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| Ïîèñê ïî óêàçàòåëÿì |
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| Donea J., Huerta A. — Finite Element Methods for Flow Problems |
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| Ïðåäìåòíûé óêàçàòåëü |
Accuracy 99
Acoustic approximation 188—189
Adams — Bashforth method 212 226 318
Added mass concept 191
Advection see “Convection”
Advective form 81
Algebraic splitting 213 304
Amplification factor,  family methods, convection-diffusion-reaction 225
Amplification factor, family methods, least-squares 121
Amplification factor, family methods, pure convection 102
Amplification factor, exact 100—101
Amplification factor, explicit Runge — Kutta methods 217
Amplification factor, implicit multistage schemes 230
Amplification factor, Lax — Wendroff method 102
Amplification factor, Lax — Wendroff method with diagonal mass 103
Amplification factor, leap-frog method 102
Amplification factor, numerical 101
Amplification factor, Pade schemes 228
Amplification factor, semi-Lagrangian scheme 89
Amplification factor, stability 101
Amplification factor, stabilized schemes 238
Amplification factor, summary for pure convection 129
Amplification factor, third-order Taylor — Galerkin method 110
Amplification factor, two-step Taylor — Galerkin method 115
Anisotropic balancing diffusion 75
Anisotropic balancing dissipation 57
Approximate diagonalization 176
Approximate Riemann solvers 168
Arbitrary Lagrangian — Eulerian (ALE) 3 5
Arbitrary Lagrangian — Eulerian, conservation equations 18
Arbitrary Lagrangian — Eulerian, examples 196
Arbitrary Lagrangian — Eulerian, fluid-structure interaction 192
Arbitrary Lagrangian — Eulerian, fundamental equation 11
Arbitrary Lagrangian — Eulerian, kinematics 8
Artificial diffusion, linear 42 49 55—57 75 142 148 168 178 258 261 297
Artificial diffusion, nonlinear 184 (See also “Shock-capturing techniques”)
Artificial viscosity 148 177—179 183 shock-capturing techniques”)
Backward Euler 89 92 211 298
Balancing diffusion 55—56
Best fit 28
boundary conditions 19 22
Boundary conditions, convection-diffusion 34 210
Boundary conditions, Dirichlet, computational aspects 28 31
Boundary conditions, Euler equation 160 165
Boundary conditions, fluid-structure interaction 189 193
Boundary conditions, fractional-step method 297—302
Boundary conditions, imposing tractions 270
Boundary conditions, Laplace form 278—279
Boundary conditions, least-squares formulation 255
Boundary conditions, Navier — Stokes equation 270 275 278—279 294
Boundary conditions, open/artificial 313
Boundary conditions, pure convection 34 81 94
Boundary conditions, stress-divergence form 278—279
Boundary conditions, subsonic/supersonic 166
Boundary value problem, convection-diffusion 34—35
Boundary value problem, Poisson equation 23—25 27
Boundary value problem, stationary Stokes problem 275
Boundary value problem, Steady Navier — Stokes problem 293
Boussinesq approximation 317
Broken space 124 171
Bubble function stabilization 67 70
Buoyancy driven flow 317
Burgers’ equation 110 149—154 199 250—252
Butcher array 217
Cauchy problem 99 149
Cauchy stress 14 159 190 268—269 275 277—278 282
Cea’s lemma 27
Centered difference operators 100
Central difference method 39 41 43 96 103 106
CFL property 103 110
Characteristic direction 82
Characteristic Galerkin method 89 91 110
Characteristic lines 82—87 149—152 154—156 163—165 173
Characteristic variables 164 169
Characteristic-based methods 80 87 90—91 176
Characteristic-based split (CBS) algorithm 187
Chorin — Temam projection method 266 275 298—303 315
Classical solution 24
Coercive 25—26 211
Condition for uniqueness see “Uniqueness”
Conditionally stable 225
Conservation form, ALE equations 18
Conservation form, convection-diffusion 34 36
Conservation form, energy 17
Conservation form, Euler 159—161
Conservation form, mass 13
Conservation form, momentum 15
Conservation form, pure convection 81 85
