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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 54 (5 self)
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. 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...
Dynamos in AsymptoticGiantBranch Stars As the Origin of Magnetic Fields Shaping Planetary Nebulae
, 2001
"... Planetary nebulae are thought to be formed when a slow wind from the progenitor giant star is overtaken by a subsequent fast wind as the star enters its white dwarf stage1. The shock formed near the contact discontinuity between the two winds creates the relatively dense shell that forms the planeta ..."
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Planetary nebulae are thought to be formed when a slow wind from the progenitor giant star is overtaken by a subsequent fast wind as the star enters its white dwarf stage1. The shock formed near the contact discontinuity between the two winds creates the relatively dense shell that forms the planetary nebula. A spherically symmetric wind produces a spherically symmetric nebula; however, over half of the known planetary nebulae are either bipolar or elliptical, rather than spherical 2. A magnetic field may explain the launching and collimation of a bipolar outflow in a planetary nebula, but the origin of such a magnetic field has not been adequately explained. Here we show that a star on the asymptotic giant branch (AGB), which is the precursor of a planetary nebula core, can generate a strong magnetic field in a dynamo located at the coreenvelope interface. The field is sufficiently strong to shape the bipolar outflow observed in planetary nebulae and may also explain the puzzlingly slow rotation of most white dwarfs via magnetic braking. One model for producing bipolar or elliptical planetary nebulae assumes that the
A ThreeDimensional Magnetohydrodynamic Model of Planetary Nebula Jets, Knots, and Filaments
, 803
"... The morphologies of planetary nebulae are believed to be selforganized configurations. These configurations are modeled by threedimensional temporally selfsimilar magnetohydrodynamic solutions with radial flow, under the gravitational field of a central star of mass M. These solutions reproduce ba ..."
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The morphologies of planetary nebulae are believed to be selforganized configurations. These configurations are modeled by threedimensional temporally selfsimilar magnetohydrodynamic solutions with radial flow, under the gravitational field of a central star of mass M. These solutions reproduce basic features, such as jets, pointsymmetric knots, and filaments, through plasma pressure, mass density, and magnetic field lines. The time evolution function of the radial velocity starts as a slow wind and terminates as a fast wind. Subject headings: 2 1.