| Sr. No. | Method/Theory/Approach | Action and Explanation | Limitation to Explanation | Group/Institute | Year | Reference |
|
| Part Scale Modelling | |||||
|
|
| Analytical Modelling | ||||
| 1 | Deterministic/Continuum Model | Non-random 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 co-workers (LANL) | 1953 and 1993 | [284] [285] [286] [287] |