Results 1 
8 of
8
Balancing Source Terms and Flux Gradients in HighResolution Godunov Methods: The QuasiSteady WavePropogation Algorithm
 J. Comput. Phys
, 1998
"... . Conservation laws with source terms often have steady states in which the flux gradients are nonzero but exactly balanced by source terms. Many numerical methods (e.g., fractional step methods) have difficulty preserving such steady states and cannot accurately calculate small perturbations of suc ..."
Abstract

Cited by 116 (5 self)
 Add to MetaCart
(Show Context)
. Conservation laws with source terms often have steady states in which the flux gradients are nonzero but exactly balanced by source terms. Many numerical methods (e.g., fractional step methods) have difficulty preserving such steady states and cannot accurately calculate small perturbations of such states. Here a variant of the wavepropagation algorithm is developed which addresses this problem by introducing a Riemann problem in the center of each grid cell whose flux difference exactly cancels the source term. This leads to modified Riemann problems at the cell edges in which the jump now corresponds to perturbations from the steady state. Computing waves and limiters based on the solution to these Riemann problems gives highresolution results. The 1D and 2D shallow water equations for flow over arbitrary bottom topography are use as an example, though the ideas apply to many other systems. The method is easily implemented in the software package clawpack. Keywords: Godunov meth...
Nonlinear Conservation Laws and Finite Volume Methods for Astrophysical Fluid Flow
 Computational Methods for Astrophysical Fluid Flow, 27th SaasFee Advanced Course Lecture Notes
, 1998
"... Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.1 Software : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 Notation : : : : : : : : : : : : : : : : : : : : : : : : : : ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.1 Software : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2 Notation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.3 Classification of differential equations : : : : : : : : : : : : : : : : : : : : : : : 7 2. Derivation of conservation laws : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.1 The Euler equations of gas dynamics : : : : : : : : : : : : : : : : : : : : : : : 13 2.2 Dissipative fluxes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 2.3 Source terms : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 2.4 Radiative trans
Numerical Study of Singularity Formation in Relativistic Euler Flows
, 2014
"... Abstract. The formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite lifespan; the possible breakdown mechanisms are shock formation, violation of the subluminal conditions andmass concentration. We p ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite lifespan; the possible breakdown mechanisms are shock formation, violation of the subluminal conditions andmass concentration. We propose a new hybrid Glimm/centralupwind scheme for relativistic flows. The scheme is used to numerically investigate, for a family of problems, which of the above mechanisms is involved.
RESEARCH ARTICLE Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations
"... The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the nonrelativistic ones due to the nonlinear relations between t ..."
Abstract
 Add to MetaCart
(Show Context)
The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the nonrelativistic ones due to the nonlinear relations between the conserved and state variables. A highresolution shockcapturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCLtype initial reconstruction and RungeKutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and twodimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic fluxvector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic twodimensional test problems.
www.livingreviews.org/Articles/Volume2/19993marti Living Reviews in Relativity
, 1999
"... Both authors would be glad to receive suggestions, references, and new results for the next update of this review article. This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a c ..."
Abstract
 Add to MetaCart
(Show Context)
Both authors would be glad to receive suggestions, references, and new results for the next update of this review article. This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of highresolution shockcapturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discussed. An evaluation of the various numerical methods is given and future developments are analyzed. c©1999 MaxPlanckGesellschaft and the authors. Further information on copyright is given at
Physics
, 2013
"... In this thesis we develop and test methods for numerically evolving hydrodynamics coupled to the Einstein field equations, and then apply them to several problems in gravitational physics and astrophysics. The hydrodynamics scheme utilizes highresolution shockcapturing techniques with flux corre ..."
Abstract
 Add to MetaCart
(Show Context)
In this thesis we develop and test methods for numerically evolving hydrodynamics coupled to the Einstein field equations, and then apply them to several problems in gravitational physics and astrophysics. The hydrodynamics scheme utilizes highresolution shockcapturing techniques with flux corrections while the Einstein equations are evolved in the generalized harmonic formulation using finite difference methods. We construct initial data by solving the constraint equations using a multigrid algorithm with free data chosen based on superposing isolated compact objects. One application we consider is the merger of black holeneutron star and neutron starneutron star binaries that form through dynamical capture, as may occur in globular clusters or galactic nuclei. These systems can merge with nonnegligible orbital eccentricity and display significant variability in dynamics and outcome as a function of initial impact parameter. We study the electromagnetic and gravitationalwave transients that these mergers may produce and their prospects for being detected with upcoming observations.