Numerical methods in smog prediction:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
1997
|
| Series: | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract
120 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 149 S. graph. Darst. |
| ISBN: | 9061964733 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical methods in smog prediction |c M. van Loon |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Contents i
1 Introduction 1
1.1 Smog 1
1.2 Predicting smog 1
1.3 The project EUSMOG 2
1.4 This work 3
1.5 Mathematical framework 4
1.6 Outline of the book 5
2 Model Description 7
2.1 The model domain 7
2.1.1 Vertical stratification 7
2.2 The physical model 10
2.2.1 The modeled species 10
2.2.2 The model equation 10
2.2.3 Advection 11
2.2.4 Horizontal diffusion 12
2.2.5 Vertical diffusion and dry deposition 12
2.2.6 Wet deposition 12
2.2.7 Fumigation 13
2.2.8 Emission 14
2.3 The chemical model 18
2.4 Meteorological parameters 21
2.4.1 Input parameters 21
2.4.2 Stability and deposition parameters 22
3 Local Uniform Grid Refinement 25
3.1 Introduction 25
3.2 Choice of method 26
3.3 Local Uniform Grid Refinement 27
3.3.1 Algorithmic Outline 27
3.3.2 How to refine? 28
3.3.3 Where to refine? 28
3.3.4 Interpolation of initial values 30
ii Contents
3.3.5 Injection of solution values 31
3.3.6 Boundary conditions 33
3.3.7 Mass conservation 33
3.3.8 Time stepping 34
3.3.9 The datastructure 34
3.4 Application to the four layer model 35
3.4.1 The grid 35
3.4.2 When to refine? 35
3.4.3 The refinement criterion 36
3.4.4 Computational efficiency 36
3.5 Numerical illustration 37
4 Finite Volume Numerical Advection Schemes 39
4.1 Preliminaries 39
4.1.1 The advection equation 40
4.1.2 Derivation of semi discrete equations 41
4.2 The donor cell algorithm 43
4.3 The K discretizations 46
4.3.1 ID formulation 46
4.3.2 2D formulation 48
4.3.3 Time integration aspects 49
4.3.4 Discussion of the K limiter 55
4.4 Flux Corrected Transport 56
4.4.1 FCT in ID 56
4.4.2 FCT in 2D 58
4.4.3 Application to MoL schemes 58
4.4.4 Application in spherical coordinates 59
4.4.5 Discussion of FCT 59
4.5 Making wind fields divergence free 59
4.5.1 Preliminaries 59
4.5.2 Necessity of the procedure 60
4.5.3 The procedure of Endlich 61
4.5.4 Connection with advection schemes 62
4.6 Numerical experiments 62
4.6.1 Results for Problem I 65
4.6.2 Results for Problem II 68
4.6.3 Conclusions 68
5 Chemical Solution Methods 69
5.1 Introduction 69
5.1.1 Mass conservation, positivity and stability 70
5.2 TWOSTEP 71
5.2.1 Conservation of mass 72
5.2.2 The time stepping mechanism 74
Contents iii
5.2.3 The first steps 74
5.2.4 Variants 75
5.3 QSSA methods 76
5.3.1 First order QSSA methods 77
5.3.2 Second order QSSA methods 78
5.4 Other solvers 81
5.5 Improving the iteration process 82
5.5.1 Lumping 82
5.5.2 The EBI method 83
5.6 Linear analysis for TWOSTEP 84
5.6.1 Convergence of the iteration process 86
5.6.2 Effect of not continuing the iteration process 86
5.6.3 Evaluation of the example problem 87
5.7 Linear analysis for QSSA 91
5.7.1 Stability for QSSA schemes 92
5.7.2 Example problem: Classical QSSA 93
5.7.3 Example problem: The midpoint QSSA scheme 94
5.7.4 Example problem: Extrapolated QSSA 95
6 A Comparison for chemical solution methods 96
6.1 Introduction 96
6.2 Test methodology 97
6.2.1 The box model 97
6.2.2 Set up of experiments 98
6.3 Application of the solvers 99
6.3.1 TWOSTEP and 3STEP 99
6.3.2 QSSA 100
6.3.3 VODE 100
6.4 Results for the box model test: variable step sizes 101
6.4.1 Results for the special purpose solvers 102
6.4.2 Results for VODE 106
6.5 Results for the box model test: fixed step sizes 107
6.6 Further testing: general results 109
6.6.1 The methane CIRK chemistry 109
6.6.2 The EMEP chemistry Ill
6.6.3 Benchmarking Stiff ODE solvers 112
6.7 Concluding remarks 112
7 Model comparisons 115
7.1 The November/December 1989 episode 116
7.1.1 Comparison between EUROS and CWIROS 116
7.1.2 Grid refinement 117
7.1.3 Comparison with Dutch measurements 119
7.2 The July 1989 episode 123
iv Contents
7.2.1 Grid refinement 124
7.2.2 Comparison with Dutch measurements 124
7.2.3 Timings 126
7.3 Summary and conclusions 126
8 Summary and conclusions 128
Bibliography 131
A Shifted pole coordinates 137
A.I Transforming 9 and f 137
A.2 Transforming u and v 138
B Time factors for emissions 140
C Datastructure for grid refinement 142
C.I Approach 142
C.2 Integer array(s) 142
D Mass conservation for implicit BDF methods 145
E Coefficients for 3STEP 147
Index 148
|
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| id | DE-604.BV011543412 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:33Z |
| institution | BVB |
| isbn | 9061964733 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007770983 |
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| physical | IV, 149 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
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| series | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| spelling | Loon, M. van Verfasser aut Numerical methods in smog prediction M. van Loon Amsterdam 1997 IV, 149 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 120 Analyse numérique ram Numerieke methoden gtt Prognoses gtt Smog gtt Mathematisches Modell Numerical grid generation (Numerical analysis) Smog Europe Mathematical models Europa Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 120 (DE-604)BV001902011 120 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Loon, M. van Numerical methods in smog prediction Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract Analyse numérique ram Numerieke methoden gtt Prognoses gtt Smog gtt Mathematisches Modell Numerical grid generation (Numerical analysis) Smog Europe Mathematical models |
| title | Numerical methods in smog prediction |
| title_auth | Numerical methods in smog prediction |
| title_exact_search | Numerical methods in smog prediction |
| title_full | Numerical methods in smog prediction M. van Loon |
| title_fullStr | Numerical methods in smog prediction M. van Loon |
| title_full_unstemmed | Numerical methods in smog prediction M. van Loon |
| title_short | Numerical methods in smog prediction |
| title_sort | numerical methods in smog prediction |
| topic | Analyse numérique ram Numerieke methoden gtt Prognoses gtt Smog gtt Mathematisches Modell Numerical grid generation (Numerical analysis) Smog Europe Mathematical models |
| topic_facet | Analyse numérique Numerieke methoden Prognoses Smog Mathematisches Modell Numerical grid generation (Numerical analysis) Smog Europe Mathematical models Europa |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT loonmvan numericalmethodsinsmogprediction |