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Abstract: We describe an adaptive higher-order Godunov method for the compressible Euler equations with an arbitrary convex equation of state in a three-dimensional system of orthogonal curvilinear coordinates. The single grid algorithm is a fractional-step method which uses a second-order Godunov method for gas dynamics in each fractional step. The single grid algorithm is coupled to a conservative local adaptive mesh refinement algorithm that selectively refines regions of the computational grid to... (Update)
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BibTeX entry: (Update)
@misc{ pember-adaptive,
author = "Richard B. Pember and Jeffrey A. Greenough and Phillip Colella",
title = "An Adaptive, Higher-Order Godunov Method For Gas Dynamics In Three-Dimensional
Orthogonal Curvilinear Coordinates",
url = "citeseer.ist.psu.edu/372056.html" }
Citations (may not include all citations):131 Adaptive mesh refinement for hyperbolic partial differential.. (context) - Berger, Oliger - 1984
123 Approximate Riemann solvers (context) - Roe - 1981
108 Local adaptive mesh refinement for shock hydrodynamics (context) - Berger, Colella - 1989
66 Towards the ultimate conservative difference scheme (context) - van Leer - 1979
54 Numerical methods for hyperbolic conservation laws with stif.. - Pember - 1993
53 the construction and comparison of difference schemes (context) - Strang - 1968
45 The piecewise parabolic method (context) - Colella, Woodward - 1984
39 Multidimensional upwind methods for hyperbolic conservation .. (context) - Colella - 1990
33 The method of fractional steps for conservation laws (context) - Crandall, Majda - 1980
32 A direct Eulerian MUSCL scheme for gas dynamics (context) - Colella - 1985
31 Three dimensional adaptive mesh refinement for hyperbolic co.. (context) - Bell, Berger et al. - 1994
31 An Introduction to the Mechanics of a Continuous Medium (context) - Malvern - 1969
23 Upwind difference schemes for hyperbolic systems of conserva.. (context) - Osher, Solomon - 1982
22 An adaptive Cartesian grid method for unsteady compressible .. - Pember, Bell et al. - 1995
20 Stable and entropy satisfying approximations for transonic f.. (context) - Engquist, Osher - 1980
16 Higher order Godunov methods for general systems of hyperbol.. (context) - Bell, Colella et al. - 1989
10 Efficient solution algorithms for the Riemann problem for re.. (context) - Colella, Glaz - 1985
4 An adaptive multifluid interface-capturing method for compre.. - Greenough, Bell et al. - 1993
4 An adaptive multifluid interface-capturing method for compre.. - Greenough, Bell et al.
3 Multifluid algorithms for Eulerian finite difference methods (context) - Colella, Ferguson et al.
3 Multidimensional numerical simulation of a pulse combustor (context) - Marcus, Pember et al. - 1994
3 A high-order Godunov method for multiple condensed phases (context) - Miller, Puckett - 1995
2 Numerical simulation of a wave-guide mixing layer on a Cray .. (context) - Greenough, Bell et al. - 1995
2 Introduction to Applied Mathematics (context) - Murnaghan - 1948
1 An implicit-explicit Eulerian scheme for compressible flow (context) - Collins, Colella et al. - 1991
1 A numerical study of shock-acceleration of a diffuse helium .. (context) - Greenough, Jacobs - 1995
1 The numerical computation of high-velocity impact phenomena (context) - Puckett, Miller - 1995
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