added full list of subphase quantities

docs/source/userGuide/models/color/analysis/subphase.rst

@@ -14,7 +14,7 @@ to perform between analyses. The subphase analys routine performs the following
 Since it is more computationally expensive to carry out these operations compared to the
 basic analysis, it may be useful to choose ``subphase_analysis_interval`` to be larger than
 ``analysis_interval``. Nevertheless, since analysis is performed in memory, it is orders of
-magnitude faster than to analyze data in situ rather than writing fields to disc. Monitoring
+magnitude faster than to analyze data *in situ* rather than writing fields to disc. Monitoring
 the performance in MLUPS provides an easy way to tune the analysis interval so that the
 overall simulation performance is not subject to significant penalties. 
 
@@ -22,20 +22,135 @@ There are three main entities that are constructed for subphase analysis
 
 * :math:`\Omega_w:\phi<0` : region of space filled by fluid w
 * :math:`\Omega_n:\phi<0` : region of space filled by fluid n
-* :math:`\Omega_i: |\nabla \phi<0| > \epsilon` : region of space for the interface region
+* :math:`\Omega_i: |\nabla \phi|<0 > \epsilon` : region of space for the interface region
 
 The phase regions are defined identical to what is reported in ``timelog.csv``.
 The interface region is defined explicitly as the portion of space where
-significant composition gradients are present. 
+significant composition gradients are present. For each entity, sub-entities are
+constructed by running a connected components algorithm on the set. This is done to
+separate the connected part of the phase from the disconnected part. This subset operation
+is performed by identifying the largest connected component (based on volume)
+and denoting this as the connected part of that region. The remaining portion of the
+phase is lumped into a disconnecte sub-entity. Subphase analysis is therefore performed
+for the following six entities
 
-The list of measures logged to ``subphase.csv`` are defined as follows.
-The region of space occupied by the wetting fluid is determined from the
-phase indicator field, :math:`\Omega_w:\phi<0` 
+* ``wc`` -- connected part of phase w
+* ``wd`` -- disconnected part of phase w
+* ``nc`` -- connected part of phase n
+* ``nd`` -- disconnected part of phase n
+* ``ic`` -- connected part of interface region
+* ``id`` -- disconnected part of interface region
 
-* ``sw`` -- water saturation (fluid component 2)
-* ``krw`` -- water effective permeability 
-* ``krn`` -- non-wetting fluid effective permeability
-* ``krn`` -- non-wetting fluid effective permeability
-* ``krwf`` -- non-wetting fluid effective permeability
-* ``krnf`` -- non-wetting fluid effective permeability
+For each entity :math:`\Omega_k` with :math:`k\in\{wc,wd,nc,nd,ic,id\}`
+an isosurface is constructed to approximate the boundary of the region,
+:math:`\Gamma_k`. Once each region is identified, the following measures are determined
 
