A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
TLDR
In this article, a 3D spatially unsplit implementation of the piecewise parabolic (PPM) method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions.About:
This article is published in Journal of Computational Physics.The article was published on 2002-11-20 and is currently open access. It has received 226 citations till now. The article focuses on the topics: Riemann problem & Godunov's scheme.read more
Citations
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Second-order accurate volume-of-fluid algorithms for tracking material interfaces
TL;DR: A design criteria for a volume-of-fluid interface reconstruction algorithm to be second-order accurate is proposed, which is that it reproduce lines in two space dimensions or planes in three space dimensions exactly.
Journal ArticleDOI
An unsplit Godunov method for ideal MHD via constrained transport
TL;DR: A single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method for performing spatial reconstruction, the corner transport upwind method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field is described.
Journal ArticleDOI
The pluto code for adaptive mesh computations in astrophysical fluid dynamics
Andrea Mignone,Claudio Zanni,Petros Tzeferacos,B. van Straalen,Phillip Colella,Gianluigi Bodo +5 more
TL;DR: The adaptive mesh refinement (AMR) as mentioned in this paper implementation of the PLUTO code for solving the equations of classical and relativistic magnetohydrodynamics (MHD and RMHD) exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids.
Journal ArticleDOI
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
TL;DR: This paper describes the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ''MHD source terms'' and naturally respect the balance implicit in these terms by the @?B=0 condition and compares two different forms for the CTU integration algorithm.
Journal ArticleDOI
Castro: a new compressible astrophysical solver. i. hydrodynamics and self-gravity
Ann S. Almgren,V E Beckner,John B. Bell,Marcus S. Day,Louis H. Howell,Candace C. Joggerst,Candace C. Joggerst,Michael J. Lijewski,Andrew Nonaka,M. Singer,Michael Zingale +10 more
TL;DR: CASTRO as discussed by the authors uses an Eulerian grid and incorporates adaptive mesh refinement (AMR), which uses a nested hierarchy of logically rectangular grids with simultaneous refinement in both space and time.
References
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Journal ArticleDOI
Volume of fluid (VOF) method for the dynamics of free boundaries
C.W Hirt,B. D. Nichols +1 more
TL;DR: In this paper, the concept of a fractional volume of fluid (VOF) has been used to approximate free boundaries in finite-difference numerical simulations, which is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations.
Book
Physical properties of crystals
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Journal ArticleDOI
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
Journal ArticleDOI
The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations
Phillip Colella,Paul R. Woodward +1 more
TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
Book
Thermodynamics and an Introduction to Thermostatics
TL;DR: The Canonical Formalism Statistical Mechanics in the Entropy Representation as discussed by the authors is a generalization of statistical mechanics in the Helmholtz Representation, and it has been applied to general systems.
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