![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
A Lagrangian–Eulerian advection scheme (LEAS) with Moment-of-Fluid (MoF) interface reconstruction is presented for interfacial flows. In MoF method, in addition to the volume fraction field, material centroid is used for interface reconstruction. Physically material centroid indicates the material location inside a mixed cell. Therefore, MoF method reconstructs linear interfaces exactly and is second order accurate for curved interfaces. Despite being second order accurate for static interface reconstruction, MoF reconstruction is inaccurate when centroid is not properly advected. An accurate centroid advection method based on Barycenter of centroid is discussed here. A comparison of this centroid advection with the pure Lagrangian advection based on Runge–Kutta integrator is demonstrated for two different advection tests. The superiority of MoF is established by comparing the volume error norm with other interface reconstructions. Significant improvement in accuracy is observed when LEAS material advection is used in conjuction with accurate centroid advection for MoF reconstruction.
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 |
| x: | = | centroid |
| M: | = | first moment of material |
| EMoF: | = | optimization function for MoF method |
| E: | = | Geometrical error |
| V: | = | volume |
| p: | = | direction vector |
| Greek symbols | = | |
| Ωc: | = | computational cell |
| α: | = | step length |
| Ψ: | = | stream function |
| ω: | = | angular velocity |
| Superscripts | = | |
| n, n + 1: | = | old and new time levels |
| T: | = | final time |
| 0: | = | initial time |
| Subscripts | = | |
| ref: | = | reference or primary value |
| i, j: | = | mesh indices along x and y |
| k: | = | iteration counter for BFGS routine |
| L: | = | Lagrangian precell |
| c: | = | Centroid |
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 |
| x: | = | centroid |
| M: | = | first moment of material |
| EMoF: | = | optimization function for MoF method |
| E: | = | Geometrical error |
| V: | = | volume |
| p: | = | direction vector |
| Greek symbols | = | |
| Ωc: | = | computational cell |
| α: | = | step length |
| Ψ: | = | stream function |
| ω: | = | angular velocity |
| Superscripts | = | |
| n, n + 1: | = | old and new time levels |
| T: | = | final time |
| 0: | = | initial time |
| Subscripts | = | |
| ref: | = | reference or primary value |
| i, j: | = | mesh indices along x and y |
| k: | = | iteration counter for BFGS routine |
| L: | = | Lagrangian precell |
| c: | = | Centroid |