+**Geometric invariants**
+
+* Volume -- :math:`V_k=\int_{\Omega_k} dV`
+* Surface area -- :math:`A_k=\int_{\Gamma_k} dS`
+* Integral mean curvature -- :math:`H_k=\int_{\Gamma_k} \frac 12 (\kappa_1 + \kappa_2) dS`
+* Euler characteristic -- :math:`\chi_k= \frac{1}{4\pi} \int_{\Gamma_k} \kappa_1 \kappa_2 dS`
+      
+**Conserved quantities**
+
+* Total mass within the region :math:`M_k=\int_{\Omega_k} \rho dV`
+* Total momentum within the region :math:`\mathbf{P}_k=\int_{\Omega_k} \rho \mathbf{u} dV`
+* Total kinetic energy within the region :math:`K_k=\frac 12 \int_{\Omega_k} \rho \mathbf{u} \cdot \mathbf{u} dV`
+
+**Thermodynamic quantities**
+      
+* Pressure -- :math:`p_k=\frac{1}{V_k}\int_{\Omega_k} p dV`
+* Solid wetting energy -- :math:`\gamma_s=\int_{\Gamma_s}\gamma dS`
+* Viscous dissipation -- :math:`\Phi_k=\int_{\Omega_k} \nabla \mathbf{u} : \mathbf{\Pi} dV`
+
+The total solid wetting energy is determined by integrating the interfacial stresses in the
+immediate vicinity of the solid surface :math:`\Gamma_s`. The integral of the viscous
+dissipation function is determined based on the stress tensor, denoted by :math:`\mathbf{\Pi}`.
+
+
+The full list of measures are associated with the labels in ``subphase.csv``
+
+* ``time`` -- timestep 
+* ``rn`` -- density for phase n (input parameter)
+* ``rw`` -- density for phase w (input parameter)
+* ``nun`` -- kinematic viscosity for phase n (input parameter)
+* ``nuw`` -- kinematic viscosity for phase w (input parameter)
+* ``Fx`` -- external force in x direction (input parameter)
+* ``Fy`` -- external force in y direction (input parameter)
+* ``Fz`` -- external force in z direction (input parameter)
+* ``iftwn`` -- interfacial tension (input parameter)
+* ``wet`` -- total solid wetting energy 
+* ``pwc`` -- average pressure for connected part of phase w
+* ``pwd`` -- average pressure for disconnected part of phase w
+* ``pnc`` -- average pressure for connected part of phase n
+* ``pnd`` -- average pressure for disconnected part of phase n
+* ``Mwc`` -- mass for connected part of phase w 
+* ``Mwd`` --mass for disconnected part of phase w
+* ``Mwi`` -- mass for phase within diffuse interface region 
+* ``Mnc`` -- mass for connected part of phase n 
+* ``Mnd`` -- mass for disconnected part of phase n 
+* ``Mni`` -- mass for phase n within diffuse interface region
+* ``Msw`` -- mass for component w within 2 voxels of solid
+* ``Msn`` -- mass for component n within 2 voxels of solid
+* ``Pwc_x`` -- x- momentum for connected part of phase w
+* ``Pwd_x`` -- x- momentum for disconnected part of phase w
+* ``Pwi_x`` -- x- momentum for phase w within diffuse interface
+* ``Pnc_x`` -- x- momentum for connected part of phase n
+* ``Pnd_x`` -- x- momentum for disconnected part of phase n
+* ``Pni_x`` -- x- momentum for phase n within diffuse interface
+* ``Psw_x`` -- x- momentum for phase w within 2 voxels of solid
+* ``Psn_x`` -- x- momentum for phase n within 2 voxels of solid
+* ``Pwc_y`` -- y- momentum for connected part of phase w
+* ``Pwd_y`` -- y- momentum for disconnected part of phase w
+* ``Pwi_y`` -- y- momentum for phase w within diffuse interface
+* ``Pnc_y`` -- y- momentum for connected part of phase n
+* ``Pnd_y`` -- y- momentum for connected part of phase n
+* ``Pni_y`` -- y- momentum for phase n within diffuse interface
+* ``Psw_y`` -- y- momentum for phase w within 2 voxels of solid
+* ``Psn_y`` -- y- momentum for phase n within 2 voxels of solid
+* ``Pwc_z`` -- z- momentum for connected part of phase w
+* ``Pwd_z`` -- z- momentum for disconnected part of phase w
+* ``Pwi_z`` -- z- momentum for phase w within diffuse interface
+* ``Pnc_z`` -- z- momentum for connected part of phase n
+* ``Pnd_z`` -- z- momentum for disconnected part of phase n
+* ``Pni_z`` -- z- momentum for phase n within diffuse interface
+* ``Psw_z`` -- z- momentum for phase w within 2 voxels of solid
+* ``Psn_z`` -- z- momentum for phase n within 2 voxels of solid
+* ``Kwc`` -- Kinetic energy for transport within connected part of phase w
+* ``Kwd`` -- Kinetic energy for transport within disconnected part of phase w
+* ``Kwi`` -- Kinetic energy for transport of phase w within diffuse interface region
+* ``Knc`` -- Kinetic energy for transport in connected part of phase n
+* ``Knd`` -- Kinetic energy for transport within disconnected part of phase n
+* ``Kni`` -- Kinetic energy for transport of phase n within diffuse interface region
+* ``Dwc`` -- Viscous dissipation for conneced pathway for phase w
+* ``Dwd`` -- Viscous dissipation for disconnected part of phase w
+* ``Dnc`` -- Viscous dissipation for connected pathway for phase n
+* ``Dnd`` -- Viscous dissipation for disconnected part of phase n
+* ``Vwc`` -- Volume for connected pathway for phase w
+* ``Awc`` -- Surface area for connected pathway for phase w
+* ``Hwc`` -- Integral mean curvature for connected pathway for phase w
+* ``Xwc`` -- Euler characteristic for connected pathway for phase w
+* ``Vwd`` -- Volume for disconnected phase w
+* ``Awd`` -- Surface area for disconnected phase w
+* ``Hwd`` -- Integral mean curvature for disconnected phase w
+* ``Xwd`` -- Euler characteristic for disconnected phase w
+* ``Nwd`` -- Number of connected components in disconnected phase w
+* ``Vnc`` -- Volume for connected pathway for phase n
+* ``Anc`` -- Surface area for connected pathway for phase n
+* ``Hnc`` -- Integral mean curvature for connected pathway for phase n
+* ``Xnc`` -- Euler characteristic for connected pathway for phase n
+* ``Vnd`` -- Volume for disconnected phase n
+* ``And`` -- Surface area for disconnected phase n
+* ``Hnd`` -- Integral mean curvature for disconnected phase n
+* ``Xnd`` -- Euler characteristic for disconnected phase n
+* ``Nnd`` -- number of connected components within disconnected phase n
+* ``Vi`` -- volume for diffuse interface region
+* ``Ai`` -- surface area for boundary of diffuse interface region
+* ``Hi`` -- integral mean curvature for boundary of diffuse interface region
+* ``Xi`` -- Euler characteristic for diffuse interface region
+* ``Vic`` -- volume for connected interface region
+* ``Aic`` -- surface area for boundary of connected interface region
+* ``Hic`` -- Integral mean curvature for connected interface region
+* ``Xic`` -- Euler characteristic for connected interface region
+* ``Nic`` -- number of connected components in connected interface region