Detail Enhancement And Air-Liquid Coupling Simulation For Physically-based Fluid Animation

Physically-based fluid animation is widely applied in the fields of film and television Special Effects,video games,and Virtual Reality.It also plays a vital auxiliary role in maritime military simulation and industrial fluid modeling.The existing fluid animation technique can simulate the macroscopic motion of fluid and the fluid-solid coupling scene efficiently and realistically,but it is still unable to completely prevent the numerical dissipation to retain enough details of the fluid surface,nor can it efficiently generate the air-liquid coupling animation with high realistic sense.With the development of technology and the progress of society,people have put forward higher requirements for fluid animation,including more accurate flow trends,more realistic animation result,more efficient calculation methods,and richer micro-details,which brings great challenges to physically-based fluid animation technology.This thesis chooses the continuous fluid controlled by Navier-Stokes(N-S)equations as the research object,and uses Smoothed Particle Hydrydynamics(SPH)as the discretization method.Focusing on the problem of detail enhancement and air-liquid coupling simulation in fluid animation,the thesis and gradually improves the fidelity,artistry,richness and realism of fluid animation with low computational overhead,so as to achieve low dissipation,multi-detail,multi-element and high realism fluid animation under the unified particle framework.The main work and innovations of this thesis are listed as follows:(1)To solve the problem of numerical dissipation caused by the missing angular velocity tensors of fluid particles under rough discretization,a linear velocity correction method based on Rankine vortex model is proposed.First,such method describes the rotation state of particles according to the difference of angular velocity between two time-steps.Then,rotating particles are approximated as rigid-like cores of Rankine vortex,and the core radius is calculated adaptively.Finally,according to the angular velocity loss of neighbor particles,the linear velocity of the target particles is corrected based on the induction velocity profile.I this method the influence on the trajectory of the target particle from the tangential viscosity generated by the rotation of neighbor particles is taken into account,making the simulation result more realistic.The experimental results show that the proposed algorithm does not introduce more positive feedback than viscous damping,and can restore the surface details of the fluid animation effectively under the premise of ensuring stability.(2)To solve the problem of vorticity dissipation in fluid field caused by the loss of the normal velocity of the particles in the vortex during the advection-projection process,a turbulence enhancement algorithm is proposed in this thesis and it is named Vorticity refinement(VR)method.Firstly,the vorticity equation is derived from the curl form of the N-S equation,and the vorticity dissipation is calculated based on the difference between the theoretical vorticity and the actual vorticity.Furthermore,the particle discretization is conducted on the flow function,and the dissipated vorticity is fed back to the linear velocity field,so that the vorticity of the vortex can be maintained.The experimental results show that this method can achieve the enhancement of turbulence effect with ignorable computational overhead.It can not only enhance the existing vortices,but also generate new vortices at potential locations.(3)Aiming at the high-efficiency simulation of foam details,an efficient one-way coupling model based on velocity field is established in this thesis.First,the amount of the new generated foam particles is determined based on the kinetic energy and the velocity difference between fluid particles,and random initialization is performed based on the source fluid particles.Then,by ignoring the influence of small-mass foam on large-mass fluids,a high-efficiency air-liquid coupling based on the velocity field is achieved,and the coupling parameters are set according to the degree of coupling.Finally,the Brownian motion of foam particles is achieved based on the Schlick random function,which solves the problem of the distortion of the regular distribution of foam particles.Experimental results show that this method can achieve a more filling foam effect and a more realistic movement trend description.At the same time,the proposed method avoids the two-way neighbor search,which greatly improves the simulation efficiency.(4)To solve the problem of multi-scale air-liquid coupling simulation,this thesis proposes a multi-scale air-liquid simulation method under a unified framework to simulate air particles with different radii in the liquid and their coupling process with liquid particles.The air in the liquid includes a large-size air material with a visible shape and a small-size air material with an invisible shape.Different radii make them have different coupling characteristics.Therefore,the air-liquid coupling simulation problem has multi-scale complex characteristics.First,this method uses the probability density function of log-normal distribution to calculate the size of air particls where the large-sized gas particles have a random large radius,and the small-sized gas particles have a uniform small radius.Then,based on the particle radius and the existence time,a gas particle deletion mechanism based on the half-life is designed.Next,six dynamic models are extablished according to the size of the air particles and their coupling degree with fluid,and the improved high-order kernel function is used to simulate the weak attractive force and strong repulsive forces between particles.Finally,the mass transfer phenomenon between large-size air particles is implemented based on the reverse diffusion equation.Experimental results show that the proposed method can achieve multi-scale air simulation in liquid under a unified particle framework,while avoiding the instability caused by random initialization.Based on the above efforts,this thesis carried out research on physics-based fluid animation,and put forward a series of algorithms in SPH method numerical correction,high-frequency turbulence simulation,high-efficiency foam simulation,multi-scale gas-liquid coupling simulation,to achieve a unified particle framework for high-efficiency,high-realistic fluid simulation system.The research work of this thesis not only has high theoretical value in the research field of computer graphics,but also provides strong technical support for the development of industries including film,video,game,virtual reality,etc.