Holdings: The hybrid multiscale simulation technology

The hybrid multiscale simulation technology: an introduction with application to astrophysical and laboratory plasmas

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Bibliographic Details
Main Author:	Lipatov, Alexander S. (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2002
Series:	Scientific computation
Online Access:	Inhaltsverzeichnis
Physical Description:	XVIII, 403 S. Ill., graph. Darst.
ISBN:	3540417346

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245	1	0	\|a The hybrid multiscale simulation technology \|b an introduction with application to astrophysical and laboratory plasmas \|c Alexander S. Lipatov
264		1	\|a Berlin [u.a.] \|b Springer \|c 2002
300			\|a XVIII, 403 S. \|b Ill., graph. Darst.
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adam_text	CONTENTS PART I. COMPUTATIONAL MODELS AND NUMERICAL METHODS 1. PHYSICAL SYSTEMS AND COMPUTATIONAL MODELS ............. 3 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 THE BASIC STEPS OF COMPUTATIONAL EXPERIMENTS . . . . . . . . . . . . 3 1.3 CLASSIFICATION OF THE PLASMA SYSTEMS. SPACE AND TIME SCALES . 6 1.3.1 SOLAR WIND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2 SOLAR-WINDEARTH INTERACTION . . . . . . . . . . . . . . . . . . . . . 7 1.3.3 SOLAR-WINDMOON INTERACTION . . . . . . . . . . . . . . . . . . . . . 8 1.3.4 SOLAR-WINDVENUS AND SOLAR-WINDMARS INTERACTION . 8 1.3.5 SOLAR-WINDCOMET INTERACTION . . . . . . . . . . . . . . . . . . . . 10 1.3.6 SOLAR-WINDHELIOSPHERE INTERACTION . . . . . . . . . . . . . . . . 12 1.3.7 COLLISIONLESS SHOCKS AND NEUTRAL CURRENT LAYERS . . . . . 12 1.3.8 BEAMS AND PLASMA CLOUDS . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.9 FUSION PLASMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 CLASSIFICATION OF THE COMPUTATIONAL MODELS . . . . . . . . . . . . . . . 16 1.4.1 DIRECT SOLUTION OF THE VLASOVMAXWELL EQUATIONS . . . . 17 1.4.2 WATER-BAG METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.3 VLASOV HYBRID SIMULATION (VHS) METHOD . . . . . . . . . . . 21 1.4.4 CONVENTIONAL PARTICLE MODELS . . . . . . . . . . . . . . . . . . . . . 22 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. PARTICLE-MESH MODELS .................................... 25 2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 HYBRID QUASINEUTRAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.1 ELECTROSTATIC MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 AMPERE MAGNETOINDUCTIVE MODEL . . . . . . . . . . . . . . . . . . 27 2.2.3 PARTICLE-IONFLUID-ELECTRON MODEL . . . . . . . . . . . . . . . . . 29 2.2.4 PARTICLE-IONFLUID-IONFLUID-ELECTRON MODEL . . . . . . . . 36 2.2.5 PARTICLE-ION-ELEMENTFLUID-ELECTRON MODEL . . . . . . . . . 37 2.2.6 GYROKINETIC-IONFLUID-IONFLUID-ELECTRON MODELS. F METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2.7 GUIDING-CENTER-IONFLUID-ELECTRON MODEL . . . . . . . . . . 45 2.2.8 PARTICLE-ELECTRONFLUID-ION MODEL . . . . . . . . . . . . . . . . . 48 2.3 PARTICLE NONNEUTRAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 XIV CONTENTS 2.3.1 FULL PARTICLE MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3.2 PARTICLE-IONGUIDING-CENTER-ELECTRON MODEL . . . . . . . . 53 2.3.3 GUIDING-CENTER-IONGUIDING-CENTER-ELECTRON (DRIFT-KINETIC) MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.3.4 PARTICLE-ELECTRONIMMOBILE-ION MODEL . . . . . . . . . . . . . . 56 2.4 PHOTO-IONIZATION AND CHARGE EXCHANGE PROCESSES . . . . . . . . . . 56 2.4.1 HYBRID PARTICLE-NEUTRAL-COMPONENTFLUID- PLASMA MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4.2 HYBRID PARTICLE-NEUTRAL-COMPONENTKINETIC- PLASMA MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 EXERCISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3. TIME INTEGRATION OF THE PARTICLE MOTION EQUATIONS ....... 67 3.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 EXPLICIT LEAPFROG METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3 IMPLICIT METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4 OPERATOR SPLITTING METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4.1 SPLITTING OF THE PARTICLE MOTION EQUATIONS. BORISS SCHEME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4.2 ANALYTICAL TIME INTEGRATION. BUNEMANS SCHEME . . . . . 74 3.4.3 TIME INTEGRATION WITH * T 1 . . . . . . . . . . . . . . . . . . 75 3.5 STABILITY AND ACCURACY OF THE LEAPFROG SCHEMES . . . . . . . . . . . 