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Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection

Takahiro Sato, Christopher Batty, Takeo Igarashi, Ryoichi Ando
2018 Computational Visual Media  
Our main contribution is the use of long-term temporal changes in pressure to extend the commonly used semi-Lagrangian scheme further back along the time axis.  ...  We introduce a new advection scheme for fluid animation.  ...  The authors thank Toshiya Hachisuka for insightful discussions.  ... 
doi:10.1007/s41095-018-0117-9 fatcat:4dc2qgwkkbbindthb2f5ajigvq

Reducing numerical dissipation in smoke simulation

Zhanpeng Huang, Ladislav Kavan, Weikai Li, Pan Hui, Guanghong Gong
2015 Graphical Models  
in terms of visual quality, computational overhead, ease of implementation, adaptivity, and scalability, which leads to their different applicability to various application scenarios.  ...  Methods are investigated from various aspects including grid variation, high-order advection, subgrid compensation, invariant conservation, and particle-based improvement, followed by discussion and comparison  ...  High-order advection The basic semi-Lagrangian advection is popular for smoke simulation.  ... 
doi:10.1016/j.gmod.2014.12.002 fatcat:tyd5pbuw5rfklpqedqrtzwtx5u

A fast and accurate semi-Lagrangian particle level set method

Douglas Enright, Frank Losasso, Ronald Fedkiw
2005 Computers & structures  
We use an efficient, first order accurate semi-Lagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function.  ...  In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces.  ...  Although a low order accurate semi-Lagrangian scheme was used by [20] for level set advection, computationally expensive higher order accurate semi-Lagrangian methods are usually preferred, see [21]  ... 
doi:10.1016/j.compstruc.2004.04.024 fatcat:v3bkodcx35cp7dedktwli27p5q

An Unconditionally Stable MacCormack Method

Andrew Selle, Ronald Fedkiw, ByungMoon Kim, Yingjie Liu, Jarek Rossignac
2007 Journal of Scientific Computing  
Recent work replaced each of the three BFECC advection steps with a simple first order accurate unconditionally stable semi-Lagrangian method yielding a second order accurate unconditionally stable BFECC  ...  Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms.  ...  YIP award and a PECASE award (ONR N00014-01-1-0620), a Packard Foundation Fellowship, a Sloan Research Fellowship, ONR N0014-06-1-0393, ONR N00014-03-1-0071, ONR N00014-02-1-0720, ONR N00014-05-1-0479 (for  ... 
doi:10.1007/s10915-007-9166-4 fatcat:zwcrvhiq6bax5ju47vfpzf3zwy

Toward a Fully Lagrangian Atmospheric Modeling System

Jahrul M. Alam, John C. Lin
2008 Monthly Weather Review  
Comparison with Eulerian and semi-Lagrangian models shows that the proposed fully Lagrangian model is more accurate for the sea-breeze circulation problem.  ...  The cost of semi-Lagrangian models is too high for many applications.  ...  JCL thanks Daniel McKenna for first inspiring the possibility that the atmosphere can be  ... 
doi:10.1175/2008mwr2515.1 fatcat:skx3b5nyqfa33ilqdvmh7ubd3m

Dimension Splitting and a Long Time-Step Multi-Dimensional Scheme for Atmospheric Transport [article]

Yumeng Chen, Hilary Weller, Stephen Pring, James Shaw
2017 arXiv   pre-print
Accurate long time-steps can be achieved without significant cost using the flux-form semi-Lagrangian technique.  ...  As is expected for implicit time-stepping, phase errors occur when using long time-steps but the spatially well resolved features are advected at the correct speed and the multi-dimensional scheme is always  ...  for long time-steps whereas the accuracy of semi-Lagrangian is less sensitive to time-step (?).  ... 
arXiv:1701.06907v1 fatcat:bh3bmxxlirbdlc6skn7whhvq4u

Semi-Lagrangian Exponential Integration with application to the rotating shallow water equations [article]

Pedro da Silva Peixoto, Martin Schreiber
2019 arXiv   pre-print
It also provides a sufficiently accurate representation of the nonlinear advection, even with large time-step sizes, a property inherited by the semi-Lagrangian method.  ...  and semi-Lagrangian methods.  ...  We would also like to thank Saulo Barros for discussions with respect to semi-Lagrangian spectral schemes. Appendix A.  ... 
arXiv:1904.09189v1 fatcat:ty5nqrgicna3holvgdl2bcfe4a

