Changes between Version 35 and Version 36 of AstroBearProjects/resistiveMHD
- Timestamp:
- 01/07/14 19:44:03 (11 years ago)
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AstroBearProjects/resistiveMHD
v35 v36 29 29 centered on the cell faces. Its curl therefore reside on the cell edges. Here is an example on calculating the diffusive current on the x direction, notice [[BR]] 30 30 that the red arrow is where we are calculating the diffusive current, the green arrows are where the magnetic field originally resides: [[BR]] 31 [[Image(resistive_diagram.png, 20%)]] [[BR]] 32 [[Image(http://www.pas.rochester.edu/~shuleli/res_dia1.png, 20%)]] [[BR]] 31 [[Image(resistive_diagram.png, 20%)]][[Image(http://www.pas.rochester.edu/~shuleli/res_dia1.png, 20%)]] [[BR]] 33 32 The actual code looks like the following in 2D (jy are initialized to 1): [[BR]] 34 33 {{{ … … 112 111 where [[latex($\rho_0 = 1$)]] and [[latex($a = 0.5$)]]. The temperature is set to be constant as 0.5. [[BR]] 113 112 The domain is set to be -6.4 < x < 6.4 and -12.8< y < 12.8, with fixed resolution 480 * 960. The boundaries are all open. The initial profile is plotted below: [[BR]] 114 [[Image(http://www.pas.rochester.edu/~shuleli/hhc_plot.png, 20%)]][[BR]][[BR]]113 [[Image(http://www.pas.rochester.edu/~shuleli/hhc_plot.png, 30%)]][[BR]][[BR]] 115 114 The initial state is in pressure equilibrium though unstable. There are two ways to generate instabilities. The first way is to artificially increase the resistivity [[BR]] 116 115 at the center of the domain. This increase will result in a higher reconnectivity, which will eventually bend magnetic field. This creates an X point where field [[BR]] … … 118 117 to the direction of the sheer pinch. The box surrounding the X point where the outflows (Petschek shock) come out of is called the "Sweet-Parker Box". The following [[BR]] 119 118 diagrams show how increased resistivity at the center of a sheer pinch drives Petschek shock.[[BR]] 120 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/resistive_instab.png, 20%)]] [[Image(http://www.pas.rochester.edu/~shuleli/hhc_flowpattern.png, 20%)]] [[BR]][[BR]]119 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/resistive_instab.png,30%)]] [[Image(http://www.pas.rochester.edu/~shuleli/hhc_flowpattern.png, 30%)]] [[BR]][[BR]] 121 120 The Mach number in 2D case is plotted in pseudo-color: [[BR]] 122 [[Image(http://www.pas.rochester.edu/~shuleli/hhc_mach.png, 20%)]][[BR]][[BR]]121 [[Image(http://www.pas.rochester.edu/~shuleli/hhc_mach.png, 30%)]][[BR]][[BR]] 123 122 124 123 To test Sweet-Parker problem in AstroBEAR, we construct the sheer pinch using the above setup, and modify the resistivity at the center of the simulation box. [[BR]][[BR]] … … 126 125 The following figure shows the Petschek shock from a reconnection spot at the center. Colored variable is the kinetic energy in log scale, magnetic field is illustrated [[BR]] 127 126 by white lines. [[BR]] 128 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/sp1_0020.png, 20%)]]127 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/sp1_0020.png, 30%)]] 129 128 [[BR]] 130 129 A movie with 2-level AMR:[[BR]] … … 139 138 of pressure imbalance, which creates periodical dense "islands".The growth rate and the size of the "islands" depend on resistivity and the strength of the perturbation.[[BR]][[BR]] 140 139 141 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/mihr_0180.png, 20%)]][[BR]][[BR]]140 [[Image(http://www.pas.rochester.edu/~shuleli/multi_test/mihr_0180.png, 30%)]][[BR]][[BR]] 142 141 143 142 To watch a full movie, [http://www.pas.rochester.edu/~shuleli/multi_test/mihr.gif click here][[BR]][[BR]] … … 158 157 159 158 where T is the electron temperature in eV, Zeff is the effective ion charge.The Coulomb logarithm for interested number density is plotted below: [[BR]] 160 [[Image(http://www.pas.rochester.edu/~shuleli/CoulombLog.png, 20%)]][[BR]]159 [[Image(http://www.pas.rochester.edu/~shuleli/CoulombLog.png, 30%)]][[BR]] 161 160 [[BR]][[BR]] 162 161