76 3.6 IMPLICIT TIME INTEGRATION. C1 AND D1 CLASS SCHEMES . . . . . . . . 78 3.6.1 C1 CLASS SCHEME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6.2 D1 CLASS SCHEME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.7 RUNGEKUTTA SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.8 RELATIVISTIC PARTICLE MOTION EQUATIONS . . . . . . . . . . . . . . . . . . . . 81 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4. DENSITY AND CURRENT ASSIGNMENT. FORCE INTERPOLATION. CONSERVATION LAWS ........................................ 83 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 CLOUD AND ASSIGNMENT FUNCTION SHAPES . . . . . . . . . . . . . . . . . . 83 4.3 NGP, CIC AND TSC WEIGHTING . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.1 CLOUD ( S ) AND ASSIGNMENT ( W ) FUNCTION HIERARCHY . . . 85 4.3.2 WEIGHTING IN TWO- AND THREE-DIMENSIONAL SPACE . . . . . 87 4.4 FORCE INTERPOLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.5 MASS,MOMENTUM AND ENERGY CONSERVATION . . . . . . . . . . . . . . . 92 4.5.1 MASS CONSERVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5.2 MOMENTUM CONSERVATION . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.5.3 ENERGY CONSERVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.6 PERIODIC SYSTEMS. MULTIPOLE EXPANSION METHOD . . . . . . . . . . . . 102 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 CONTENTS XV 5. TIME INTEGRATION OF THE FIELD AND ELECTRON PRESSURE EQUATIONS ......................... 105 5.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 PREDICTORCORRECTOR METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.1 THE UPWIND METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.2.2 THE LEAPFROG SCHEME . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.2.3 LAXWENDROFF SCHEME. EXPLICIT CALCULATION OF THE ELECTRIC FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2.4 IMPLICIT CALCULATION OF THE ELECTRIC FIELD . . . . . . . . . . . . 114 5.3 OPERATOR SPLITTING METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.3.1 SPLITTING SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.3.2 PREDICTORCORRECTOR/OPERATOR SPLITTING SCHEME . . . . . 120 5.4 THE TRANSPORTIVE PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.5 HIGH-ORDER SCHEMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.5.1 MULTIPOINT STENCIL SCHEMES . . . . . . . . . . . . . . . . . . . . . . . 124 5.5.2 DIFFERENTIAL CONSEQUENCES FROM THE GOVERNING EQUATIONS . . . . . . . . . . . . . . . . . . . . . 125 5.5.3 COMPACT SCHEMES WITH SPECTRAL-LIKE RESOLUTION . . . . . 125 5.5.4 ADVECTION AND DIFFUSION EQUATIONS . . . . . . . . . . . . . . . . . 131 5.5.5 MAXWELLS EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.5.6 FILTERING OF SPURIOUS OSCILLATIONS . . . . . . . . . . . . . . . . . . 134 5.6 TIME INTEGRATION OF THE EQUATIONS FOR ELECTROMAGNETIC POTENTIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.7 TIME INTEGRATION OF THE GENERALIZED FIELD EQUATIONS . . . . . . . . 138 5.8 TIME INTEGRATION OF THE ELECTRON PRESSURE EQUATION . . . . . . . . 140 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6. GENERAL LOOPS FOR HYBRID CODES. MULTISCALE METHODS .... 143 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.2 EXAMPLES OF THE CONVENTIONAL HYBRID SIMULATION LOOPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.2.1 GENERAL PREDICTORCORRECTOR LOOP . . . . . . . . . . . . . . . . . 143 6.2.2 IMPLICIT TIME INTEGRATION OF THE ELECTROMAGNETIC EQUATIONS . . . . . . . . . . . . . . . . . . . 144 6.2.3 THE MOMENT METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.2.4 THE RICHARDSON EXTRAPOLATION METHOD . . . . . . . . . . . . . 147 6.3 MULTIPLE-TIME-SCALE METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.3.1 ELECTROMAGNETIC FIELD SUBCYCLING. CURRENT ADVANCED METHODS AND CYCLIC LEAPFROG SCHEMES . . . . . . . . . . . . . . . . . . . . . . 148 6.3.2 LIGHT ION (ELECTRON) SUBCYCLING . . . . . . . . . . . . . . . . . . . 151 6.3.3 ORBIT AVERAGING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.4 MULTIPLE-SPACE/TIME-SCALE METHODS . . . . . . . . . . . . . . . . . . . . . 156 6.4.1 VARIATIONAL METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 XVI CONTENTS 6.4.2 ADAPTIVE MESH AND PARTICLE REFINEMENT METHODS . . . . 158 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7. PARTICLE LOADING AND INJECTION. BOUNDARY CONDITIONS ..... 165 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 7.2 LOADING THE PARTICLES INSIDE THE COMPUTATIONAL DOMAIN . . . . . 