intent(in)			::	omegaT

Return Value real(kind=rk)

public pure function getNonEqFac_intp_coarse_to_fine(omegaC, omegaF) result(fac)

Calculate the conversion factor to convert nonEq pdfs from coarse to fine.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	omegaC
real(kind=rk),	intent(in)			::	omegaF

Return Value real(kind=rk)

public pure function getNonEqFac_intp_fine_to_coarse(omegaC, omegaF) result(fac)

Calculate the conversion factor to convert nonEq pdfs from fine to coarse.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	omegaC
real(kind=rk),	intent(in)			::	omegaF

Return Value real(kind=rk)

public pure function getEquilibriumIncomp(dens, vel, layout, rho0) result(equil)

Calculate the equilibrium distribution function in all directions This is the incompressible formulation with reference density rho0

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	dens
real(kind=rk),	intent(in)	::	vel(3)
type(mus_scheme_layout_type),	intent(in)	::	layout
real(kind=rk),	intent(in)	::	rho0

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

public pure function secondMom_2D(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, $m_1 = \sum_{i=1}^{Q} c_{i1} c_{i1} f_i$ $m_2 = \sum_{i=1}^{Q} c_{i2} c_{i2} f_i$ $m_3 = \sum_{i=1}^{Q} c_{i1} c_{i2} f_i$ This function is used by shear stress and strain rate. 1=xx, 2=yy, 3=xy

Arguments

Type	Intent		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), (3)

public pure function secondMom_3D(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. 1=xx, 2=yy, 3=zz, 4=xy, 5=yz, 6=xz in 2D: 1=xx, 2=yy, 3=xy

Arguments

Type	Intent		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)

public pure function secondMom_minus_cs2_2D(cxcx, f, QQ) result(m)

Arguments

Type	Intent		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), (3)

public pure function secondMom_minus_cs2_3D(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. 1=xx, 2=yy, 3=zz, 4=xy, 5=yz, 6=xz

Arguments

Type	Intent		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)

private pure function getDensity_forPdfSubset(subset, stencil, varPos) result(res)

Calculate the density of a given subset of pdfs vector (sum up all values)

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk)

private pure function getDensity_forElemFromState(state, elem, stencil, varPos, nScalars) result(res)

Calculate the density of a given element number with the given state vector (sum up all values)

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars

Return Value real(kind=rk)

private pure function getVelocity_forPdfSubset(subset, stencil, varPos) result(vel)

Calculate the velocity in all 3 directions from a subset given, ordered according to the stencil

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk), (3)

private pure function getVelocity_forPdfSubset_incomp(subset, stencil, varPos) result(vel)

Calculate the velocity in all 3 directions from a subset given, ordered according to the stencil

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)

Return Value real(kind=rk), (3)

private pure function getVelocity_forElemFromState_noForce(state, elem, stencil, varPos, nScalars) result(vel)

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem	element index, for which to calc velocity
type(tem_stencilHeader_type),	intent(in)	::	stencil
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars

Return Value real(kind=rk), (3)

private pure function getEquilibrium_forPdfSubset(subset, layout, varPos) result(equil)

Calculate the equilibrium distribution function in all directions

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	subset(:)
type(mus_scheme_layout_type),	intent(in)	::	layout
integer,	intent(in)	::	varPos(:)

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

private pure function getEquilibrium_forElemfromState(state, elem, layout, varPos, nScalars, neigh) result(equil)

Calculate the equilibrium distribution function in all directions

Arguments

Type	Intent		Name
real(kind=rk),	intent(in)	::	state(:)
integer,	intent(in)	::	elem
type(mus_scheme_layout_type),	intent(in)	::	layout
integer,	intent(in)	::	varPos(:)
integer,	intent(in)	::	nScalars
integer,	intent(in)	::	neigh(:)

mus_derivedQuantities_module2 Module

Contents

Interfaces

Functions

Uses

Interfaces

public interface getEquilibrium

private pure function getEquilibrium_forElemfromState(state, elem, layout, varPos, nScalars, neigh) result(equil)

Arguments

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

public pure function getEqByDensVel(dens, vel, layout) result(equil)

Arguments

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

private pure function getEquilibrium_forPdfSubset(subset, layout, varPos) result(equil)

Arguments

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

public interface getDensity

private pure function getDensity_forElemFromState(state, elem, stencil, varPos, nScalars) result(res)

Arguments

Return Value real(kind=rk)

private pure function getDensity_forPdfSubset(subset, stencil, varPos) result(res)

Arguments

Return Value real(kind=rk)

public interface getVelocity

private pure function getVelocity_forElemFromState_noForce(state, elem, stencil, varPos, nScalars) result(vel)

Arguments

Return Value real(kind=rk), (3)

private pure function getVelocity_forPdfSubset(subset, stencil, varPos) result(vel)

Arguments

Return Value real(kind=rk), (3)

public interface getVelocity_incomp

private pure function getVelocity_forPdfSubset_incomp(subset, stencil, varPos) result(vel)

Arguments

Return Value real(kind=rk), (3)

Functions

public pure function getEqByDensVel(dens, vel, layout) result(equil)

Arguments

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

public pure function getShearRate(strain) result(shear)

Arguments

Return Value real(kind=rk)

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

Arguments

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

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

Arguments

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

public pure function convPrePost(omega) result(conv)

Arguments

Return Value real(kind=rk)

public pure function getNonEqFac_intp(omegaS, omegaT) result(fac)

Arguments

Return Value real(kind=rk)

public pure function getNonEqFac_intp_coarse_to_fine(omegaC, omegaF) result(fac)

Arguments

Return Value real(kind=rk)

public pure function getNonEqFac_intp_fine_to_coarse(omegaC, omegaF) result(fac)

Arguments

Return Value real(kind=rk)

public pure function getEquilibriumIncomp(dens, vel, layout, rho0) result(equil)

Arguments

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

public pure function secondMom_2D(cxcx, f, QQ) result(m)

Arguments

Return Value real(kind=rk), (3)

public pure function secondMom_3D(cxcx, f, QQ) result(m)

Arguments

Return Value real(kind=rk), (6)

public pure function secondMom_minus_cs2_2D(cxcx, f, QQ) result(m)

Arguments

Return Value real(kind=rk), (3)

public pure function secondMom_minus_cs2_3D(cxcx, f, QQ) result(m)

Arguments

Return Value real(kind=rk), (6)

private pure function getDensity_forPdfSubset(subset, stencil, varPos) result(res)

Arguments

Return Value real(kind=rk)

private pure function getDensity_forElemFromState(state, elem, stencil, varPos, nScalars) result(res)

Arguments

Return Value real(kind=rk)