Mathematical Physics - Volume II - Numerical Methods

284

INDEX

disorder, 256 dissipative terms, 112

Jacobian, 117

Lagrange interpolation, 39 Lennard-Jones 6-12 potential, 224 linear space, 36 list of neighbors, 235 load vector, 37 localization of deformation, 215

EAM, 226 eigenvalue, 126 eigenvalues of flux matrices, 118 element master, 75 elementary flux, 110 embedded atom method, 226 entropy condition, 148 Euler equations, 110, 115 explicit method, 14 approximation, 42 approximations, 67 interpolation, 62 finite element matrices, 42, 79 finite element matrix, 74 finite element method 2D, 72 finite elements, 42 finite volume method, 109 flow quasi one-dimensional, 128 flux of flow quantities, 111 fluxes, 110 forward difference, 14 geometric discretization, 110 geometrically regular, 256 Godunov scheme, 123 finite difference method, 11 finite element

Mach number, 119

undisturbed flow, 115 many-body potentials, 226 Maxwell-Boltzmann distribution, 231

mesh, 11 meshless

Lagrangian method, 161 micro-polar continuum, 251 Mohr-Coulomb type limit, 260 monotonic numerical scheme, 148 natural boundary condition, 34 Navier-Stokes equations, 115 nearest neighbors, 224 Neumann problem, 25 node, 11 non-cohesive systems, 261 non-stationary flow, 121 numerical boundary conditions, 139 numerical flux, 127 pair potentials, 224 pairwise additivity, 224 partial differential equation, 12 linear, 82 periodic boundary conditions, 234 physical boundary conditions, 138 post-critical softening regime, 249 postprocessor, 83 potential Lennard-Jones 6-12, 224 potential theory, 110

Hertzian contact, 260 homogenization, 259

implicit method, 14 integration weight function, 81 interpolation within triangles, 64 interpolation error, 67 intramolecular bonding interactions, 227

potential well, 225 Prandtl number, 150 preprocessor, 83 procedure