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ABSTRACT
Moment-of-fluid (MOF) method is an extended volume-of-fluid method which incorporates material centroid in addition to material volume fraction for interface reconstruction. MOF is an exact method for linear interfaces and second-order accurate for curved interfaces. The interface reconstruction in the MOF is based on the best possible approximation of material centroid. Exact matching of the reconstructed centroid with the reference centroid produces the exact material configuration. This is however possible only for linear interfaces when the material volume and centroid are consistent. Consistent moments can be obtained by adaptive mesh refinement moment-of-fluid method (AMR–MOF) in the interfacial cells based on a refinement criterion. In the case of AMR–MOF, the centroid error is used as the refinement criterion. Since the material centroid is approximated to the reference centroid in interface reconstruction, centroid error is always higher than the prescribed tolerance. Therefore, intermediate interface reconstructions in AMR–MOF are insignificant and increase the computational time as the refinement always proceeds to the maximum level. In the present article, a refined moment-of-fluid (RMOF) method for evolving interfaces is proposed. In RMOF, each mixed cell is refined to the prescribed level of refinement as opposed to AMR–MOF where refinement is dependent on a refinement criterion. Since the number of interface reconstructions performed at each level of refinement in AMR–MOF is much higher than that of the fixed level of refinement in RMOF, the computation time is significantly reduced in RMOF. The reduction in computational time for the proposed RMOF method in comparison to the standard MOF and AMR–MOF is demonstrated in this work through a series of time-reversed advection tests.
Nomenclature
| Roman symbols | = | |
| f | = | volume fraction |
| t | = | time |
| u | = | velocity vector |
| n | = | unit outward interface normal vector |
| r | = | position vector of a point on interface |
| d | = | signed normal distance |
| x, y | = | coordinate directions |
| = | volume | |
| EMOF | = | optimization function for MOF method |
| M | = | first moment of material |
| E | = | Geometrical error |
| Greek symbols | = | |
| ΩC | = | computational cell |
| ℒC | = | Lagrangian precell |
| Ψ | = | stream function |
| Superscripts | = | |
| n, n + 1 | = | old and new time levels |
| T | = | final time |
| 0 | = | initial time |
| ref | = | reference material |
| Subscripts | = | |
| ref | = | reference material value |
| i | = | material index |
| c | = | cell under consideration |
Nomenclature
| Roman symbols | = | |
| f | = | volume fraction |
| t | = | time |
| u | = | velocity vector |
| n | = | unit outward interface normal vector |
| r | = | position vector of a point on interface |
| d | = | signed normal distance |
| x, y | = | coordinate directions |
| = | volume | |
| EMOF | = | optimization function for MOF method |
| M | = | first moment of material |
| E | = | Geometrical error |
| Greek symbols | = | |
| ΩC | = | computational cell |
| ℒC | = | Lagrangian precell |
| Ψ | = | stream function |
| Superscripts | = | |
| n, n + 1 | = | old and new time levels |
| T | = | final time |
| 0 | = | initial time |
| ref | = | reference material |
| Subscripts | = | |
| ref | = | reference material value |
| i | = | material index |
| c | = | cell under consideration |