Dynamic BFECC Characteristic Mapping method for fluid simulations

In this paper, we present a new numerical method for advection in fluid simulation. The method is built on the Characteristic Mapping method. Advection is solved via grid mapping function. The mapping function is maintained with higher order accuracy BFECC method and dynamically reset to identity mapping whenever an error criterion is met. Dealing with mapping function in such a way results in a more accurate mapping function and more details can be captured easily with this mapping function. Our error criterion also allows one to control the level of details of fluid simulation by simply adjusting one parameter. Details of implementation of our method are discussed and we present several techniques for improving its efficiency. Both quantitative and visual experiments were performed to test our method. The results show that our method brings significant improvement in accuracy and is efficient in capturing fluid details.

[1]  Eric Galin,et al.  Proceedings of the Second Eurographics conference on Natural Phenomena , 2005 .

[2]  Toshiya Hachisuka.  Combined Lagrangian-Eulerian approach for accurate advection , 2005, SIGGRAPH '05.

[3]  Jerry Tessendorf,et al.  The Characteristic Map for Fast and Efficient VFX Fluid Simulations , 2011 .

[4]  Ronald Fedkiw,et al.  A vortex particle method for smoke, water and explosions , 2005, ACM Trans. Graph..

[5]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[6]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[7]  Ronald Fedkiw,et al.  An Unconditionally Stable MacCormack Method , 2008, J. Sci. Comput..

[8]  Ignacio Llamas,et al.  FlowFixer: Using BFECC for Fluid Simulation , 2005, NPH.

[9]  Ronald Fedkiw,et al.  Animation and rendering of complex water surfaces , 2002, ACM Trans. Graph..

[10]  T. Dupont,et al.  Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function , 2003 .

[11]  Hyeong-Seok Ko,et al.  A Semi‐Lagrangian CIP Fluid Solver without Dimensional Splitting , 2008, Comput. Graph. Forum.

[12]  S. Zalesak.  Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[13]  Greg Humphreys,et al.  Physically Based Rendering, Second Edition: From Theory To Implementation , 2010 .

[14]  James F. O'Brien,et al.  A semi-Lagrangian contouring method for fluid simulation , 2006, ACM Trans. Graph..

[15]  James F. O'Brien,et al.  A semi-Lagrangian contouring method for fluid simulation , 2005, TOGS.

[16]  Benjamin Seibold,et al.  A gradient-augmented level set method with an optimally local, coherent advection scheme , 2009, J. Comput. Phys..

[17]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[18]  Ignacio Llamas,et al.  Advections with Significantly Reduced Dissipation and Diffusion , 2007, IEEE Transactions on Visualization and Computer Graphics.

[19]  Yongning Zhu,et al.  Animating sand as a fluid , 2005, SIGGRAPH 2005.