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Mathematical modelling and computer simulation have wide range of applications in metallurgical systems and have since been embraced by Materials and Metallurgical Engineers in solving many problems involving solidification.
Simulation was run for different times and these show levels of temperature as solidification progresses.
Beckermann, Simulation of Micro/Macrosegregation during the Solidification of a Low-Alloy Steel, ISIJ International, Vol. 35, No. 6, 1995
Egole, Simulation of Temperature Distribution and Solidification in Direct Chill Casting of Al-3%Si Alloy, International Journal of Numerical Methods and Applications, Vol. 15, No. 1, 2016
Raad, Procedure for Estimation and Reporting Uncertainty Due to Discretization in CFD Applications, J.

Afonso et. al. [19], reported the influence of flame and flame stability by the design of the burner through a numerical simulation for the combustion of premixed hydrogen/air in an undulate microchannel.
Dabade et al., “CFD Simulation of Confined Non-Premixed Flames,” in Heat Transfer Summer Conference, vol. 44786, pp. 235–242, 2012

It is shown that experimental measurements, analytical quantification and numerical simulation present different advantages and disadvantages in describing the ice slurry flow and heat transfer that occurs.
Zhang & Shi. (2015) Numerical CFD (Euler-Euler approach) 10.3% Ethanol-water solution Distribution of ice volume fraction and heat transfer Heat transfer coefficient decreases initially and increases along the pipe after the ice melts.
Mi et al. (2024) Numerical CFD (Euler-Euler approach) Water without additives Secondary flow behavior and concentration distribution Increasing inlet velocity results in more uniform ice concentration along the vertical profile.
Yoshino, “Particle-resolved simulations of ice slurry flows in a square duct by the thermal immersed boundary–lattice Boltzmann method,” Comput Fluids, vol. 228, Oct. 2021, doi: 10.1016/j.compfluid.2021.105064

The simulation results show 82.90% efficiency for PM machine, 73.04% for IM and 70.50% for SRM.
Mahkamov, ‘Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling’, J.
Sayyaadi, ‘Differential Polytropic Model for Simulation of Stirling Engines Considering Various Regenerators Models’, Modares Mech.
Bell, ‘Simulation, manufacture and experimental validation of a novel single-acting free-piston Stirling engine electric generator’, Appl.
Andraka, ‘Numerical Simulation of Heat Pipe-Assisted Latent Heat Thermal Energy Storage Unit for Dish-Stirling Systems’, J.

Jalali, Performance analysis of cross-flow forward osmosis membrane modules with mesh feed spacer using three-dimensional computational fluid dynamics simulations, Chemical Engineering and Processing - Process Intensification 168 (2021) 108583. https://doi.org/10.1016/j.cep.2021.108583
Fletcher, CFD study of the effect of unsteady slip velocity waveform on shear stress in membrane systems, Chem.
Dosoretz, Experimental characterization and numerical simulation of the anti-biofuling activity of nanosilver-modified feed spacers in membrane filtration, Journal of Membrane Science 475 (2015) 320-329. https://doi.org/10.1016/j.memsci.2014.10.042

In order to study the penetration of the cutting fluid to the cutting zone, the computational fluid dynamics (CFD) simulation was also performed.
Liu, Investigations of tool edge radius effect in micromachining: A FEM simulation approach, Journal of Materials Processing Technology, 195 (2008) 204-211.

Simulation 0: Base Project The inputs, along with the climatic file, allow the simulation to run.
Table 11 presents a summary of the simulations of the base project – Simulations 0.
Synthesis of the Thermo-Energetic Simulations of Sky House The following figures are a synthesis of the simulations executed: Figure 17 - Simulation 0: Base project Figure 18- Simulation 1: Building optimization with passive solutions Figure 19 - Simulation 2: Building optimization with passive and active solutions 4.
Simulation 1.2: Triple Glazing Window In this simulation, the double pane window is replaced by a triple glazing window.
Thesis, Universidade de Coimbra, 2017 [62] https://www.linkedin.com/pulse/role-cfd-evaluating-occupant-thermal-comfort-sandip-jadhav/.

The two volume fraction images in Figure 1, which are obtained from CFD numerical simulations, intuitively show the stratification and focusing behaviors of micro fluids within the device (given in the top and lateral view respectively).
The simulation results demonstrate that under the appropriate scale and motion conditions, the introduced feature steps have no substantial impact on flowing properties of the micro fluids.

C.F.D. simulations were performed to initially evaluate the frequency and velocity fields of the vortex streets for typical projectile flight: MACH 2.5 at muzzle decreasing to MACH 1.5 throughout flight range of 1000 m (Figure 9).
In turn, a simulation of bullet and harvester assembly dynamics is to be performed to evaluate the dynamic performance of the system in terms of stability and trajectory change.

Recent laboratory observations and computer simulations indicate that hardware modifications to the GLCC can have a profound effect on GLCC performance [4].
Shirazi, Local velocity measurements and computational fluid dynamics (CFD) simulations of swirling flow in a gas–liquid cylindrical cyclone separator, Engineering Technology Conference on Energy, Texas, (2001) 15, pp 23–30