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

R. Elliot English, Linhai Qiu, Yue Yu, Ronald Fedkiw
2013 Journal of Computational Physics  
Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes.  ...  We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity  ...  Figure 13 shows that the ALE SL-MacCormack method achieves second order accuracy using time t n+1/2 velocities for advection, while the ALE semi-Lagrangian method is near first order accurate.  ... 
doi:10.1016/ fatcat:y76cq2c7wrghnazo7vigdb54um

An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension

T. Yabe, R. Tanaka, T. Nakamura, F. Xiao
2001 Monthly Weather Review  
Two semi-Lagrangian schemes that guarantee exactly mass conservation are proposed.  ...  Consequently, the resulting schemes conserve the mass for each computational grid cell.  ...  This research is partly supported by the Frontier Research System for Global Change.  ... 
doi:10.1175/1520-0493(2001)129<0332:aecsls>;2 fatcat:rvobtifrovhrlftgg3yrg2truu

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Linhai Qiu, Wenlong Lu, Ronald Fedkiw
2016 Journal of Computational Physics  
A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion.  ...  Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure.  ...  This may be alleviated by utilizing higher order accurate conservative semi-Lagrangian methods.  ... 
doi:10.1016/ fatcat:pgicrex4dbcsjlrqwoq535pqju

The next generation CIP as a conservative semi-Lagrangian solver for solid, liquid and gas

T Yabe, Y Ogata, K Takizawa, T Kawai, A Segawa, K Sakurai
2002 Journal of Computational and Applied Mathematics  
The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme.  ...  We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible ow in the framework of compressible uid.  ...  Although the semi-Lagrangian scheme has been successfully used in short-term atmospheric problems, the loss of exact conservation makes the scheme inappropriate for long-term problems and oceanic problems  ... 
doi:10.1016/s0377-0427(02)00535-6 fatcat:usst2fyzenfdpfvpwqo4ag3zfe

A Hybrid Lagrangian/Eulerian Collocated Advection and Projection Method for Fluid Simulation [article]

Steven W. Gagniere, David A. B. Hyde, Alan Marquez-Razon, Chenfanfu Jiang, Ziheng Ge, Xuchen Han, Qi Guo, Joseph Teran
2020 arXiv   pre-print
A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of Burgers' equation.  ...  We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids.  ...  Semi-Lagrangian techniques for velocity advection utilize the implicit relation associated with solution of Burgers' equation Evans 2010) .  ... 
arXiv:2003.12227v1 fatcat:t2heumfg3rdabbfuipq5wzav7e

A Characteristic Mapping Method for the two-dimensional incompressible Euler equations [article]

Xi-Yuan Yin, Olivier Mercier, Badal Yadav, Kai Schneider, Jean-Christophe Nave
2019 arXiv   pre-print
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid.  ...  The computational efficiency and the high precision of the method are illustrated for a vortex merger and a four mode and a random flow. Comparisons with a Cauchy-Lagrangian method are also presented.  ...  Another large family of numerical solvers are the semi-Lagrangian methods.  ... 
arXiv:1910.10841v1 fatcat:5rf7i5btq5exxpgndhrnmthrp4

Application of the Semi-Lagrangian Method to Global Spectral Forecast Models

Harold Ritchie
Recherche en prévision numérique Service de 1 'environnement atmosphtrique Qukbec, Canada H9P 153 [Original Since the original demonstration of the eficiency advantage of the semi-Lagrangian semi-implicit  ...  Linear stability and geometric aspects are considered for the problem of simple advection on the Gaussian grid that is used in spectral models.  ...  In a companion paper documenting an interview in 1987 (Ritchie and Robert, this volume), Andre expressed his long-term career objective as being several decades of high productivity, followed by the chance  ... 
doi:10.1080/07055900.1997.9687360 fatcat:72rp64kq3bc55ji6jvvtuzvayi

A semi-Lagrangian contouring method for fluid simulation

Adam W. Bargteil, Tolga G. Goktekin, James F. O'brien, John A. Strain
2006 ACM Transactions on Graphics  
In this article, we present a semi-Lagrangian surface tracking method for use with fluid simulations.  ...  Semi-Lagrangian backward path tracing is used to advect the signed-distance function.  ...  In particular, we thank Ravi Kolluri, Okan Arikan, and Bryan Feldman for many fruitful discussions. We also thank the anonymous reviewers for their many helpful comments and suggestions.  ... 
doi:10.1145/1122501.1122503 fatcat:6bge3p2do5bo5ora4oj6hldsba
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