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3D multi-fluid model

3D multi-fluid model. Erika Harnett University of Washington. Equations solved. }. For each species . Numerical scheme. Second-order Runge-Kutta with flux correction smoothing on the plasma parameters only (B not smoothed), no time averaging.

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3D multi-fluid model

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  1. 3D multi-fluid model Erika Harnett University of Washington

  2. Equations solved } For each species 

  3. Numerical scheme • Second-order Runge-Kutta with flux correction smoothing on • the plasma parameters only (B not smoothed), no time • averaging. • Solved on a Cartesian grid. The spacing on each grid is equal • in all three dimensions • Nested grid system is used for higher resolution (see next section) • Assume continuous boundary conditions at the outer boundaries • Assume a constant density and temperature (thus pressure) for • all species at inner (planetary) boundary, and plasma • assumed to have no bulk speed (but has a thermal vel.) • No chemistry used in this version of the model

  4. Numerical scheme - continued • Variable time step used, determined from stability conditions • i.e. t < (smallest x) / (fasted speed) • divB correction can be turned on/off. Only necessary when simulating • strong shocks at unmagnetized planets after initialization

  5. Nested Grid System • All grids are assumed to have shape (nx,ny,nz) • All formulas are solved on each grid independently • Values from inner portion of higher resolution grids (X) reset • overlapping points in lower resolution grids when the • boundary conditions are determined in each time step. • Values at outer boundary of high • resolution grid (O) are • taken from overlapping • points in lower res. grid o s o s o s o s s o x x o s s o x x o • Remaining boundary values (S) • are determined from • interpolation s s o s o s o s o

  6. Gridding System 4 grids, each with the shape (nx,ny,nz) = 111 x 89 x 89 Grid 1 - resolution: x = 168 km outer edge of grid along x: -2.67 RM & 2.77 RM y,z: -2.18 RM & < 2.18 RM Grid 2 - resolution: x = 336 km outer edge of grid along x: -4.46 RM & 6.53 RM y,z: -4.36 RM & 4.36 RM Grid 3 - resolution: x = 673 km outer edge of grid along x: -5.94 RM &15.8 RM y,z: -8.71 RM & 8.71 RM Grid 4 - resolution: x = 1345 km outer edge of grid along x: -13.9 RM & 73.3 RM y,z:-17.4 RM & 17.4 RM

  7. Model Input Parameters Three species: H+ (solar wind), H+ (ionosphere), O+(ionosphere) Note: A small amount of ionospheric species must be present in solar wind and a small amount of solar wind species at inner boundary to prevent divide by zero errors. • Solar Wind (set statically or driven with changing conditions • read in from an input file): • Density = 3 cm-3 • Velocity = 400 km s-1 in x direction • Te = 10 eV, Ti = 4.3 eV • Bx = -1.64 nT, By = 2.52 nT, Bz = 0 nT

  8. Model Input Parameters - continued • Planetary (inner) boundary (single grid point width): • Altitude = 302 km • O+ Density = 875 cm-3 @ equator (decreases to 70% less at poles) • H+ Density = 100 cm-3 @ equator (decreases to 70% less at poles) • No day/night asymmetry in density • Te = 0.3 eV, Ti = 0.07 eV • Rotation period = 24.6 earth hours

  9. Odds and Ends • Code written in Fortran, fastest code with Intel compiler. • Parallelized to run on multi-core processors using OpenMP. • Currently run on a high-end desktop (dual quad-core Intel • chips ~ 3 GHz, ~ 4-8G of RAM) • Output necessary to restart simulation (density, momentum, • pressure, magnetic field for each species at all grid points) • written in binary during course of simulation and at the end • of a run. Time between outputs varies, set as in input • parameter. • Wave reflection only an issue for sub-sonic/sub-Alfvenic • incident winds. Prevent reflections at outflow boundary by • having large outer simulation grid such that bow shock • contacts outer boundaries down-stream of planet

  10. Validation • Comparison to hybrid results: • Harnett, E., R. Winglee, and P. Delamere (2005), "3D multi-fluid • simulations of Pluto's magnetosphere - a comparison with 3D • hybrid simulation results", Geophys. Res. Lett., 32, L19104, • doi:10.1029/2005GL023178 • Standard reconnection (Harris current sheet) problem: • Winglee R. M., E. Harnett, A. Stickle, J. Porter (2008), • "Multiscale/multifluid simulations of flux ropes at the • magnetopause within a global magnetospheric model" , • J. Geophys. Res., 113, A02209, doi:10.1029/2007JA012653. • Comparison to satellite observations: • Paty, C., W. Paterson, and R. Winglee (2008), Ion energization in • Ganymede’s magnetosphere: Using multifluid simulations to • interpret ion energy spectrograms, J. Geophys. Res., 113, A06211, • doi:10.1029/2007JA012848.

  11. Validation - continued • Comparison to satellite observations: • Snowden, D., R. Winglee, C. Bertucci, and M. Dougherty (2007), • Three-dimensional multifluid simulation of the plasma interaction • at Titan, J. Geophys. Res., 112, A12221, • doi:10.1029/2007JA012393. Convergence • Spatial tested with results from: • Harnett E. M., R. M. Winglee, C. Paty (2006), • Multi-scale/multi-fluid simulations of the post plasmoid current • sheet in the terrestrial magnetosphere, Geophys. Res. Lett., 33, • L21110, doi:10.1029/2006GL027376. • Temporal not really an issue.

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