| Numerically Stable Fluid-Structure Interactions Between Compressible Flow and Solid Structures |
28 Jan 2011 |
32 pages |
| Authors:
Jon T Gretarsson; Nipun Kwatra; Ronald Fedkiw; STANFORD UNIV CA
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 | We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tn+1 using an implicit pressure, obtained by solving a modified ... |
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| A Symmetric Positive Definite Formulation for Monolithic Fluid Structure Interaction |
09 Aug 2010 |
26 pages |
| Authors:
Avi Robinson-Mosher; Craig Schroeder; Ronald Fedkiw; STANFORD UNIV CA
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| In this paper we consider a strongly coupled (monolithic) fluid structure interaction framework for incompressible flow, as opposed to a loosely coupled (partitioned) method. This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid. In our previous work, we were able to obtain a symmetric formulation of this coupled system; however, it was also indefinite, making it more ... |
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| An Unconditionally Stable Fully Conservative Semi-Lagrangian Method (PREPRINT) |
07 Aug 2010 |
35 pages |
| Authors:
Michael Lentine; Jon T Gretarsson; Ronald Fedkiw; STANFORD UNIV CA
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| Semi-Lagrangian 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 CFL-based 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. ... |
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| A Method for Avoiding the Acoustic Time-Step Restriction in Compressible Flow |
28 Aug 2008 |
24 pages |
| Authors:
Nipun Kwatra; Jonathan Su; Jon T Gretarsson; Ronald Fedkiw; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| We propose a novel method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species etc, and is derived in a straightforward manner. Similar methods have been proposed in the literature, but the equations they are based on and the ... |
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| A Computing Cluster for Numerical Simulation |
23 OCT 2006 |
6 pages |
| Authors:
Ronald Fedkiw; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| The acquired computing cluster is used in the development of novel techniques for computational fluid dynamics and continuum mechanics, with a focus on large Eulerian or Lagrangian discretizations. Applications that receive particular emphasis include the following: (1) simulation of discontinuous flows resulting from the interaction of several immiscible or chemically reacting phases; (2) adaptive discretizations of large fluid volumes that can resolve turbulent flows and the effects of highly variable ... |
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| On Boundary Condition Capturing for Multiphase Interfaces |
31 MAR 2006 |
26 pages |
| Authors:
Jeong-Mo Hong; Tamar Shinar; Myungjoo Kang; Ronald Fedkiw; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| This paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although, the authors' original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched the idea that ghost cells could be defined and used in the usual manner. Instead the boundary conditions had to be implicitly captured by the matrix formulation itself, ... |
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| Spatially Adaptive Techniques for Level Set Methods and Incompressible Flow |
03 MAY 2005 |
42 pages |
| Authors:
Frank Losasso; Ronald Fedkiw; Stanley Osher; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also ... |
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| A Fourth Order Accurate Discretization for the Laplace and Heat Equations on Arbitrary Domains, with Applications to the Stefan Problem |
27 APR 2004 |
41 pages |
| Authors:
Frederic Gibou; Ronald Fedkiw; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an implicit time discretization to avoid the stringent time step restrictions associated with explicit schemes. They then turn their focus to the Stefan problem and construct a third order accurate method ... |
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| A Fast and Accurate Semi-Lagrangian Particle Level Set Method |
25 APR 2004 |
25 pages |
| Authors:
Douglas Enright; Frank Losasso; Ronald Fedkiw; STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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| In this paper, we present an efficient semi-Lagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD Runge-Kutta and HJ-WENO schemes. We demonstrate that these ... |
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| Practical Animation of Liquids |
AUG 2001 |
9 pages |
| Authors:
NICK FOSTER; Ronald Fedkiw; STANFORD UNIV CA
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| We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semi-Lagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a ... |
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