ADI	Alternating-Direction Implicit
ALE	Arbitrary Lagrangian Eulerian
BiCGStab	Bi-Conjugate Gradient-Stable Algorithm
CSF	Continuum Surface Force
CUBISTA	Convergent and Universally Bounded Interpolation Scheme
	for the Treatment of Advection
FTM	Front-Tracking Method
GAMG	Geometric-Algebraic Multi-Grid
IBM	Immersed Boundary Method
IFEM	Immersed-Finite-Element Method
ILU	Incomplete Lower-Upper
LSM	Level-Set Method
MAC	Marker-And-Cell
MULES	Multidimensional Universal Limiter with Explicit Solution
MVP-RIA	Multiphase Viscoelastic PLIC-RDF isoAdvector
OpenFOAM	Open Source Field Operation and Manipulation
PFM	Phase Field Method
PIMPLE	Mixture of PISO and SIMPLE
PISO	Pressure Implicit with Splitting of Operator
PLIC	Piecewise Linear Interface Construction
RDF	Reconstructed Distance Function
SIMPLE	Semi-Implicit Method for Pressure Linked Equations
VOF	Volume-Of-Fluid
Nomenclature
Physical and mathematical quantities
u	Velocity vector
$\rho$	Density
p	Pressure
g	Gravity acceleration
${\mathit{f}}_{\mathit{s}}$	Surface tension force
$\mathsf{\tau }$	Stress tensor
${\mathsf{\tau }}_S$	Newtonian (Solvent) stress tensor
${\mathsf{\tau }}_P$	Polymeric extra-stress tensor
${\eta }_S$	Solvent dynamic viscosity
${\eta }_P$	Polymeric dynamic viscosity
$\alpha$	Mobility parameter
$\lambda$	Relaxation factor, relaxation time
$\epsilon$	Extensibility parameter
${\sigma }_D$	Deviatoric part of stress tensor
$\overline{\sigma }$	Second invariant of the deviatoric stress tensor
$\mathit{I}$	Identity tensor
${\mathsf{\tau }}_0$	Yield stress
${\stackrel{\square }{\mathsf{\tau }}}_P$	Gordon-Schowalter derivative
$\zeta$	Non-affine deformation parameter
${\stackrel{▿}{\mathsf{\tau }}}_P$	Upper-convective time derivative of the polymeric extra-stress tensor
$\mathit{A}$	Conformation tensor
$\gamma$	Volume fraction
u ${}_r$	Relative velocity vector of two fluids
$\sigma$	Surface tension coefficient
$U^{*}$	Calculated rise velocity
$\mathit{\theta }$	Natural logarithm of the conformation tensor
k	Consistency index
n	Shear-thinning exponent
G	Elastic modulus of the material
Geometrical parameters
W	Domain width
H	Domain height
d	Initial bubble diameter
R	Initial bubble radius
$V_b$	Initial bubble volume
$R_{eff}$	Effective bubble radii
Non-dimensional numbers
$Ar$	Archimedes number
$Bo$	Bond (Eötvös) number
$Mo$	Morton number
$Re$	Reynolds number
$Wi$	Weissenberg number
$Bn$	Bingham number
$Eg$	Elastogravity number
Operators
∇	Gradient
$\nabla .$	Divergence
${\displaystyle \frac{D(.)}{Dt}}$	Total time derivative
$\mathrm{tr}(.)$	Trace operator
$\max (.,.)$	Maximum operator
${(.)}^T$	Transpose operator
:	Double dot product