High accuracy non-centered compact difference schemes for fluid dynamics applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1994
|
| Series: | Series on advances in mathematics for applied sciences
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 314 S. graph. Darst. |
| ISBN: | 9810216688 |
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| 100 | 1 | |a Tolstykh, Andrei I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a High accuracy non-centered compact difference schemes for fluid dynamics applications |c Andrei I. Tolstykh |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1994 | |
| 300 | |a XIII, 314 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 21 | |
| 650 | 7 | |a Fluides, Dynamique des - Modèles mathématiques |2 ram | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Fluid dynamics |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804127406439530496 |
|---|---|
| adam_text | Contents
0 Introduction 1
0.1 History 1
0.2 Motivations. High accuracy methods 2
0.3 High order schemes 6
1 Third order schemes with compact upwind differencing 15
1.1 Third order compact differencing and corresponding schemes 15
1.1.1 Derivation of compact differencing formulas 15
1.1.2 Compact third order schemes 17
1.2 Compact schemes as approximations of conservation laws 20
1.2.1 Equations of balance 20
1.2.2 Conservation property in the case of sonic points 21
1.3 Dispersion and dissipation properties of CUD 3 operators 23
1.4 Difference equations 25
1.4.1 Analysis of conditioning 25
1.4.2 Solution procedures 28
1.5 CUD 3 with different time discretizations 29
1.5.1 Three level schemes 29
1.5.2 Explicit forms of third order compact schemes 32
1.6 Two level 0{t3 + ft3) scheme 33
vii
viii CONTENTS
1.6.1 Derivation of two level scheme 33
1.6.2 Estimates of stability, dissipation and dispersion 35
2 Some extensions of basic ideas 38
2.1 Generalizations of the CUD 3 operators 38
2.2 Applications to discontinuous solutions 41
2.2.1 Comparison of non conservative and conservative forms .... 41
2.2.2 Entropy consistent forms 43
2.2.3 CUD 3 schemes with flux correction 45
2.2.4 Steady state computations: comparisons with first and second
order schemes 48
2.3 Discretization of equations in non divergent forms 50
2.4 Another form of third order compact upwind differencing (CUD II 3) 52
2.4.1 Difference operators 52
2.4.2 Some properties of CUD II 3 54
2.4.3 Conservative forms 55
2.4.4 Some comments on CUD II 3 schemes 58
2.4.5 Flux splitted forms of third order CUD 59
2.5 Symmetrization of the CUD 3 operators 61
2.5.1 Fourth order compact approximations 61
2.5.2 CUD 3 with MacCormack type time stepping 62
2.6 Third order compact differencing as discretized Pade approximants . 64
3 Fifth order non centered compact schemes 66
3.1 Fifth order compact upwind differencing 66
3.1.1 Properties of CUD 5 operators 69
3.2 Other forms of compact upwind differencings (CUD II 5) 72
CONTENTS ix
3.2.1 Using Pade approximants 72
3.2.2 Families of compact differencing operators 77
3.2.3 Positivity, dispersion and dissipation 79
3.2.4 Conservation laws treatment 82
3.3 Fifth order compact schemes for scalar conservation laws 86
3.3.1 Explicit schemes. Numerical example: unsteady discontinu¬
ous solutions of the Burgers equation 86
3.3.2 Implicit schemes 89
3.4 Steady state algorithms 91
3.5 Compact upwind differencing of arbitrary n th order 95
3.5.1 Method of attack 95
3.5.2 Examples: 5 th and 7 th order compact upwind differencing
without degrees of freedom 98
4 Hyperbolic systems 101
4.1 CUD 3 schemes for vector conservation laws 101
4.1.1 Matrix difference operators obtained via diagonalization . . . 101
4.1.2 Analysis of non conservative and conservative forms 104
4.1.3 First order upwind schemes as the generators of generalized
CUD 3 for vector conservation laws 107
4.1.4 Difference equations 108
4.1.5 Non divergent systems of equations 110
4.2 Stability analysis 110
4.2.1 Matrix difference operators 110
4.2.2 Stability in energetic norms 114
4.3 Extensions to other forms of CUD 116
4.4 Flux splitted forms of CUD 118
x CONTENTS
4.5 Application to Riemann problem 120
5 Compact upwind schemes for convection diffusion equations 124
5.1 Discretization of diffusive terms 124
5.1.1 General considerations 124
5.1.2 Schemes with tridiagonal matrices 126
5.1.3 Schemes with block tridiagonal matrices 128
5.1.4 Factored schemes 130
5.2 Difference equations 131
5.2.1 Analysis of conditioning 131
5.2.2 Boundary conditions 136
5.2.3 Steady state solutions. Cell Reynolds number 138
5.3 Examples of computations for small diffusion coefficients 139
5.3.1 Third order scheme with adaptive grid 139
5.3.2 Comparison of third and fifth order compact schemes with
low order methods 145
5.4 Centered compact schemes for convection diffusion equations 148
5.4.1 Using Hermite formulas 148
5.4.2 Cubic spline approximations. OCI methods 149
5.4.3 General forms of n th order centered compact approximations 151
5.4.4 Cell Reynolds number limitations 152
5.5 Compact schemes for systems of equations with diffusive terms .... 154
5.5.1 Approximating operators. Three point schemes 154
5.5.2 Using conjugate operators 156
5.6 Schemes with simplified implicit operators 157
5.6.1 Structure of the schemes 157
5.6.2 Analysis for CUD 3 approximation 159
CONTENTS xi
5.6.3 Schemes with factored operators 162
5.6.4 Comments on general approach 163
6 Multidimensional problems 165
