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34
ROSSIGNAC J.: An unconditionally stable MacCormack method
 SIAM J. Sci. Comput
, 2008
"... The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for ..."
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Cited by 65 (16 self)
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The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advection raising the method to second order accuracy, even though each individual step is only first order accurate. In this paper, we rewrite the MacCormack method to illustrate that it estimates the error in the same exact fashion as BFECC. The difference is that the MacCormack method uses this error estimate to correct the already computed forward advected data. Thus, it does not require the third advection step in BFECC reducing the cost of the method while still obtaining second order accuracy in space and time. Recent work replaced each of the three BFECC advection steps with a simple first order accurate unconditionally stable semiLagrangian method yielding a second order accurate unconditionally stable BFECC scheme. We use a similar approach to create a second order accurate unconditionally stable MacCormack method. 1
An unconditionally stable fully conservative semilagrangian method
 J. Comput. Phys
"... SemiLagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFLbased time step restriction of the smallest cell can ..."
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Cited by 19 (10 self)
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SemiLagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFLbased time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semiLagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semiLagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressiblestyle pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. 1.
Textured liquids based on the marker level set
 Computer Graphics Forum
, 2007
"... In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for track ..."
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Cited by 13 (3 self)
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In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for tracking the surface of the liquid, yielding more efficient and accurate results than popular methods like the Particle Level Set method (PLS). Another novelty is that the surface markers allow the MLS to handle nondiffusively surface texture advection, a rare capability in the realm of Eulerian simulation of liquids. We present several simulations of the dynamical evolution of liquids and their surface textures.
Articulated Swimming Creatures
"... We present a general approach to creating realistic swimming behavior for a given articulated creature body. The two main components of our method are creature/fluid simulation and the optimization of the creature motion parameters. We simulate twoway coupling between the fluid and the articulated ..."
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Cited by 12 (3 self)
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We present a general approach to creating realistic swimming behavior for a given articulated creature body. The two main components of our method are creature/fluid simulation and the optimization of the creature motion parameters. We simulate twoway coupling between the fluid and the articulated body by solving a linear system that matches acceleration at fluid/solid boundaries and that also enforces fluid incompressibility. The swimming motion of a given creature is described as a set of periodic functions, one for each joint degree of freedom. We optimize over the space of these functions in order to find a motion that causes the creature to swim straight and stay within a given energy budget. Our creatures can perform path following by first training appropriate turning maneuvers through offline optimization and then selecting between these motions to track the given path. We present results for a clownfish, an eel, a sea turtle, a manta ray and a frog, and in each case the resulting motion is a good match to the realworld animals. We also demonstrate a plausible swimming gait for a fictional creature that has no realworld counterpart.
WOJTAN C.: Tracking surfaces with evolving topology
 ACM Trans. Graph. (SIGGRAPH
, 2012
"... Figure 1: Our method recovers a sequence of highquality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for ..."
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Cited by 12 (2 self)
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Figure 1: Our method recovers a sequence of highquality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multiresolution nonrigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process.
Largescale Fluid Simulation using VelocityVorticity Domain Decomposition
"... through smoke (c) smoke flow around a sphere. We achieve up to three orders of magnitude of performance over standard gridonly techniques. Simulating fluids in largescale scenes with appreciable quality using stateoftheart methods can lead to high memory and compute requirements. Since memory r ..."
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Cited by 6 (0 self)
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through smoke (c) smoke flow around a sphere. We achieve up to three orders of magnitude of performance over standard gridonly techniques. Simulating fluids in largescale scenes with appreciable quality using stateoftheart methods can lead to high memory and compute requirements. Since memory requirements are proportional to the product of domain dimensions, simulation performance is limited by memory access, as solvers for elliptic problems are not computebound on modern systems. This is a significant concern for largescale scenes. To reduce the memory footprint and memory/compute ratio, vortex singularity bases can be used. Though they form a compact bases for incompressible vector fields, robust and efficient modeling of nonrigid obstacles and freesurfaces can be challenging with these methods. We propose a hybrid domain decomposition approach that couples Eulerian velocitybased simulations with vortex singularity simulations. Our formulation reduces memory footprint by using smaller Eulerian domains with compact vortex bases, thereby improving the memory/compute ratio, and simulation performance by more than 1000x for single phase flows as well as significant improvements for freesurface scenes. Coupling these two heterogeneous methods also affords flexibility in using the most appropriate method for modeling different scene features, as well as allowing robust interaction of vortex methods with freesurfaces and nonrigid obstacles.
