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24
Wave Propagation Algorithms for Multidimensional Hyperbolic Systems
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1997
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An Adaptive Cartesian Grid Method For Unsteady Compressible Flow In Irregular Regions
 J. Comput. Phys
, 1993
"... In this paper we describe an adaptive Cartesian grid method for modeling timedependent inviscid compressible flow in irregular regions. In this approach a body is treated as an interface embedded in a regular Cartesian mesh. The single grid algorithm uses an unsplit secondorder Godunov algorithm fo ..."
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Cited by 48 (14 self)
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In this paper we describe an adaptive Cartesian grid method for modeling timedependent inviscid compressible flow in irregular regions. In this approach a body is treated as an interface embedded in a regular Cartesian mesh. The single grid algorithm uses an unsplit secondorder Godunov algorithm followed by a corrector applied to cells at the boundary. The discretization near the fluidbody interface is based on a volumeoffluid approach with a redistribution procedure to maintain conservation while avoiding time step restrictions arising from small cells where the boundary intersects the mesh. The single grid Cartesian mesh integration scheme is coupled to a conservative adaptive mesh refinement algorithm that selectively refines regions of the computational grid to achieve a desired level of accuracy. Examples showing the results of the combined Cartesian grid integration/adaptive mesh refinement algorithm for both two and threedimensional flows are presented. (This page intent...
Adaptive Mesh and Algorithm Refinement using Direct Simulation Monte Carlo
 J. Comput. Phys
, 1999
"... Adaptive Mesh and Algorithm Refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and c ..."
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Cited by 23 (4 self)
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Adaptive Mesh and Algorithm Refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embeded within a Godunovtype compressible Navier Stokes solver. Several examples are presented and compared with purely continuum calculations. Permanent address: Physics Dept., San Jose State University, San Jose, Calf. 95192 1 Introduction When a large range of scales must be spanned, computational fluid dynamics (CFD) calculations often employ local mesh refinement so that a fine grid is used only in those regions that require high resolution. However, hydrodynamic formulations break down as the grid spacing approaches the molecular scale, for example, the mean free path in a gas. This paper ...
A Wave Propagation Method for Three Dimensional Hyperbolic Problems
, 1996
"... A class of wave propagation algorithms for threedimensional conservation laws is developed. This unsplit nite volume method is based on solving onedimensional Riemann problems at the cell interfaces and applying fluxlimiter functions to suppress oscillations arising from second derivative terms. ..."
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Cited by 23 (5 self)
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A class of wave propagation algorithms for threedimensional conservation laws is developed. This unsplit nite volume method is based on solving onedimensional Riemann problems at the cell interfaces and applying fluxlimiter functions to suppress oscillations arising from second derivative terms. Waves emanating from the Riemann problem are further split by solving Riemann problems in the transverse direction to model crossderivative terms. Due to proper upwinding, the method is stable for Courant numbers up to one. Several examples using the Euler equations are included.
A conservative threedimensional Eulerian method for coupled solidfluid shock capturing
 Copyright © by SIAM. Unauthorized reproduction of this article is prohibited
"... A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions ..."
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Cited by 20 (9 self)
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A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions artificially extended representations of the individual phases. For fluids we use a new 3D spatially unsplit implementation of the piecewise parabolic (PPM) method of Colella and Woodward. For solids we use the 3D spatially unsplit Eulerian solid mechanics method of Miller and Colella. Vacuum and perfectly incompressible obstacles may also be employed as phases. A separate problem is the time evolution of material interfaces, which are represented by planar segments constructed with a volumeoffluid method. The volume fractions are advanced in time using a secondorder 3D spatially unsplit advection routine with a velocity field determined by solution of interfacenormal twophase Riemann problems. From the Riemann problem solutions we also determine crossinterface momentum and energy fluxes.
An adaptive, formally second order accurate version of the immersed boundary method
, 2006
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A HighOrder Eulerian Godunov Method for Elastic/Plastic Flow in Solids
 J. Comput. Phys
"... INTRODUCTION In this work, we present a higherorder Godunov method for computing in Eulerian coordinates the multidimensional dynamics of elasticplastic solids undergoing large deformations. Our approach is based on a new formulation of the equations of solid mechanics as a firstorder system of ..."
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Cited by 10 (4 self)
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INTRODUCTION In this work, we present a higherorder Godunov method for computing in Eulerian coordinates the multidimensional dynamics of elasticplastic solids undergoing large deformations. Our approach is based on a new formulation of the equations of solid mechanics as a firstorder system of hyperbolic PDE's, a modification of that used by Trangenstein and Colella [24]. In [24], the usual conservation laws for mass, momentum and energy, plus a constitutive model, are augmented by a form of equality of mixed partial derivatives that yields conservation equations for the entries of the inverse deformation gradient. This leads to equations of the form @U @t ###F #U##S#U#: (1) Work at the Lawrence Berkeley National Laboratory was sponsored by the US Department of Energy (DOE) Mathematical, Information, and Computing Sciences Division contract DEAC0376SF00098. Other work was sup
Threedimensional hybrid continuumatomistic simulations for multiscale hydrodynamics
 Journal of Fluids Engineering
"... We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multiscale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust fluxbased method for coupling an atomistic fluid representation to a continuum ..."
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Cited by 7 (2 self)
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We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multiscale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust fluxbased method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is invalid or inaccurate, such as near strong flow gradients and at fluid interfaces, or when the continuum grid is refined to the molecular scale. The need for such ‘‘hybrid’ ’ methods arises from the fact that hydrodynamics modeled by continuum representations are often underresolved or inaccurate while solutions generated using molecular resolution globally are not feasible. In the implementation described herein, Direct Simulation Monte Carlo (DSMC) provides an atomistic description of the flow and the compressible twofluid Euler equations serve as our continuumscale model. The AMR methodology provides local grid refinement while the algorithm refinement feature allows the transition to DSMC where needed. The continuum and atomistic representations are coupled by matching fluxes at the continuumatomistic interfaces and by proper averaging and interpolation of data between scales. Our AMAR application code is implemented in C� � and is built upon the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) framework developed
Block Structured Adaptive Mesh and Time Refinement for Hybrid, Hyperbolic + Nbody Systems
, 2007
"... We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the num ..."
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Cited by 5 (0 self)
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We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.
Threedimensional Euler Computations using CLAWPACK
 in Conf. on Numer. Meth. for Euler and NavierStokes Eq
, 1995
"... this paper will be submitted for publication elsewhere. ..."
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Cited by 4 (2 self)
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this paper will be submitted for publication elsewhere.