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A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid

This paper presents a novel prediction-correction approach to enhance Lagrangian simulations of melting and solidification processes in Stable Smoothed Particle Hydrodynamics (SPH). The proposed method aims to improve stability, reduce computational times, and provide better control over the simulation of phase transitions from liquid to rigid states. It incorporates a rigorous handling of rigidity forces, adaptive time-stepping, and heat diffusion to address challenges in current Lagrangian techniques. Results demonstrate significant improvements over traditional methods, despite limitations such as rotational movement handling.

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A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid

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  1. A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid François Dagenais Jonathan Gagnon Eric Paquette

  2. Melting and solidification • Animation of transition between • Liquid phase • Rigid phase • Non-elasticmaterials • Lagrangian simulation • Almostrigid longer computational times

  3. Goals • Improvedlagrangian simulation of meltingobjects • Improvedstability • Shortercomputational times • Easier control

  4. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  5. 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

  6. 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]

  7. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  8. Melting and solidification • Integrated in a SPH fluidsolver • Minimisation problem

  9. Deformationerror • Differencebetween • Currentdeformation • Target deformation

  10. Target Deformation • Based on relative position of neighbors

  11. Rigidity forces correction

  12. Rigidity forces correction

  13. Rigidity forces correction

  14. 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

  15. Integration Initialise rigidity forces Predictparticles position Computeparticles deformationerror Adjustrigidity forces Stoppingcriterion met? no yes

  16. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  17. Why? • Particlesonly affect neighbors • Slow convergence • Earlytermination Almost no variation of !

  18. Constraints propagation

  19. Constraints propagation

  20. Constraints propagation

  21. Constraints propagation

  22. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  23. Stability • Other sources of instability • Pressure forces • Heat diffusion

  24. Adaptative time step • Advantages • Stable simulation • Shortercomputational times • « Courant–Friedrichs–Lewy » condition

  25. Adaptative time step • Maximum velocity estimation • Previous maximal velocity • Maximal acceleration

  26. Heat diffusion • Increases simulation realism • A temperature Tiisassigned to eachparticle • Specified by the user • Updatedusingheat diffusion equation • Temperature affects rigidity

  27. Heat diffusion • Unstablewhen • Large time step • Large heat diffusion coefficient

  28. Heat diffusion • Proposedapproach • Implicit formulation • Handleindividuallyeach pair of neighborparticles

  29. Heat diffusion – Implicit formulation

  30. Heat diffusion - video

  31. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  32. Video

  33. 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

  34. Comparisonwithtraditionnalviscosity

  35. Overview • Previouswork • ProposedApproach • Melting and solidification • Constraints propagation • Stabilityimprovements • Results • Limitations and conclusion

  36. Limitations • Model does not support rotationnal mouvements • Too slow for small si • Not physically exact, but visually plausible

  37. Conclusion • Improvedlagrangian simulation of melting and solidification • Smallercomputational times • Improvedstability and control • Futur works • Handlerotationalbehaviors • Furtherimprovecomputational times

  38. Thankyou!

  39. Heat diffusion • Proposedapproach • Implicit formulation • Handleindividuallyeach pair of neighborparticles 1 2 4 3

  40. Heat diffusion • Neighbors traversalorder affects results • Solutions • Randomizetraversalorder • Average of normal and reverse order • Used in ourexamples

  41. Adaptive time step

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