Enhancing fluid animation with adaptive, controllable and intermittent turbulence. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2010) Zhi Yuan is currently an assistant professor in the Department of Computer Science at th
 Department of Computer Science at the Kent State University. Fan Chen is
"... This paper proposes a new scheme for enhancing fluid animation with controllable turbulence. An existing fluid simulation from ordinary fluid solvers is fluctuated by turbulent variation modeled as a random process of forcing. The variation is precomputed as a sequence of solenoidal noise vector fie ..."
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Cited by 6 (3 self)
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This paper proposes a new scheme for enhancing fluid animation with controllable turbulence. An existing fluid simulation from ordinary fluid solvers is fluctuated by turbulent variation modeled as a random process of forcing. The variation is precomputed as a sequence of solenoidal noise vector fields directly in the spectral domain, which is fast and easy to implement. The spectral generation enables flexible vortex scale and spectrum control following a user prescribed energy spectrum, e.g. Kolmogorov’s cascade theory, so that the fields provide fluctuations in subgrid scales and/or in preferred large octaves. The vector fields are employed as turbulence forces to agitate the existing flow, where they act as a stimulus of turbulence inside the framework of the NavierStokes equations, leading to natural integration and temporal consistency. The scheme also facilitates adaptive turbulent enhancement steered by various physical or userdefined properties, such as strain rate, vorticity, distance to objects and scalar density, in critical local regions. Furthermore, an important feature of turbulent fluid, intermittency, is created by applying turbulence control during randomly selected temporal periods.
Previewbased Sampling for Controlling Gaseous Simulations
"... In this work, we describe an automated method for directing the control of a high resolution gaseous fluid simulation based on the results of a lower resolution preview simulation. Small variations in accuracy between low and high resolution grids can lead to divergent simulations, which is problema ..."
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Cited by 5 (0 self)
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In this work, we describe an automated method for directing the control of a high resolution gaseous fluid simulation based on the results of a lower resolution preview simulation. Small variations in accuracy between low and high resolution grids can lead to divergent simulations, which is problematic for those wanting to achieve a desired behavior. Our goal is to provide a simple method for ensuring that the high resolution simulation matches key properties from the lower resolution simulation. We first let a user specify a fast, coarse simulation that will be used for guidance. Our automated method samples the data to be matched at various positions and scales in the simulation, or allows the user to identify key portions of the simulation to maintain. During the high resolution simulation, a matching process ensures that the properties sampled from the low resolution simulation are maintained. This matching process keeps the different resolution simulations aligned even for complex systems, and can ensure consistency of not only the velocity field, but also advected scalar values. Because the final simulation is naturally similar to the preview simulation, only minor controlling adjustments are needed, allowing a simpler control method than that used in prior keyframing approaches.
Langevin particle: A selfadaptive lagrangian primitive for flow simulation enhancement. Computer Graphics Forum (Eurographics
, 2011
"... We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the ge ..."
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Cited by 5 (3 self)
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We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the generalized Langevin equation, a well known stochastic differential equation that describes the particle’s motion as a random Markov process. The resultant particle trajectory shows selfadapted fluctuation in accordance to the turbulence energy, while following the global flow dynamics. We then feed back Langevin forces to the simulation based on the stochastic trajectory, which drive the flow with necessary turbulence. The new hybrid flow simulation method features nonrestricted particle evolution requiring minimal extra manipulation after initiation. The flow turbulence is easily controlled and the total computational overhead of enhancement is minimal based on typical fluid solvers.
Anisotropic level set adaptation for accurate interface capturing
 in: Proceedings of the 17th International Meshing Rountable
, 2008
"... Summary. In fluidstructure interactions and fluid simulations, like incompressible twophase flows involving high viscosity and density ratios, interface capturing and tracking is considered as a very challenging problem and has a strong impact on industrial applications. Usually, an adaptive grid ..."
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Cited by 3 (2 self)
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Summary. In fluidstructure interactions and fluid simulations, like incompressible twophase flows involving high viscosity and density ratios, interface capturing and tracking is considered as a very challenging problem and has a strong impact on industrial applications. Usually, an adaptive grid is used to resolve the problem as well as to track the interface. In this paper, we describe an adaptive scheme based on the definition of an anisotropic metric tensor to control the generation of highly streched elements near an interface described with a level set function. In our approach, quasiuniform anisotropic meshes are created with the objective of minimizing the interpolation errors by capturing the interface features using curvatureadapted anisotropic elements. The accuracy of the method is verified and numerical experiments are presented to show its efficiency. 1