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Donea J., Huerta A. Ч Finite Element Methods for Flow Problems
Donea J., Huerta A. Ч Finite Element Methods for Flow Problems

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Ќазвание: Finite Element Methods for Flow Problems

јвторы: Donea J., Huerta A.

јннотаци€:

In recent years there have been significant developments in the development of stable and accurate finite element procedures for the numerical approximation of a wide range of fluid mechanics problems. Taking an engineering rather than a mathematical bias, this valuable reference resource details the fundamentals of stabilised finite element methods for the analysis of steady and time-dependent fluid dynamics problems. Organised into six chapters, this text combines theoretical aspects and practical applications and offers coverage of the latest research in several areas of computational fluid dynamics.
- Coverage includes new and advanced topics unavailable elsewhere in book form
- Collection in one volume of the widely dispersed literature reporting recent progress in this field
- Addresses the key problems and offers modern, practical solutions
Due to the balance between the concise explanation of the theory and the detailed description of modern practical applications, this text is suitable for a wide audience including academics, research centres and government agencies in aerospace, automotive and environmental engineering.


язык: en

–убрика: ћатематика/„исленные методы/ онечные элементы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2003

 оличество страниц: 350

ƒобавлена в каталог: 20.02.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Accuracy      99
Acoustic approximation      188Ч189
Adams Ч Bashforth method      212 226 318
Added mass concept      191
Advection      see УConvectionФ
Advective form      81
Algebraic splitting      213 304
Amplification factor, $\theta$ family methods, convection-diffusion-reaction      225
Amplification factor, $\theta$ family methods, least-squares      121
Amplification factor, $\theta$ family methods, pure convection      102
Amplification factor, exact      100Ч101
Amplification factor, explicit Runge Ч Kutta methods      217
Amplification factor, implicit multistage schemes      230
Amplification factor, Lax Ч Wendroff method      102
Amplification factor, Lax Ч 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 Ч Galerkin method      110
Amplification factor, two-step Taylor Ч Galerkin method      115
Anisotropic balancing diffusion      75
Anisotropic balancing dissipation      57
Approximate diagonalization      176
Approximate Riemann solvers      168
Arbitrary Lagrangian Ч Eulerian (ALE)      3 5
Arbitrary Lagrangian Ч Eulerian, conservation equations      18
Arbitrary Lagrangian Ч Eulerian, examples      196
Arbitrary Lagrangian Ч Eulerian, fluid-structure interaction      192
Arbitrary Lagrangian Ч Eulerian, fundamental equation      11
Arbitrary Lagrangian Ч Eulerian, kinematics      8
Artificial diffusion, linear      42 49 55Ч57 75 142 148 168 178 258 261 297
Artificial diffusion, nonlinear      184 (See also УShock-capturing techniquesФ)
Artificial viscosity      148 177Ч179 183 shock-capturing techniquesФ)
Backward Euler      89 92 211 298
Balancing diffusion      55Ч56
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      297Ч302
Boundary conditions, imposing tractions      270
Boundary conditions, Laplace form      278Ч279
Boundary conditions, least-squares formulation      255
Boundary conditions, Navier Ч Stokes equation      270 275 278Ч279 294
Boundary conditions, open/artificial      313
Boundary conditions, pure convection      34 81 94
Boundary conditions, stress-divergence form      278Ч279
Boundary conditions, subsonic/supersonic      166
Boundary value problem, convection-diffusion      34Ч35
Boundary value problem, Poisson equation      23Ч25 27
Boundary value problem, stationary Stokes problem      275
Boundary value problem, Steady Navier Ч Stokes problem      293
Boussinesq approximation      317
Broken space      124 171
Bubble function stabilization      67 70
Buoyancy driven flow      317
BurgersТ equation      110 149Ч154 199 250Ч252
Butcher array      217
Cauchy problem      99 149
Cauchy stress      14 159 190 268Ч269 275 277Ч278 282
CeaТs 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      82Ч87 149Ч152 154Ч156 163Ч165 173
Characteristic variables      164 169
Characteristic-based methods      80 87 90Ч91 176
Characteristic-based split (CBS) algorithm      187
Chorin Ч Temam projection method      266 275 298Ч303 315
Classical solution      24
Coercive      25Ч26 211
Condition for uniqueness      see УUniquenessФ
Conditionally stable      225
Conservation form, ALE equations      18
Conservation form, convection-diffusion      34 36
Conservation form, energy      17
Conservation form, Euler      159Ч161
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 95Ч96 104Ч105 131 182Ч183 223
Consistent stabilization      59Ч60 233Ч234
Constitutive law      16 159 275Ч277
Constrained equilibrium problem      275
Continuity equation      13
Continuous functional form      25Ч26
Convection matrix      37Ч39 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      222Ч223
Convection-diffusion, unsteady, strong form      210
Convective form      81
Convective transport problems      see УPure convectionФ
Convective velocity      10
Convergence of Galerkin      27Ч28
Convergence, time-stepping schemes      98
Courant number      101
Crank Ч Nicolson      92 211 213 222
Crosswind diffusion      57Ч58 185
Crouzeix Ч Raviart element      285Ч286