6.1 Implicit two level schemes 165
6.1.1 Multidimensional approximations 165
6.1.2 Stability estimates 169
6.1.3 Systems with diffusion terms 170
6.2 Approximate factorization 173
6.2.1 Structure of CUD 3 factored schemes . 173
6.2.2 Stability estimates 176
6.2.3 Compact factored schemes in convection diffusion problems . . 178
6.2.4 Advantages and drawbacks of factored schemes 180
6.3 An unconditionally stable method with factored operators 181
6.3.1 Description of method in a general form 181
6.3.2 Application to compact approximations 188
6.4 Unfactored CUD schemes 190
6.4.1 Time stepping schemes 190
6.4.2 Defect correction approach: general considerations 192
6.4.3 Defect correction approach: one dimensional analysis 195
6.4.4 Application of one dimensional analysis 201
7 Compressible gas flows described by Navier Stokes equations 205
7.1 General formulations 206
7.1.1 Forms of the governing equations 206
7.1.2 Comments on high order discretizations in the case of curvi¬
linear coordinates 209
xii CONTENTS
7.1.3 Stretching transformations 210
7.2 CUD 3 algorithms with adaptive grids 212
7.2.1 Outline of method 212
7.2.2 Sample calculations 214
7.3 Factored schemes for viscous gas flow computations 221
7.3.1 Factored schemes with CUD 3 221
7.3.2 Factored schemes with centered fourth order compact approx¬
imations 224
7.3.3 Sample computations: external separated flows 226
7.3.4 Sample computations: internal flows 231
7.4 Marching algorithms 239
7.4.1 Outlines of numerical method 241
7.4.2 Numerical examples 244
8 Applications to incompressible flow problems 247
8.1 Schemes based on vorticity formulation 248
8.1.1 Algorithms with CUD 3 248
8.1.2 Numerical examples 251
8.1.3 Algorithm with CUD 5 and its application to unsteady flow
about the cylinder 255
8.1.4 Fast method for reconstructing velocity for known vorticity in
3 D case 260
8.2 Compact upwind methods with pressure correction 268
8.2.1 Outlines of algorithms 268
8.2.2 Application of compact approximations 271
8.2.3 Stability estimates 274
8.3 CUD schemes for steady state solutions 276
CONTENTS xiii
8.3.1 Schemes based on artificial compressibility 276
8.3.2 Marching algorithms 278
8.4 Fifth order compact approximations in atmosphere modelling 280
8.4.1 Tests with model equations 281
8.4.2 Application to moisture transport in climate modelling .... 285
A Solution dependent coordinates for grid generation 289
B Some relevant mathematical topics 293
B.I Comments on approximation and stability 293
B.2 Spectral method for stability analysis 294
B.3 Method of operator inequalities 297
Bibliography 301
Index 312
|
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| indexdate | 2024-07-09T18:32:51Z |
| institution | BVB |
| isbn | 9810216688 |
| language | English |
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| physical | XIII, 314 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | World Scientific |
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| series2 | Series on advances in mathematics for applied sciences |
| spelling | Tolstykh, Andrei I. Verfasser aut High accuracy non-centered compact difference schemes for fluid dynamics applications Andrei I. Tolstykh Singapore [u.a.] World Scientific 1994 XIII, 314 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 21 Fluides, Dynamique des - Modèles mathématiques ram Mathematisches Modell Fluid dynamics Mathematical models Differenzenverfahren (DE-588)4134362-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Differenzenverfahren (DE-588)4134362-1 s DE-604 Series on advances in mathematics for applied sciences 21 (DE-604)BV004569239 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tolstykh, Andrei I. High accuracy non-centered compact difference schemes for fluid dynamics applications Series on advances in mathematics for applied sciences Fluides, Dynamique des - Modèles mathématiques ram Mathematisches Modell Fluid dynamics Mathematical models Differenzenverfahren (DE-588)4134362-1 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4134362-1 (DE-588)4077970-1 |
| title | High accuracy non-centered compact difference schemes for fluid dynamics applications |
| title_auth | High accuracy non-centered compact difference schemes for fluid dynamics applications |
| title_exact_search | High accuracy non-centered compact difference schemes for fluid dynamics applications |
| title_full | High accuracy non-centered compact difference schemes for fluid dynamics applications Andrei I. Tolstykh |
| title_fullStr | High accuracy non-centered compact difference schemes for fluid dynamics applications Andrei I. Tolstykh |
| title_full_unstemmed | High accuracy non-centered compact difference schemes for fluid dynamics applications Andrei I. Tolstykh |
| title_short | High accuracy non-centered compact difference schemes for fluid dynamics applications |
| title_sort | high accuracy non centered compact difference schemes for fluid dynamics applications |
| topic | Fluides, Dynamique des - Modèles mathématiques ram Mathematisches Modell Fluid dynamics Mathematical models Differenzenverfahren (DE-588)4134362-1 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Fluides, Dynamique des - Modèles mathématiques Mathematisches Modell Fluid dynamics Mathematical models Differenzenverfahren Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT tolstykhandreii highaccuracynoncenteredcompactdifferenceschemesforfluiddynamicsapplications |