Physically Based Real-Time Fluid Simulation Technique

Navier-Stokes equations has been developed and consummated as early as the18th century, which are a set of precise modeling of ?uid behavior of partial differen-tial equations. It describes the internal changes and relationship between the rate andpressure of the ?uids. Based in these equations and according to the discrete solutionour paper implement the real-time simulation of the realistic ?uid initially. Becauseof the physically based model, our simulation can re?ect the details of the ?uid morerealistically and can realize some complex scene more conveniently, such as the in-teraction of the rigid and ?uids, multiple interacting liquids, fire effect, bubble effect,explosion effect, etc.The second chapter firstly presentate and analyse the N-S equation from a math-ematical point. In order to deepen understanding, we also give a presentation of therelated derivation. Based on these, we further analyse the method of numerically solu-tion of the N-S equations. There we introduce the grid method and the finite differencemethod. Next we focuse on how to solve these equations which laid the foundationof the following work. According to the Helmhotz-Hodge decompose theorem, webreak down the complex partial differential into some steps which are easy to solve.Finally we recommend the MOC method in dealing with the partial differential equa-tion, which is the mathematical footstone of the reverse method for the solution of theadvection equation.In the third chapter, we give the all-around process for solving the N-S equationsand show the arithmetic detailly. For the diffusion step, we refer the book for thepartial differential and numerically calculation, research the principle and differentmethods of it. For the advect step, which is the most complex part of the equations,we discuse not only the foward method but also the reverse method and the BFECCmethod. Finally we focuse on the numerical dissipation question, present a variety ofsolutions.The process in our paper is different from the commen stable ?uids scheme. weapply the diffusion and advect step not only on the the velocity component but also onthe pressure component, temperature component and density component. because of this the final projection step is changed in our method. Further more, we combine thefoward method and reverse method of together when dealing with the advect equation.In our realization, we define a lot of controlable parameters for the simulation, and wecan set a contrast mode in the simulation which can observe the effect of differentparameters easily.The fourth chapter is focuse on the obstacle, we analyse and design both of thedata structure, the definetion and realization of the different types of the obstacle andthe questions appear in the simulation. We introduce the Cohen-Sutherland methodwhen dealing with the collision detection question. Based of this, we make a deep andinteresting disussion. There are a lot of ?aws in our realization which impulse us inthe futher study.