165 7.2.1 LOADING NONUNIFORM DISTRIBUTIONS F 0 ( V ) ,N 0 ( X ) . . . . . . 165 7.2.2 LOADING A MAXWELLIAN VELOCITY DISTRIBUTION . . . . . . . . . 166 7.2.3 LOADING A RING VELOCITY DISTRIBUTION . . . . . . . . . . . . . . . 167 7.2.4 LOADING A SHELL VELOCITY DISTRIBUTION . . . . . . . . . . . . . . . 173 7.3 PARTICLE INJECTION AT BOUNDARIES . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.3.1 LOADING A MAXWELLIAN VELOCITY DISTRIBUTION FLUX . . . . 174 7.3.2 LOADING A RING VELOCITY DISTRIBUTION FLUX . . . . . . . . . . 176 7.3.3 LOADING A SHELL VELOCITY DISTRIBUTION FLUX . . . . . . . . . . 178 7.4 CHARGE EXCHANGE PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 7.5 BOUNDARY CONDITIONS FOR PARTICLES AND THE ELECTROMAGNETIC FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.5.1 PLASMAVACUUM INTERFACE . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.5.2 FIELD RADIATION AND ABSORPTION AT THE BOUNDARIES . . . . 182 7.5.3 BOUNDARY CONDITIONS AT THE CONDUCTING WALL . . . . . . . . 185 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 PART II. APPLICATIONS 8. COLLISIONLESS SHOCK SIMULATION ........................... 189 8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8.2 COLLISIONLESS SHOCKS WITHOUT MASS LOADING . . . . . . . . . . . . . . . 192 8.2.1 QUASIPERPENDICULAR SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . 192 8.2.2 OBLIQUE SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 8.2.3 QUASIPARALLEL SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 8.3 COLLISIONLESS SHOCKS WITH MASS LOADING BY HEAVY IONS . . . . . . 208 8.3.1 QUASIPERPENDICULAR SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . 210 8.3.2 OBLIQUE SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 8.3.3 QUASIPARALLEL SHOCKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 8.3.4 PICKUP ION ACCELERATION AT SHOCK FRONT. SHOCK SURFING 224 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 9. TANGENTIAL DISCONTINUITY SIMULATION ...................... 237 9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 9.2 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL . . . . . . . 238 9.3 ONE-DIMENSIONAL STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 9.4 TWO-DIMENSIONAL STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 CONTENTS XVII 9.4.1 MAGNETIC FIELD ORIENTED PERPENDICULAR TO THE SIMULATION PLANE . . . . . . . . . . . . . . . . . . . . . . . . . . 241 9.4.2 MAGNETIC FIELD IN THE SIMULATION PLANE . . . . . . . . . . . . . 243 9.4.3 ANALYSIS OF THE WAVES AT THE TD AND THE WAVEPARTICLE CROSS-FIELD TRANSPORT . . . . . . . . 243 9.4.4 DEPENDENCE OF THE FINAL THICKNESS OF TDS ON INITIAL CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 9.4.5 DEPENDENCE OF THE TD WIDTH ON ANOMALOUS RESISTIVITY AND NUMERICAL VISCOSITY . . . . . . . . . . . . . . . . . 247 9.4.6 THE KELVINHELMHOLTZ INSTABILITY AT THE TD . . . . . . . . 248 10. MAGNETIC FIELD RECONNECTION SIMULATION ................. 255 10.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 10.2 ION TEARING INSTABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 10.2.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL 257 10.2.2 MULTIMODE REGIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 10.2.3 SINGLE-MODE REGIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 10.2.4 EXPLOSIVE REGIME. ION ACCELERATION . . . . . . . . . . . . . . . . 264 10.3 ELECTRON EFFECTS ON RECONNECTION . . . . . . . . . . . . . . . . . . . . . . . . 268 10.3.1 EFFECTS OF ELECTRON INERTIA AND ELECTRON PRESSURE ANISOTROPY . . . . . . . . . . . . . . . . . . 270 10.3.2 EFFECTS OF ANOMALOUS RESISTIVITY ON RECONNECTION . . . . 275 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 11. BEAM DYNAMICS SIMULATION .............................. 283 11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 11.2 COLD BEAM DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 11.2.1 ONE-DIMENSIONAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . 285 11.2.2 TWO-DIMENSIONAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . 288 11.3 MASS LOADING OF THE SUPERSONIC FLOW BY HEAVY IONS . . . . . . . . 291 11.3.1 ONE-DIMENSIONAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . 291 11.3.2 TWO-DIMENSIONAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . 295 11.4 FINITE SIZE BEAM (PLASMA CLOUD) DYNAMICS . . . . . . . . . . . . . . . 