Page 12 - The Combined Finite-Discrete Element Method

CONTENTS ix

5.3 Alternative Explicit Time Integration Schemes 203
5.3.1 The Central Difference time integration scheme (CD) 203
5.3.2 Gear’s predictor-corrector time integration schemes (PC-3, PC-4, and
PC-5) 204
5.3.3 CHIN integration scheme 205
5.3.4 OMF30 time integration scheme 206
5.3.5 OMF32 time integration scheme 206
5.3.6 Forest & Ruth time integration scheme 207
5.4 The Combined Finite-Discrete Element Simulation of the State of Rest 211

6 Sensitivity to Initial Conditions in Combined Finite-Discrete Element
Simulations 219
6.1 Introduction 219
6.2 Combined Finite-Discrete Element Systems 220

7 Transition from Continua to Discontinua 231
7.1 Introduction 231
7.2 Strain Softening Based Smeared Fracture Model 232
7.3 Discrete Crack Model 239
7.4 A Need for More Robust Fracture Solutions 254

8 Fluid Coupling in the Combined Finite-Discrete Element Method 255
8.1 Introduction 255
8.1.1 CFD with solid coupling 255
8.1.2 Combined finite-discrete element method with CFD coupling 257
8.2 Expansion of the Detonation Gas 259
8.2.1 Equation of state 259
8.2.2 Rigid chamber 259
8.2.3 Isentropic adiabatic expansion of detonation gas 262
8.2.4 Detonation gas expansion in a partially filled non-rigid chamber 264
8.3 Gas Flow Through Fracturing Solid 266
8.3.1 Constant area duct 267
8.4 Coupled Combined Finite-Discrete Element Simulation of Explosive Induced
Fracture and Fragmentation 270
8.4.1 Scaling of coupled combined finite-discrete element problems 274
8.5 Other Applications 276

9 Computational Aspects of Combined Finite-Discrete Element Simulations 277
9.1 Large Scale Combined Finite-Discrete Element Simulations 277
9.1.1 Minimising RAM requirements 278
9.1.2 Minimising CPU requirements 279
9.1.3 Minimising storage requirements 279
9.1.4 Minimising risk 279
9.1.5 Maximising transparency 280
9.2 Very Large Scale Combined Finite-Discrete Element Simulations 280
9.3 Grand Challenge Combined Finite-Discrete Element Simulations 281
9.4 Why the C Programming Language? 283
9.5 Alternative Hardware Architectures 283
9.5.1 Parallel computing 283