422
Index
Enthalpy, 10
Equation of state, 310
Euler equations, 13, 309, 319, 349
Explicit Euler method, 136, 137, 179,
376
False diffusion, 45, 66, 76, 87
Fick's law, 9
Filter kernel, 278
Flux-corrected transport, 326
Forward elimination, 93-95
Fourier series, 60, 61, 270
Fourier's law, 9
Froude number, 11, 280
Full approximation scheme, 115
Full multigrid method, 115, 345, 350
Fully-implicit schemes, 379
Gauss theorem, 4, 6, 233, 235, 239, 346
Gauss-Seidel method, 100, 107, 112,
115, 116, 129, 357
Generic conservation equation, 10, 39,
71, 227, 230
Grid refinement, 334
Grid velocity, 3744377
Grid-independent solution, 32
Grid:non-orthogonality, 342
Grid:warp, 343
H-type grid, 27, 223
Hanging nodes, 242
Implicit Euler method, 136, 137, 185,
375-377
Inflow conditions
- DNS, 273
Initial conditions
- DNS, 272
Integral scale, 267
Iteration errors, 34, 97-100, 112, 124,
127, 128, 131, 355
Iteration matrix, 98, 101, 124, 243, 360
Iterations
- inner, 117, 118, 126, 173, 189, 228,
361, 365
- outer, 117, 118, 121, 126, 173, 189,
228, 345, 350, 363, 365, 372, 373, 391
Jacobi method, 100, 112, 116
Jacobian, 120
Kolmogoroff scale, 268
Kronecker symbol, 6
Lagrange multiplier, 203
Laplace equation, 14
Lax equivalence theorem, 32
Leapfrog method, 136, 147
Leibniz rule, 374
Level-set methods, 387
Linear upwind scheme, 81
Local grid refinement, 88, 223, 384
Mach number, 2, 12, 314
Marangoni number, 382
Marker-and-cell method, 383
Maxwell equations, 370
Midpoint rule, 74, 78, 136, 141, 189,
231, 238
Mixed model, 281
Modeling errors, 34
Newtonian fluid, 5
Non-matching interface, 223, 242, 245
non-Newtonian fluid, 369
Numerical grid
- block-structured, 27, 58, 353
- Chimera, 28
- composite, 28, 58
- structured, 26, 40
- unstructured, 29, 58, 107, 111, 353
Numerical methods
- for DNS, 269
0-type grid, 27, 223, 242
One-point closure, 266
Order of accuracy, 31, 35, 44, 52, 59,
74, 79, 138, 237, 240, 271, 334, 376
Packet methods, 400
Pad6 schemes, 45, 80
Peclet number, 64, 67, 68, 86, 145, 148
Picard iteration, 121, 190
PIS0 algorithm, 176, 178, 195
Positive definite matrix, 108
Prandtl number, 10, 215, 372
Pre-conditioning matrix, 97, 109, 110
Projection methods, 175
Prolongation, 113-1 15, 346
Rayleigh number, 214, 372
Reconstruction polynomial, 327
Residual, 97, 104, 110, 112, 113, 126,
128, 132, 345, 351
Restriction, 112, 114, 115, 345
Reynolds
- averaging, 293
- number, 11, 259, 268
Index
Enthalpy, 10
Equation of state, 310
Euler equations, 13, 309, 319, 349
Explicit Euler method, 136, 137, 179,
376
False diffusion, 45, 66, 76, 87
Fick's law, 9
Filter kernel, 278
Flux-corrected transport, 326
Forward elimination, 93-95
Fourier series, 60, 61, 270
Fourier's law, 9
Froude number, 11, 280
Full approximation scheme, 115
Full multigrid method, 115, 345, 350
Fully-implicit schemes, 379
Gauss theorem, 4, 6, 233, 235, 239, 346
Gauss-Seidel method, 100, 107, 112,
115, 116, 129, 357
Generic conservation equation, 10, 39,
71, 227, 230
Grid refinement, 334
Grid velocity, 3744377
Grid-independent solution, 32
Grid:non-orthogonality, 342
Grid:warp, 343
H-type grid, 27, 223
Hanging nodes, 242
Implicit Euler method, 136, 137, 185,
375-377
Inflow conditions
- DNS, 273
Initial conditions
- DNS, 272
Integral scale, 267
Iteration errors, 34, 97-100, 112, 124,
127, 128, 131, 355
Iteration matrix, 98, 101, 124, 243, 360
Iterations
- inner, 117, 118, 126, 173, 189, 228,
361, 365
- outer, 117, 118, 121, 126, 173, 189,
228, 345, 350, 363, 365, 372, 373, 391
Jacobi method, 100, 112, 116
Jacobian, 120
Kolmogoroff scale, 268
Kronecker symbol, 6
Lagrange multiplier, 203
Laplace equation, 14
Lax equivalence theorem, 32
Leapfrog method, 136, 147
Leibniz rule, 374
Level-set methods, 387
Linear upwind scheme, 81
Local grid refinement, 88, 223, 384
Mach number, 2, 12, 314
Marangoni number, 382
Marker-and-cell method, 383
Maxwell equations, 370
Midpoint rule, 74, 78, 136, 141, 189,
231, 238
Mixed model, 281
Modeling errors, 34
Newtonian fluid, 5
Non-matching interface, 223, 242, 245
non-Newtonian fluid, 369
Numerical grid
- block-structured, 27, 58, 353
- Chimera, 28
- composite, 28, 58
- structured, 26, 40
- unstructured, 29, 58, 107, 111, 353
Numerical methods
- for DNS, 269
0-type grid, 27, 223, 242
One-point closure, 266
Order of accuracy, 31, 35, 44, 52, 59,
74, 79, 138, 237, 240, 271, 334, 376
Packet methods, 400
Pad6 schemes, 45, 80
Peclet number, 64, 67, 68, 86, 145, 148
Picard iteration, 121, 190
PIS0 algorithm, 176, 178, 195
Positive definite matrix, 108
Prandtl number, 10, 215, 372
Pre-conditioning matrix, 97, 109, 110
Projection methods, 175
Prolongation, 113-1 15, 346
Rayleigh number, 214, 372
Reconstruction polynomial, 327
Residual, 97, 104, 110, 112, 113, 126,
128, 132, 345, 351
Restriction, 112, 114, 115, 345
Reynolds
- averaging, 293
- number, 11, 259, 268