Smoothed particle hydrodynamics simulation: a tool for accurate characterization of microfluidic devices

Numerical study of single bubble rising dynamics for the variability of moderate Reynolds and sidewalls influence: A bi-phase SPH approach

“…Table 1: The analysis of error norms for the rising bubble temporal evolution with the SPH approach for the comparison between different ∆x, with the ∆x = 1/500 results as the reference solution. Consequently, even with a distance of 1/200, it is consistent with the result of ∆x = 1/500 and suitable for solving bubbles in an ellipsoidal regime [43,30]. Thus, after realizing that the examples with a resolution between 1/200 and 1/500 reflect coherent results.…”

“…These two examples of ∆x describe correspondence in the velocities and the contours. Consequently, even with a distance of 1/200, it is consistent with the result of ∆x = 1/500 and suitable for solving bubbles in an ellipsoidal regime[43,30]. Thus, after realizing that the examples with a resolution between 1/200 and 1/500 reflect coherent results.…”

“…It is implemented that initial density with the effect of hydrostatic pressure condition -HPC (Appendix F). Meanwhile, the boundary wall conditions applying are defined through dummy particle methodology [44,30] that is introduced the Appendix G for the free-slip and no-slip conditions. Furthermore, it is presented the summary of the solution algorithm procedure for the bi-phase SPH approach in Appendix H.…”

“…1 are used: i) with a blue star, Re = 35 and Eo = 10, for an ellipsoidal bubble; and ii) with orange star, Re = 35 and Eo = 125, for a dimpled ellipsoidal cap bubble. Both examples are widely used in the validation of numerical simulations in the formation of rising bubbles [30,41].…”

“…The ∇ • ∇( * ) MO shape used a derivation similar to the other proposed [54,30]. However, due to the precision and efficiency requirements, the most common form used is constructed, like a combination of the finite difference approach, and the expansion of the Taylor series.…”