Sr. No.  Method/Theory/Approach  Action and Explanation  Limitation to Explanation  Group/Institute  Year  Reference 
 Part Scale Modelling  

 Analytical Modelling  
1  Deterministic/Continuum Model  Nonrandom methods, produce same types of exact results  Does not depend on initial state/point 
 1993  [266] 
2  Probabilistic/Stochastic Models  Randomised result based methods  Does depend on initial state 
 2016  [267] [268] 

 Computational Modelling  
3  Lattice Boltzmann Methods (LBM)  Solution of basic “Continuity” and “Naiver Stokes” Equations for CFD based on Ludwig Boltzmann’s Kinetic theory of gases  Limited to CFD type problems  Raabe, D (MPIE, Dusseldorf)  2004  [269]  [275] 
4  Phase Field Method (PFM)  Solution of phase field parameter ϕ to describe physical state (liquid/solid) of material  Limited by type of ϕ for a particular situation  Napolitano, R. E (Iowa State)  2002 and 2012  [190] [195] 
5  Cellular Automaton (CA) Method  Division of entire volume into finite cells and solution of transport equations applied to individual cell  Large initial Capital (Processor/RAM)  Rappaz, M (EPFL)  1993  [196] [197] [270] [277] [278] 
6  Virtual Front Tracking (VFT) Method  Dendritic growth in low Péclet number systems  Best in 2D  Stefanescu, D.M (OSU)  2007  [279] 
7  Sharp Interface (SIF) Method  Evolution of Interface as a function of time  Best in simple cases  Vermolen, F.J (Delft)  2006  [280] 
8  CAFÉ  Combine Cellular Automaton (CA) Scheme with Finite Element (FE) Method 
 Rappaz, M (EPFL)  1994  [200] 
9  PFFE  Combine Phase Field (PF) with Finite Element (FE) Method 
 Britta Nestler (KIT)  2011  [281] 
10  PFCA  Combine Phase Field (PF) with Cellular Automata (CA) Regime 
 Shin, Y.C (Purdue)  2011  [259] 
 Atomistic Modelling  
10  Classical MD  Exact Solutions  Computing power  Alder and Wainwright (Lawrence Livermore)  1957  [62] [282] [283] 
11  Monte Carlo (MC) Simulation  Set of probability based possible outcomes  Range of Solutions  Metropolis, Nicholas and coworkers (LANL)  1953 and 1993  [284] [285] [286] [287] 