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Nonunique steady flow solutions for pressure correction equations applied in the regime of natural convection inside free vented enclosures

ABSTRACT Thermal buoyancy-driven natural convection in partial enclosures with multiple free openings is investigated regarding the coupling of the pressure correction algorithm with inner-loop iterations of the pressure correction equation. Unexpected steady flow phenomena, i.e., nonunique steady flow states, are observed when different inner-loop iterations m and relaxation factors α of the pressure correction equation are implemented, after the appropriate assumptions on the free opening boundary conditions are made. Numerical experiments and benchmark exercises confirm that definitions on the free openings could be too weak to ensure global similarity to the results of extended domain methodology. Furthermore, inner-loop iteration m and relaxation factor α could have similar effects on the nonunique steady flow results. As thermal Rayleigh number is relatively low, a linear relationship could be established among inner-loop iteration m, relaxation factor α, and mass exchange rate, MER. In addition, harmonic arrangements on the iteration residuals of the momentum equation and the pressure correction equation could accelerate convergence of the whole pressure correction algorithm.