301 11.4.1 GENERATION OF LOW-FREQUENCY WAVES BY THREE-DIMENSIONAL AND 2.5-DIMENSIONAL BEAMS IN A HOMOGENEOUS BACKGROUND . . . . . . . . . . . . . . . . . . . . . 301 11.4.2 INTERACTION OF THE 2.5-DIMENSIONAL BEAM WITH TANGENTIAL DISCONTINUITIES . . . . . . . . . . . . . . . . . . . . . 302 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12. INTERACTION OF THE SOLAR WIND WITH ASTROPHYSICAL OBJECTS 309 12.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 12.2 INTERACTION OF THE SOLAR WIND WITH STRONG COMETS . . . . . . . . . 309 12.2.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL 310 XVIII CONTENTS 12.2.2 STRUCTURE OF THE REGION OF MASS LOADING BY COMETARY IONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 12.2.3 INDUCED MAGNETOSPHERE,BOW WAVE AND MAGNETIC BARRIER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 12.3 INTERACTION OF THE SOLAR WIND WITH WEAK COMETS AND RELATED OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 12.3.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL 320 12.3.2 INTERACTION OF THE SOLAR WIND WITH VERY WEAK COMETS 321 12.3.3 INTERACTION OF THE SOLAR WIND WITH WEAK COMETS . . . . 329 12.3.4 INTERACTION OF THE SOLAR WIND WITH PLUTO . . . . . . . . . . . 329 12.4 INTERACTION OF THE SOLAR WIND WITH VENUS . . . . . . . . . . . . . . . . . 333 12.4.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL 333 12.4.2 RESULTS AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 334 12.5 INTERACTION OF THE SOLAR WIND WITH THE MOON . . . . . . . . . . . . . . 337 12.5.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL 338 12.5.2 METHOD OF SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 12.5.3 RESULTS AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 342 12.6 INTERACTION OF NEUTRAL INTERSTELLAR ATOMS WITH THE HELIOSPHERE 344 12.6.1 FORMULATION OF THE PROBLEM AND MATHEMATICAL MODEL . 344 12.6.2 RESULTS AND CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 346 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 13. APPENDIX ................................................. 355 13.1 COORDINATE FORM OF MAXWELLS EQUATIONS AND THE ELECTRON PRESSURE EQUATIONS . . . . . . . . . . . . . . . . . . . . . 355 13.1.1 CARTESIAN COORDINATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 13.1.2 CYLINDRICAL COORDINATES . . . . . . . . . . . . . . . . . . . . . . . . . . 357 13.1.3 SPHERICAL COORDINATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 13.2 SOLVING ONE-DIMENSIONAL DIFFERENCE EQUATIONS . . . . . . . . . . . . . 361 13.2.1 THREE-POINT DIFFERENCE EQUATION WITH NONPERIODIC BOUNDARY CONDITIONS: FORWARD-ELIMINATIONBACKWARD-SUBSTITUTION METHOD . 361 13.2.2 THREE-POINT DIFFERENCE EQUATION WITH PERIODIC BOUNDARY CONDITIONS: FORWARD-ELIMINATIONBACKWARD-SUBSTITUTION METHOD . 362 13.2.3 FIVE-POINT DIFFERENCE EQUATION: FORWARD-ELIMINATION*BACKWARD-SUBSTITUTION METHOD . 363 14. SOLUTIONS ................................................. 365 REFERENCES .................................................... 380 INDEX ......................................................... 401
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spelling	Lipatov, Alexander S. Verfasser aut The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas Alexander S. Lipatov Berlin [u.a.] Springer 2002 XVIII, 403 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Scientific computation SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019927978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lipatov, Alexander S. The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas
title	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas
title_auth	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas
title_exact_search	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas
title_full	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas Alexander S. Lipatov
title_fullStr	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas Alexander S. Lipatov
title_full_unstemmed	The hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas Alexander S. Lipatov
title_short	The hybrid multiscale simulation technology
title_sort	the hybrid multiscale simulation technology an introduction with application to astrophysical and laboratory plasmas
title_sub	an introduction with application to astrophysical and laboratory plasmas
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019927978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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