A new grid structure for domain extension

We present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still effectively capturing fine scale details in regions of interest using dynamic adaptivity.

[1]  Peter Smereka,et al.  Axisymmetric free boundary problems , 1997, Journal of Fluid Mechanics.

[2]  Frank Losasso,et al.  Simulating water and smoke with an octree data structure , 2004, SIGGRAPH 2004.

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

[4]  Robert Bridson,et al.  Animating sand as a fluid , 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]  Jessica K. Hodgins,et al.  A point-based method for animating incompressible flow , 2009, SCA '09.

[8]  Duc Quang Nguyen,et al.  Physically based modeling and animation of fire , 2002, ACM Trans. Graph..

[9]  James F. O'Brien,et al.  Fluid animation with dynamic meshes , 2006, SIGGRAPH 2006.

[10]  James F. O'Brien,et al.  Fluids in deforming meshes , 2005, SCA '05.

[11]  Matthias Müller,et al.  Real-time Eulerian water simulation using a restricted tall cell grid , 2011, SIGGRAPH 2011.

[12]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[13]  Markus Gross,et al.  Two-scale particle simulation , 2011, SIGGRAPH 2011.

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

[15]  R. Bridson,et al.  Matching fluid simulation elements to surface geometry and topology , 2010, ACM Trans. Graph..

[16]  J. Benek,et al.  A 3-D Chimera Grid Embedding Technique , 1985 .

[17]  R. Fedkiw,et al.  USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS , 2003 .

[18]  Markus H. Gross,et al.  Two-scale particle simulation , 2011, ACM Trans. Graph..

[19]  Tayfun E. Tezduyar,et al.  Computation of free-surface flows and fluid–object interactions with the CIP method based on adaptive meshless soroban grids , 2007 .

[20]  Pradeep Dubey,et al.  Large-scale fluid simulation using velocity-vorticity domain decomposition , 2012, ACM Trans. Graph..

[21]  Robert Bridson,et al.  Matching fluid simulation elements to surface geometry and topology , 2010, ACM Transactions on Graphics.

[22]  Kenji Takizawa,et al.  Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme , 2004 .

[23]  J. Benek,et al.  A flexible grid embedding technique with application to the Euler equations , 1983 .

[24]  Ronald Fedkiw,et al.  Wrinkled flames and cellular patterns , 2007, ACM Trans. Graph..

[25]  Ronald Fedkiw,et al.  Efficient simulation of large bodies of water by coupling two and three dimensional techniques , 2006, ACM Trans. Graph..

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

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

[28]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[29]  James F. O'Brien,et al.  Fluid animation with dynamic meshes , 2006, ACM Trans. Graph..

[30]  Frédéric H. Pighin,et al.  Extended Galilean invariance for adaptive fluid simulation , 2004, SCA '04.

[31]  Yoshinori Dobashi,et al.  A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects , 2008, Comput. Graph. Forum.

[32]  Richard H. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer , 1984 .

[33]  Duc Quang Nguyen,et al.  Directable photorealistic liquids , 2004, SCA '04.

[34]  Sarah Tariq,et al.  Interactive fluid-particle simulation using translating Eulerian grids , 2010, I3D '10.

[35]  Leonidas J. Guibas,et al.  Adaptively sampled particle fluids , 2007, SIGGRAPH 2007.

[36]  Matthias Müller,et al.  Real-time Eulerian water simulation using a restricted tall cell grid , 2011, ACM Trans. Graph..

[37]  Ronald Fedkiw,et al.  Wrinkled flames and cellular patterns , 2007, SIGGRAPH 2007.

[38]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[39]  Ronald Fedkiw,et al.  Simulating water and smoke with an octree data structure , 2004, ACM Trans. Graph..

[40]  Renato Pajarola,et al.  Predictive-corrective incompressible SPH , 2009, ACM Trans. Graph..

[41]  Ken Museth,et al.  A PML-based nonreflective boundary for free surface fluid animation , 2010, TOGS.

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

[43]  E. Guendelman,et al.  Efficient simulation of large bodies of water by coupling two and three dimensional techniques , 2006, SIGGRAPH 2006.

[44]  Ken Museth,et al.  Hierarchical RLE level set: A compact and versatile deformable surface representation , 2006, TOGS.

[45]  Andrew Selle,et al.  A vortex particle method for smoke, water and explosions , 2005, ACM Trans. Graph..

[46]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

[47]  Ronald Fedkiw,et al.  Two-Way Coupled SPH and Particle Level Set Fluid Simulation , 2008, IEEE Transactions on Visualization and Computer Graphics.

[48]  Leonidas J. Guibas,et al.  Adaptively sampled particle fluids , 2007, ACM Trans. Graph..