This paper presents a physically based simulation algorithm for animating viscous fluid. This algorithm introduces an equivalent energy model to couple diffusion processes and projection processes into a single linear system for solving together. This model implicitly solves the viscous term while simultaneously solving pressure to guarantee incompressibility of fluid. Furthermore it automatically captures the vital zero-traction boundary conditions, eliminating artifacts caused by directly approximating this boundary condition. Furthermore, this paper utilizes the physical information taken by particles to solve the advection term for battling numerical dissipation and constructs an implicit surface of fluid based on particles. Finally, the test results show the efficiency, accuracy and stability of the algorithm, and it can nicely simulate deformation characteristics of various viscous fluids, efficiently supporting variable viscosity.%给出一种基于物理的粘性流体模拟算法,该算法采用一种等价的能量模型将耗散过程与投影过程耦合入一个线性系统中同时求解.实现了在全隐式求解粘性项的同时求解压力来保证流体的不可压缩性,并且自动捕捉了至关重要的零应力边界条件,从而消除了由于直接近似该边界条件而导致的失真现象,此外,利用粒子携带的物理信息来求解对流项以抑制数值耗散,同时,基于粒子构建流体的隐式表面.最后的实验结果显示出算法的有效性、精确性及稳定性.该算法可以细致地体现各种粘度的流体的形变特征,并有效地支持可变粘性.
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