Conservative discretization schemes 176
Consistency 28 98
Consistent mass matrix 39 95—96 104—105 131 182—183 223
Consistent stabilization 59—60 233—234
Constitutive law 16 159 275—277
Constrained equilibrium problem 275
Continuity equation 13
Continuous functional form 25—26
Convection matrix 37—39 46 55 72 95 223 294
Convection-diffusion, exact nodal solution 61
Convection-diffusion, steady, Galerkin 36
Convection-diffusion, steady, strong form 34
Convection-diffusion, steady, weak form 36
Convection-diffusion, unsteady, semi-discrete form 222—223
Convection-diffusion, unsteady, strong form 210
Convective form 81
Convective transport problems see “Pure convection”
Convective velocity 10
Convergence of Galerkin 27—28
Convergence, time-stepping schemes 98
Courant number 101
Crank — Nicolson 92 211 213 222
Crosswind diffusion 57—58 185
Crouzeix — Raviart element 285—286
Cubic Hermite interpolation 88 91 110 123 256
Damping error 101
Deviatoric stress tensor 268 276 278
Difference equation 44
Diffusion matrix 37—39 46 72 223
Diffusion number 101
Diffusion of Galerkin (negative) 43
Dimensionless reaction 101
Dimensionless wave vector 100
Discontinuous Galerkin 124 141 170 208
Divergence operator (discrete) 282
Douglas — Rachford method 214
Driven cavity problem 307
Eigenvalues of Euler projection matrix 163
Energy conservation equation 17
Energy norm 26
Enthalpy 17 160—161
entropy 164—165
Entropy, condition 149 152—154 156
Entropy, solution 153—154
Equation of motion 13 15
Equivalence of penalty and mixed methods 291—292
Euler equations 159
Euler equations, 1D 162
Euler equations, 2D 162
Euler equations, diagonalization 164—165
Euler equations, Galerkin 167
Euler equations, non-conservative form 161
Euler equations, strong form 159—162
Euler equations, subsonic/supersonic boundary conditions 166
Euler method 89 92 211 298
Eulerian description of motion 4
Expansion fan 152
Explicit scheme, Adams — Bashforth 212
Explicit scheme, Euler 89 92 211 298
Explicit scheme, fourth-order leap-frog 113
Explicit scheme, Lax — Wendroff 93
Explicit scheme, leap-frog 93
| Explicit scheme, linear multistep 212
Explicit scheme, Pade 219
Explicit scheme, Runge — Kutta 217
Explicit scheme, stability 225
Explicit scheme, Taylor — Galerkin 108 157
Explicit scheme, two-step Taylor — Galerkin 114 158
External boundary 166
Finite element interpolating space 22
Finite increment calculus 66
Fluid-structure interaction 187
Fluid-structure interaction, acoustic approximation 188—189
Fluid-structure interaction, ALE formulation 192
Fluid-structure interaction, boundary conditions 189 193
Fluid-structure interaction, interface conditions 195
Fluid-structure interaction, large-displacement 191
Fluid-structure interaction, nonlinear structural response 191
Flux representation 158 201
Flux vector splitting 167—168 170—172 205—207
Flux-timiter 180—181
Fourier analysis 99—101 224 238
Fractional-step methods for convection-diffusion 213—215
Fractional-step methods for Euler equations in ALE description 193
Fractional-step methods for Navier — Stokes 275 297—300 302—303 305 314
Fractional-step methods, nearly incompressible flows 186
Full upwind 50
Functional spaces for Euler 171
Functional spaces for Navier — Stokes 273—274
Functional spaces for transient problems 95
Functional spaces, continuous and differentiable functions 19
Functional spaces, finite dimensional 22
Functional spaces, least-squares 237 254
Functional spaces, Sobolev 20—21
Functional spaces, solcnoidal fields 274
Functional spaces, time-discontinuous Galerkin 127
Functional spaces, trial and test functions 21—22
Galerkin orthogonality 27
Galerkin/Least-squares 60 63 233 236
Galerkin/Least-squares, Fourier analysis 238
Galerkin/Least-squares, space-time 126 128 175 241
Galerkin/Least-squares, Stokes 287
Generalized (weak) solution 149
GLS see “Galerkin/Least-squares”
Godunov’s theorem 118
Gradient operator (discrete) 282
