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A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid. François Dagenais Jonathan Gagnon Eric Paquette. Melting and solidification. Animation of transition between Liquid phase Rigid phase Non- elastic materials Lagrangian simulation
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A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid François Dagenais Jonathan Gagnon Eric Paquette
Melting and solidification • Animation of transition between • Liquid phase • Rigid phase • Non-elasticmaterials • Lagrangian simulation • Almostrigid longer computational times
Goals • Improvedlagrangian simulation of meltingobjects • Improvedstability • Shortercomputational times • Easier control
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Previouswork • Melting and solidification • Solved for eulerian approaches[Stam 1999] [Carlson et al. 2002][Fält and Roble 2003] [Rasmussen et al. 2004][Batty and Bridson 2008] • Still a challenge for lagrangianapproaches Carlson et al.2002 Batty and Bridson2008
Previouswork • Lagrangian • Variable viscosity[Muller et al. 2003] • Elastic [Solenthaler et al. 2007] [Chang et al. 2009] • Plastic[Paivaet al. 2006] [Paiva et al. 2006] [Solenthaleret al.2007]
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Melting and solidification • Integrated in a SPH fluidsolver • Minimisation problem
Deformationerror • Differencebetween • Currentdeformation • Target deformation
Target Deformation • Based on relative position of neighbors
Integration Initializerigidity forces Computedensity and pressure Predictparticles position Compute forces (SPH) Computeparticles deformationerror Computerigidity forces Adjustrigidity forces Update velocity and position Stoppingcriterion met? t > tend ? no no yes yes END
Integration Initialise rigidity forces Predictparticles position Computeparticles deformationerror Adjustrigidity forces Stoppingcriterion met? no yes
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Why? • Particlesonly affect neighbors • Slow convergence • Earlytermination Almost no variation of !
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Stability • Other sources of instability • Pressure forces • Heat diffusion
Adaptative time step • Advantages • Stable simulation • Shortercomputational times • « Courant–Friedrichs–Lewy » condition
Adaptative time step • Maximum velocity estimation • Previous maximal velocity • Maximal acceleration
Heat diffusion • Increases simulation realism • A temperature Tiisassigned to eachparticle • Specified by the user • Updatedusingheat diffusion equation • Temperature affects rigidity
Heat diffusion • Unstablewhen • Large time step • Large heat diffusion coefficient
Heat diffusion • Proposedapproach • Implicit formulation • Handleindividuallyeach pair of neighborparticles
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Rigid forces computation takesmost of the computational times Time per iterationincreases as the fluidbecome more rigid Timestepindependent of rigidity Variable rigidity = longer computational time, because of the propagation conditions
Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion
Limitations • Model does not support rotationnal mouvements • Too slow for small si • Not physically exact, but visually plausible
Conclusion • Improvedlagrangian simulation of melting and solidification • Smallercomputational times • Improvedstability and control • Futur works • Handlerotationalbehaviors • Furtherimprovecomputational times
Heat diffusion • Proposedapproach • Implicit formulation • Handleindividuallyeach pair of neighborparticles 1 2 4 3
Heat diffusion • Neighbors traversalorder affects results • Solutions • Randomizetraversalorder • Average of normal and reverse order • Used in ourexamples