“Combined Lagrangian-Eulerian approach for accurate advection” by Hachisuka

In this poster, we propose a new algorithm to accurately calculate advection equations. Even the latest fluid simulations [Fattal and Lischinski 2004] have been suffering from the numerical errors in advection equations. These numerical errors cause mass dissipation and motion damping of fluid, so the errors hide the detail of fluid animations as the result. Unlike some previous methods [Enright et al. 2002], the proposed method can deal with not only fields with sharp boundaries but also blurry fields (i.e.no boundaries) very accurately. Calculating the advection of blurry fields is important because many physical quantities have blurry distributions. The proposed method mainly consists of the advection phase and the non-advection phase. In the advection phase, the method calculates the current field from the initial field by using the combined method of lagrangian method and eulerian method. In the non-advection phase, influences of non-advection terms are added back to the initial field by using the mapping functions of advection equations.

1. Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I. 2002. A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183, 1, 83–116.
2. Fattal, R., and Lischinski, D. 2004. Target-driven smoke animation. ACM Trans. Graph. 23, 3, 441–448.