Grid velocity 10
Group representation 159
Helmholtz decomposition principle 275 298
Hemker problem 78
High-resolution schemes 118 177 179—180 182
homogeneous functions 162
Implicit scheme, backward Euler 89 92 211 298
Implicit scheme, Crank — Nicolson 92 211 213 222
Implicit scheme, Galerkin 92
Implicit scheme, linear multistep 212
Implicit scheme, Pade 220
Implicit scheme, Runge — Kutta 217 220
Incremental projection 301
Inf-sup condition 285 (See also “LBB condition”)
Inflow boundary condition 34 81 166
Internal energy equation 16
Interpolating space 22
Inviscid fluid 16
Jacobian matrix (Euler equations) 162—163 169—170
Jump condition 149 (See also “Rankine — Hugoniot jump condition”)
Kinematic pressure 270 278
Kinematic viscosity 270 278
Kinematical description 4—5
Lagrange — Galerkin method 80
Lagrange-multipliers technique (boundary conditions) 32 194
Lagrangian description of motion 4
Lapidus viscosity 179
Lax equivalence theorem 98—99
Lax — Milgram lemma 25
Lax — Wendroff method 93 97—98
LBB condition 284—286 303
Leap-frog method 93 98
Least-squares-based spatial discretization 120
Least-squares-based spatial discretization, family of methods 121
Least-squares-based spatial discretization, Taylor least-squares method 122
Least-squares-based spatial discretization, transient problems 254
Least-squares-based spatial discretization, unsteady convection-diffusion 237
Lid-driven cavity problem 307
Limiter schemes, flux 180—181
Limiter schemes, slope 180—181
Linear multistep method 212
Lobatto implicit Runge — Kutta methods 220—221
Lumped-mass matrix 39 103 131 182—183
Mach number 161
Mass matrix, added mass 191
Mass matrix, consistent 39 95—96 131 182—183 223
Mass matrix, lumped 39 103 131 182—183
Mass-conservation equation 13
Material surface 13 15
Material time derivative 7—8 84
Mesh Peclet number 40 185
Method of lines 92
Mini element 285—286
Mixed finite element methods 273 279 284
Mixed finite element methods, equivalence with penalty formulation 291
Modified equation method 43 99 105
Modified weighting function 55
Momentum equation 13
Monotone 117
Monotonicity-preserving schemes 117—118 (See also “High-resolution schemes”)
Natural convection 317 319
Navier — Stokes equations 270
Navier — Stokes equations, dimensionless form 271
Navier — Stokes equations, steady, Galerkin 293
Navier — Stokes equations, steady, matrix problem 293
Navier — Stokes equations, steady, strong form 293
Navier — Stokes equations, unsteady, fractional-step methods 297—300
Navier — Stokes equations, unsteady, Galerkin 295
Navier — Stokes equations, unsteady, stabilized 296
Navier — Stokes equations, unsteady, strong form 294
Nearly incompressible flows 186
Newtonian fluid 268
Normal to a discrete interface 196
Open/artificial boundary conditions 313
Outflow boundary condition 166
Pade approximations, explicit 218—219
Pade approximations, implicit 220
Peaceman — Rachford method 214
Peclet number 40 185
Penalty formulation 273 288
Penalty formulation, equivalence with mixed methods 291
Penalty formulation, under-integration 290
Penalty matrix 290
Phase error 101
Plane jet problem 313
Poisson equation 23—25 27
Prandtl number 319
Pressure Poisson equation 302
Projection method 266 275 298—303 315
Propagation speed of the discontinuity 154—155
Pseudo-viscous pressure 178
Pure convection, nonlinear 86
Pure convection, semi-discrete form 94—96
Pure convection, space-time formulations 126
Pure convection, spatial discretization, discontinuous Galerkin 124
Pure convection, spatial discretization, Galerkin 94
Pure convection, spatial discretization, least-squares 120
Pure convection, strong form 81
Pure convection, time discretization 92—93
Rankine — Hugoniot jump condition 154 156 170 176
Rarefaction wave 154
Rate of deformation (or strain rate) tensor 267
Rayleigh number 319
Reduced integration 290—291
Residual decomposition 176
Reynolds number 271
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