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ABSTRACT
A convergence identification method for oscillatory numerical simulation is proposed, in which the numerical solution can converge at the inflection point with respect to the time step. In addition, an algorithm to verify the appropriate time step is also proposed. The feasibility of the proposed method is further verified by its application to a case study involving combined natural and magnetohydrodynamics convection in a Joule-heated cavity using finite-volume methods. It is found that the two approaches have the same results and can judge the validity of the time step used in accurate computation of fluid flow and heat transfer.
Nomenclature
| A | = | amplitude |
| g | = | gravitational acceleration (m/s2) |
| Ha | = | Hartmann number |
| L | = | enclosure height (m) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | period, time (s) |
| T | = | temperature (K) |
| u | = | x-velocity component (m/s) |
| U | = | dimensionless x-velocity component |
| v | = | y-velocity component (m/s) |
| V | = | dimensionless y-velocity component |
| W | = | enclosure width (m) |
| x | = | x-coordinate (m) |
| X | = | dimensionless x-coordinate |
| y | = | y-coordinate (m) |
| Y | = | dimensionless y-coordinate |
| Greek symbols | = | |
| θ | = | dimensionless temperature |
| σ | = | electrical conductivity (ms/s) |
| τ | = | dimensionless time |
| φ | = | potential difference (V) |
Nomenclature
| A | = | amplitude |
| g | = | gravitational acceleration (m/s2) |
| Ha | = | Hartmann number |
| L | = | enclosure height (m) |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| t | = | period, time (s) |
| T | = | temperature (K) |
| u | = | x-velocity component (m/s) |
| U | = | dimensionless x-velocity component |
| v | = | y-velocity component (m/s) |
| V | = | dimensionless y-velocity component |
| W | = | enclosure width (m) |
| x | = | x-coordinate (m) |
| X | = | dimensionless x-coordinate |
| y | = | y-coordinate (m) |
| Y | = | dimensionless y-coordinate |
| Greek symbols | = | |
| θ | = | dimensionless temperature |
| σ | = | electrical conductivity (ms/s) |
| τ | = | dimensionless time |
| φ | = | potential difference (V) |