Fluid & Rigid Body InteractionMotivationTypes of CouplingSolid-to-Fluid ReactionFluid-to-Solid ReactionOne-Way InadequacyTwo-Way Interaction MethodsVOFCIP methodALE methodDLM methodDLM Method (cont.)Prior Two-Way LimitationsRigid Fluid MethodRigid Fluid Method (cont.)Semi-Lagrangian MethodComputational DomainsMarker-And-Cell TechniqueMAC Technique (cont.)MAC Boundary ConditionsFluid DynamicsSimplifying AssumptionNotationDifferential OperatorsConservation of MassConservation of MomentumSlide 26Slide 27Slide 28Overview of Fluid Steps1. Best Guess Velocity2. Pressure ProjectionRigid Body DynamicsConservation of RigiditySlide 34Governing EquationsImplementation1. Solve Navier-Stokes2. Calculate Rigid Body Forces3. Enforce Rigid MotionRigid Fluid AdvantagesUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillQuickTime™ and aTIFF (LZW) decompressorare needed to see this picture.Fluid & Rigid Body InteractionFluid & Rigid Body InteractionComp 259 - Physical ModelingCraig BennettsApril 25, 2006Comp 259 - Physical ModelingCraig BennettsApril 25, 2006University of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillMotivationMotivationFluid/solid interactions are ubiquitous in our environmentRealistic fluid/solid interaction is complex not feasible through manual animationFluid/solid interactions are ubiquitous in our environmentRealistic fluid/solid interaction is complex not feasible through manual animationUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillTypes of CouplingTypes of CouplingOne-way solid-to-fluid reactionOne-way fluid-to-solid reaction Two-way coupled interactionOne-way solid-to-fluid reactionOne-way fluid-to-solid reaction Two-way coupled interactionUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillSolid-to-Fluid ReactionSolid-to-Fluid ReactionThe solid moves the fluid without the fluid affecting the solidRigid bodies are treated as boundary conditions with set velocitiesFoster and Metaxas, 1997 Foster and Fedkiw, 2001Enright et al., 2002bThe solid moves the fluid without the fluid affecting the solidRigid bodies are treated as boundary conditions with set velocitiesFoster and Metaxas, 1997 Foster and Fedkiw, 2001Enright et al., 2002bUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillFluid-to-Solid ReactionFluid-to-Solid ReactionThe fluid moves the solid without the solid affecting the fluidSolids are treated as massless particlesFoster and Metaxas,1996The fluid moves the solid without the solid affecting the fluidSolids are treated as massless particlesFoster and Metaxas,1996University of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillOne-Way InadequacyOne-Way InadequacyFails to simulate true fluid/solid interactionReactive as opposed to interactiveFails to simulate true fluid/solid interactionReactive as opposed to interactiveUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillTwo-Way Interaction MethodsTwo-Way Interaction MethodsVolume Of Fluid and Cubic Interpolated Propagation (VOFCIP)Arbitrary Lagrangian-Eulerian (ALE)Distributed Lagrange Multiplier (DLM) Rigid FluidVolume Of Fluid and Cubic Interpolated Propagation (VOFCIP)Arbitrary Lagrangian-Eulerian (ALE)Distributed Lagrange Multiplier (DLM) Rigid FluidUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillVOFCIP methodVOFCIP methodTakahashi et al. (2002,2003)Models forces due to hydrostatic pressureneglects dynamic forces and torques due to the fluid momentumOnly approximates the solid-to-fluid couplingTakahashi et al. (2002,2003)Models forces due to hydrostatic pressureneglects dynamic forces and torques due to the fluid momentumOnly approximates the solid-to-fluid couplingUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillALE methodALE methodOriginally used in the computational physics community [Hirt et al. (1974)]Finite element techniqueDrawbacks:computational grid must be re-meshed when it becomes overly distortionat least 2 layers of cell elements are required to separate solids as they approachOriginally used in the computational physics community [Hirt et al. (1974)]Finite element techniqueDrawbacks:computational grid must be re-meshed when it becomes overly distortionat least 2 layers of cell elements are required to separate solids as they approachUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillDLM methodDLM methodOriginally used to study particulate suspension flows [Glowinski et al. 1999]Finite element techniqueDoes not require grid re-meshingEnsures realistic motion for both fluid and solidOriginally used to study particulate suspension flows [Glowinski et al. 1999]Finite element techniqueDoes not require grid re-meshingEnsures realistic motion for both fluid and solidUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillDLM Method (cont.)DLM Method (cont.)Does not account for torquesRestricted to spherical solidsSurfaces restricted to be at least 1.5 times the velocity element size apartrequires application of repulsive forceDoes not account for torquesRestricted to spherical solidsSurfaces restricted to be at least 1.5 times the velocity element size apartrequires application of repulsive forceUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillPrior Two-Way LimitationsPrior Two-Way LimitationsSolids simulated as fluids with high viscosityultimately results in solid deformation, which is undesirable in modeling rigid bodiesDo not account for torque on solidsBoundary proximity restrictionsSolids simulated as fluids with high viscosityultimately results in solid deformation, which is undesirable in modeling rigid bodiesDo not account for torque on solidsBoundary proximity restrictionsUniversity of North Carolina - Chapel HillUniversity of North Carolina - Chapel HillRigid Fluid MethodRigid Fluid MethodCarlson, 2004Extends the DLM methodexcept uses finite differencesUses a Marker-And-Cell (MAC) techniquePressure projection ensures the incompressibility of fluidCarlson,