Reply to Comment on Hydrodynamic
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Hydrodynamic↗
Engineering topics
Brackbill, J. U.
Publications and source records attributed to Brackbill, J. U..
Two-Dimensional Hydrodynamic Modeling of the Solar Wind Termination Shock and the Global Heliosphere
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Pioneer Voyager VLISM↗
Time-dependent MHD modeling of the global structure of the heliosphere
We present results from time-dependent modeling of the global structure of the heliosphere with neutral and magnetic field effects included. The magnetic field is assumed parallel to the interstellar flow in this two-dimensional axisymmetric model; the neutrals are treated as a fluid. The effects of interstellar neutrals and the interplanetary magnetic field on the location of the termination shock are studied using the most recent estimate of the interstellar medium parameters, results will be compared to those of Baranov and Zaitsev. The effect of the solar wind - VLISM interaction on the density and velocity of interstellar neutrals within the heliosphere will also be presented and related to observations. The response of the termination shock to the solar cycle variation in the solar wind will be compared to the response found previously using an axisymmetric hydrodynamic model without neutrals.
Liewer, P. C.↗
The interaction of a magnetized solar wind with the VLISM
The interaction of a magnetized solar wind with magnetized interstellar flow is modelled in two dimensions. The VLISM magnetic field and flow velocity are assumed to be parallel to each other and perpendicular to the sun's magnetic axis, contrast to a recent study by Washimi. The more realistic orientation of the axis and VLISM flow requires a less realistic heliospheric field model in two dimensions. The Parker spiral is replaced by a poloidal field which is tangent to the termination shock, and whose magnitude is consistent with estimates of the heliospheric field at termination shock distances. Of particular interest is the effect of the heliospheric field on the heliospheric flow beyond the termination shock, and on the structure and location of the bow shock
Brackbill, J. U.↗
Motion of the termination shock in response to an 11 year variation in the solar wind
A two-dimensional hydrodynamic numerical model was used to study the motion of the termination shock in response to an 11 year variation in the solar wind ram pression. For a total variation in the ram pressue by a factor of 2, a termination shock at 89 AU was found to move inward and outward about +/- 8% of its distance with a typical velocity of 12 km/sec. This movement may be understood in terms of the various time scales associated with the response of the termination shock and heliopause to variations in the solar wind ram pressure.
Karmesin, S. Roy↗
Time-Dependent Hydrodynamic Modeling of the Global Structure of the Heliosphere
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solar wind plasma supersonic external flow termina↗
An adaptive grid with directional control
An adaptive grid generator for adaptive node movement is here derived by combining a variational formulation of Winslow's (1981) variable-diffusion method with a directional control functional. By applying harmonic-function theory, it becomes possible to define conditions under which there exist unique solutions of the resulting elliptic equations. The results obtained for the grid generator's application to the complex problem posed by the fluid instability-driven magnetic field reconnection demonstrate one-tenth the computational cost of either a Eulerian grid or an adaptive grid without directional control.
Brackbill, J. U.↗
Multiple switch-off slow shock solutions
A new electromagnetic quasi-neutral time-dependent implicit hybrid model for simulating the slow-mode switch-off shock is developed, in which the electrons are treated as a finite-mass adiabatic fluid (gamma sub e = 5/3), whose motion along the shock normal provides local charge neutrality. The model is used to examine the effects of various boundary conditions applied during shock formation. It is shown that, for each upstream condition, two distinctly different slow-shock structures can be obtained: a low-shock structure with a trailing magnetic wave (TMW) and a slow-shock structure without a TMW, depending strongly on the boundary conditions for the electric and magnetic fields at the physical piston which generates the shock. The results indicate that the slow-shock structure with a TMW is nonlinearly unstable with respect to changes in the upstream magnetic field, suggesting that the downstream structure of slow shocks need not be associated with a TMW.
Vu, H. X.↗
A continuum method for modeling surface tension
In the novel method presented for modeling the effects of surface tension on fluid motion, the interfaces between fluids with different, color-represented properties are finite-thickness transition regions across which the color varies continuously. A force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero. The properties of the method are illustrated by computational results for 2D flows.
Brackbill, J. U.↗
FLIP MHD - A particle-in-cell method for magnetohydrodynamics
The fluid-implicit-particle, or 'FLIP' method presently extended to 2D and 3D MHD flow incorporates a Lagrangian field representation and yields a grid magnetic Reynolds number of up to 16 while preserving contact continuities that retain the Galilean invariance of the MHD flow equations. Analytical arguments and numerical examples demonstrate the conservation of mass, momentum, magnetic flux, and energy; 2D calculation results for the illustrative cases of contact discontinuity convection, Rayleigh-Taylor unstable flow.
Brackbill, J. U.↗
Nonlinear evolution of the lower-hybrid drift instability
The results of simulations of the lower-hybrid drift instability in a neutral sheet configuration are described. The simulations use an implict formulation to relax the usual time step limitations and thus extend previous explicit calculations to weaker gradients, larger mass ratios, and long times compared with the linear growth time. The numerical results give the scaling of the saturation level, heating rates, resistivity, and cross-field diffusion and a demonstration by comparison with a fluid electron model that dissipation in the lower-hybrid drift instability is caused by electron kinetic effects.
Brackbill, J. U.↗
Collisionless dissipation in quasi-perpendicular shocks
Microscopic dissipation processes in quasi-perpendicular shocks are studied by two-dimensional plasma simulations in which electrons and ions are treated as particles moving in self-consistent electric and magnetic fields. Cross-field currents induce substantial turbulence at the shock front reducing the reflected ion fraction, increasing the bulk ion temperature behind the shock, doubling the average magnetic ramp thickness, and enhancing the upstream field aligned electron heat flow. The short scale length magnetic fluctuations observed in the bow shock are probably associated with this turbulence.
Forslund, D. W.↗
Collisionless dissipation processes in quasi-parallel shocks
The evolution of collisionless, quasi-parallel shocks (the angle between the shock normal and the upstream magnetic field being less than 45 deg) is examined using two dimensional particle simulations. Reflected ions upstream from the shock are observed with average guiding center velocity and gyrational energy which agree well with the prediction of simple specular reflection. Strong ion heating through the shock ramp is apparently caused by large amplitude whistler turbulence. A flux of suprathermal electrons is also the magnetic field direction. Much stronger ion heating occurs in the shock than electron heating. The relevance of this work to the earth's bow shock is discussed.
Quest, K. B.↗
An adaptive computation mesh for the solution of singular perturbation problems
In singular perturbation problems, control of zone size variation can affect the effort required to obtain accurate, numerical solutions of finite difference equations. The mesh is generated by the solution of potential equations. Numerical results for a singular perturbation problem in two dimensions are presented. The mesh was used in calculations of resistive magnetohydrodynamic flow in two dimensions.
Brackbill, J. U.↗