Interface Tracking in Eulerian and MMALE Calculations

Transcription

1 Interface Tracking in Eulerian and MMALE Calculation Gabi Luttwak Rafael P.O.Box 2250, Haifa 31021,Irael

2 Interface Tracking in Eulerian and MMALE Calculation 3D Volume of Fluid (VOF) baed recontruction of the interface poition (Young type) General algorithm to find boundary poition in any polyhedron independent of the meh connectivity. Applie both for Euler and moving ALE meh Wa implemented in Autodyn3D for a Carteian Meh The extenion to MMALE meh done in Autodyn 3D uing external uer routine

3 Interface Tracking In multi-material Eulerian and MMALE calculation the boundarie cut the grid line Mot Euler imulation ue Carteian meh In MMALE the grid move and cannot remain Lagrangian

4 Interface Dynamic A zone cut by the interface may include everal material The Motion of the interface will depend upon: Locating the interface poition The advection cheme ued The definition of preure and tre in the multi-material zone (ub-zone hydrodynamic)

5 Locating the interface poition Marker Particle on the interface PIC Particle in cell Interface Recontruction uing the value of ome variable advected through meh: Volume of Fluid method Level Set Method

6 Volume of Fluid Method To preerve the conervation law, the interface poition mut be conitent with the volume of material in each zone. Thu ue thi information to recontruct the interface location!

7 Volume of Fluid Baed Interface Recontruction A B Figure 1 Preferential tranport W.E.Johnon,Hirt Oil cheme donor-acceptor preferential tranport DeBar, Young 2D recontruction Luttwak 1984 Young 3D recontruction

8 3D Interface Recontruction Boundary portion cutting a zone i planar urface in 3D ( traight egment in 2D) The volume of material in the zone and it orientation uniquely determine it poition (Luttwak 1983) It normal given by the gradient of relative partial volume V nˆ V

9 3D Interface Recontruction Thi algorithm wa ued in the 2D code MMALE (Luttwak 1984,1985,1989) It i imilar to Young D method for a Carteian meh We apply it here for a more general moving meh

10 More Than Two Material in A Zone The proce i order dependent SLIC (Noh 1976): order according to the exitence of the material uptream and downtream The fluxe in SLIC like in the OIL cheme Geometry get more complicated We revert to SLIC Figure 3. A zone with 3 material and void

11 The Volume of a Polyhedron It volume i equal to the algebraic um of the volume below it face and up to a reference urface The face are plit into planar triangle V V k k Let 1, 2, 3 be the ditance from the triangle, k, vertice to the plane,then: V k a 3 with a n the projection of the triangle area onto the reference plane n 1 2 3

12 Volume of Wet Polyhedron The wet part of the zone i delimited by the zone face and the boundary plane The zone face plit into triangle The boundary plane taken a the reference plane Let be the ditance of the triangle vertice to the boundary face

13 Volume Below Wet Part of a Triangle all the triangle i wet 3 >0 wet part i a quad wet part i a triangle 1 >0, 2, 3 < a V n k a V n k a V n k

14 The Location of the Boundary Plane in the Zone coordinate along normal to the boundary V() - the wet volume i monotonically increaing function 0 V ( ) V V We olve by Newton-Raphon iteration with binary backup

15 Computation of v For 3D Carteian meh we found bet to ue the Young cheme,which ue all 26 neighbor In the 2D code MMALE, we computed vertex centered v and averaged it to the zone center alo ue all neighbor In the 3D non-carteian meh, we currently ue only the 6 face neighbor - integrating over the cell - we might change thi in future

16 Fragment,Shell or Rod v Computing, make ene only for region wider than everal zone. For fragment, thin hell or rod, when the ize i le than 1-2 zone the direction found may vary quickly and the material might kip from one zone to another We diagnoe thee if the zone doe not have at leat one full and one empty neighbor If true, we revert to SLIC

17 Iolated Fragment or Drop SLIC will remove firt all material preent downtream-may leave the fragment in the ame zone forever Bet olution might be to move them a marker particle with their material peed and integrate them back if they get into other zone where material preent...l

18 Diagonal Advection Uually fluxe computed through face Without the diagonal term un-plit code cannot be econd order. Their effect mot important at interface In the 2D code MMALE we ued re-map technique to compute thee fluxe too with good reult