Cubic Hermite interpolation      88 91 110 123 256
Damping error      101
Deviatoric stress tensor      268 276 278
Difference equation      44
Diffusion matrix      37Ч39 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 Ч Rachford method      214
Driven cavity problem      307
Eigenvalues of Euler projection matrix      163
Energy conservation equation      17
Energy norm      26
Enthalpy      17 160Ч161
entropy      164Ч165
Entropy, condition      149 152Ч154 156
Entropy, solution      153Ч154
Equation of motion      13 15
Equivalence of penalty and mixed methods      291Ч292
Euler equations      159
Euler equations, 1D      162
Euler equations, 2D      162
Euler equations, diagonalization      164Ч165
Euler equations, Galerkin      167
Euler equations, non-conservative form      161
Euler equations, strong form      159Ч162
Euler equations, subsonic/supersonic boundary conditions      166
Euler method      89 92 211 298
Eulerian description of motion      4
Expansion fan      152
Explicit scheme, Adams Ч Bashforth      212
Explicit scheme, Euler      89 92 211 298
Explicit scheme, fourth-order leap-frog      113
Explicit scheme, Lax Ч Wendroff      93
Explicit scheme, leap-frog      93
Explicit scheme, linear multistep      212
Explicit scheme, Pade      219
Explicit scheme, Runge Ч Kutta      217
Explicit scheme, stability      225
Explicit scheme, Taylor Ч Galerkin      108 157
Explicit scheme, two-step Taylor Ч Galerkin      114 158
External boundary      166
Finite element interpolating space      22
Finite increment calculus      66
Fluid-structure interaction      187
Fluid-structure interaction, acoustic approximation      188Ч189
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      167Ч168 170Ч172 205Ч207
Flux-timiter      180Ч181
Fourier analysis      99Ч101 224 238
Fractional-step methods for convection-diffusion      213Ч215
Fractional-step methods for Euler equations in ALE description      193
Fractional-step methods for Navier Ч Stokes      275 297Ч300 302Ч303 305 314
Fractional-step methods, nearly incompressible flows      186
Full upwind      50
Functional spaces for Euler      171
Functional spaces for Navier Ч Stokes      273Ч274
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      20Ч21
Functional spaces, solcnoidal fields      274
Functional spaces, time-discontinuous Galerkin      127
Functional spaces, trial and test functions      21Ч22
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 УGalerkin/Least-squaresФ
GodunovТs 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 179Ч180 182
homogeneous functions      162
Implicit scheme, backward Euler      89 92 211 298
Implicit scheme, Crank Ч Nicolson      92 211 213 222
Implicit scheme, Galerkin      92
Implicit scheme, linear multistep      212
Implicit scheme, Pade      220
Implicit scheme, Runge Ч Kutta      217 220
Incremental projection      301
Inf-sup condition      285 (See also УLBB conditionФ)
Inflow boundary condition      34 81 166
Internal energy equation      16
Interpolating space      22
Inviscid fluid      16
Jacobian matrix (Euler equations)      162Ч163 169Ч170
Jump condition      149 (See also УRankine Ч Hugoniot jump conditionФ)
Kinematic pressure      270 278
Kinematic viscosity      270 278
Kinematical description      4Ч5
Lagrange Ч Galerkin method      80
Lagrange-multipliers technique (boundary conditions)      32 194
Lagrangian description of motion      4
Lapidus viscosity      179
Lax equivalence theorem      98Ч99
Lax Ч Milgram lemma      25
Lax Ч Wendroff method      93 97Ч98
LBB condition      284Ч286 303
Leap-frog method      93 98
Least-squares-based spatial discretization      120
Least-squares-based spatial discretization, $\theta$ 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      180Ч181
Limiter schemes, slope      180Ч181
Linear multistep method      212
Lobatto implicit Runge Ч Kutta methods      220Ч221
Lumped-mass matrix      39 103 131 182Ч183
Mach number      161
Mass matrix, added mass      191
Mass matrix, consistent      39 95Ч96 131 182Ч183 223
Mass matrix, lumped      39 103 131 182Ч183
Mass-conservation equation      13
Material surface      13 15
Material time derivative      7Ч8 84
Mesh Peclet number      40 185
Method of lines      92
Mini element      285Ч286
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      117Ч118 (See also УHigh-resolution schemesФ)
Natural convection      317 319
Navier Ч Stokes equations      270
Navier Ч Stokes equations, dimensionless form      271
Navier Ч Stokes equations, steady, Galerkin      293
Navier Ч Stokes equations, steady, matrix problem      293
Navier Ч Stokes equations, steady, strong form      293
Navier Ч Stokes equations, unsteady, fractional-step methods      297Ч300
Navier Ч Stokes equations, unsteady, Galerkin      295
Navier Ч Stokes equations, unsteady, stabilized      296
Navier Ч 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      218Ч219
Pade approximations, implicit      220
Peaceman Ч 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      23Ч25 27
Prandtl number      319
Pressure Poisson equation      302
Projection method      266 275 298Ч303 315
Propagation speed of the discontinuity      154Ч155
Pseudo-viscous pressure      178
Pure convection, nonlinear      86
Pure convection, semi-discrete form      94Ч96
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      92Ч93
Rankine Ч Hugoniot jump condition      154 156 170 176
Rarefaction wave      154
Rate of deformation (or strain rate) tensor      267
Rayleigh number      319
Reduced integration      290Ч291
Residual decomposition      176
Reynolds number      271
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