پایان نامه بکارگیری روش های عددی بدون شبکه در مدلسازی امواج غیرخطی سطح آب ناشی از باد

فهرست پایان نامه بکارگیری روش های عددی بدون شبکه در مدلسازی امواج غیرخطی سطح آب ناشی از باد

فهرست:

فصل اول: مقدمه

1-1- کلیات.. 2

1-2- معرفی تحقیق حاضر. 2

 

فصل دوم: مروری بر پژوهش های پیشین

2-1- مقدمه. 10

2-2- پیشینه ی تحقیقات انجام شده بر روی موج.. 11

2-2-1- مدل های اوّلیه ی امواج غیرخطی.. 11

2-2-2- مدل های جدید امواج غیرخطی.. 13

2-2-3- روش های عددی بدون شبکه در مدلسازی امواج غیرخطی.. 15

2-3- پیشینه ی تحقیقات انجام شده بر روی روش عددی مورد استفاده. 16

2-3-1- روش عددی دیفرانسل کوادرچر (DQ) 16

2-3-2- توابع پایه ی شعاعی (RBF) 20

2-3-2-1- انواع توابع پایه ی شعاعی.. 20

2-3-2-2- کاربرد توابع پایه ی شعاعی در درونیابی.. 21

2-3-2-3- کاربرد توابع پایه ی شعاعی در حل معادلات دیفرانسیل.. 22

2-3-2-4- روش عددی RBF-DQ.. 23

2-3-2-5- تابع شعاعی MQ.. 24

 

عنوان                                                                                                                      صفحه

 

2-3-3- عوامل موثر بر دقت و خطای مدل.. 25

2-3-3-1- چگالی گره ها 26

2-3-3-2- پارامتر شکل.. 26

2-3-3-2-1- تاثیر پارامتر شکل بر خطا 26

2-3-3-2-2- پارامتر شکل بهینه. 29

2-3-3-3- پدیده ی رانچ.. 32

2-3-3-4- دقت محاسبات، خطای گرد کردن و عدد وضعیت... 33

2-4- جمع بندی و نتیجه گیری.. 33

 

فصل سوم: تئوری تحقیق

3-1- مقدمه. 36

3-2- تئوری های موج.. 36

3-2-1- تئوری موج خطی.. 36

3-2-2- تئوری موج غیرخطی.. 39

3-2-2-1- دسته بندی تئوریهای اولیهی امواج غیرخطی.. 39

3-2-2-1-1- تئوری استوکس.... 39

3-2-2-1-2- تئوری Cnoidal 41

3-2-2-1-3- تئوری Boussinesq. 42

3-2-2- شبیه سازی عددی انتشار موج غیرخطی.. 42

3-2-2-1- هندسه ی مسئله و تعریف مخزن عددی.. 42

3-2-2-2- معادله ی حاکمه و شرایط مرزی.. 44

3-2-2-2-1- تئوری موج ساز. 44

3-2-2-2-2- تابع صعودی.. 46

3-2-2-3- روش مرکب اویلری و لاگرانژی (MEL) 48

عنوان                                                                                                                      صفحه

 

3-2-2-4- ناحیه ی استهلاک یا ساحل مصنوعی.. 49

3-2-2-5- بکارگیری روش RBF-DQ برای تخمین مشتقات مکانی.. 50

3-2-2-5-1- انتخاب تابع پایه. 50

3-2-2-5-2- تخمین مشتق های مکانی با روش RBF-DQ.. 51

3-2-2-5-3- روش RBF-DQ محلی.. 52

3-2-2-5-4- چگونگی اعمال شرایط مرزی.. 53

3-2-2-5-6- انتخاب پارامتر شکل مناسب... 53

3-2-2-6- انتگرال گیری بر روی زمان.. 54

3-2-2-7- تابع یکنواختکننده. 56

 

فصل چهارم: نتایج و بحث روی آزمایش های عددی

4-1- مقدمه. 58

4-2- مثال های عددی.. 59

4-2-1- مثال عددی اول: معادله ی برگرز. 59

4-2-1-1- بررسی عوامل موثر بر افزایش دقت روش... 60

4-2-1-1-1- بررسی تاثیر فاصله ی گرهها بر مدل.. 61

4-2-1-1-2- بررسی تاثیر پارامتر شکل بر مدل.. 61

4-2-1-1-3- بررسی تاثیر پارامتر شکل و فاصله ی گره ها بصورت همزمان.. 64

4-2-1-1-4- دقت محاسبات.. 65

4-2-1-1-5- پدیدهی رانچ.. 66

4-2-1-2- مقایسه ی روش های RBF-DQ و DQ.. 67

4-2-1-3- حل مسئله با استفاده از مقدار پارامتر شکل بهینه. 68

4-2-2- مثال عددی دوم: معادله ی هلمهلتز. 69

4-2-2-1- بررسی عوامل موثر بر افزایش دقت روش... 70

عنوان                                                                                                                      صفحه

 

4-2-2-1-1- بررسی تاثیر پارامتر شکل و تعداد گره ها بصورت همزمان.. 70

4-2-2-1-2- پدیدهی رانچ.. 71

4-2-2-2- حل مسئله با استفاده از مقدار پارامتر شکل بهینه. 72

4-3- شبیه سازی انتشار موج در مخزن عددی.. 73

4-3-1- انتشار موج خطی.. 73

4-3-1-1- بررسی تاثیر همزمان تعداد گره ها و پارامتر شکل.. 75

4-3-1-1-1- تاثیر پارامتر شکل و تعداد گره ها در راستای افقی.. 78

4-3-1-1-2- تاثیر پارامتر شکل و تعداد گرهها در راستای عمق.. 80

4-3-1-1-3- بررسی تاثیر همزمان تعداد گره ها در دامنه ی تاثیر
 و پارامتر شکل.. 83

4-3-1-2- حل مسئله با استفاده از پارامتر شکل مناسب و مقایسه ی
نتایج با نتایج روش تحلیلی.. 85

4-3-1-3- تاثیر طول ناحیهی استهلاک... 88

4-3-1-4- مقایسه ی نتایج با نتایج  روش عددی RBF. 88

4-3-2- شبیه سازی انتشار موج غیرخطی در مخزن عددی.. 89

4-3-2-1- بررسی تاثیر همزمان تعداد گرهها و پارامتر شکل.. 91

4-3-2-1-1- تاثیر پارامتر شکل و تعداد گرهها در راستای افقی.. 91

4-3-2-1-2- تاثیر پارامتر شکل و تعداد گره ها در راستای عمق.. 94

4-3-2-1-3- بررسی تاثیر همزمان تعداد گره ها در دامنه ی
تاثیر و پارامتر شکل.. 96

4-3-2-2- حل مسئله با استفاده از پارامتر شکل مناسب و مقایسه ی
نتایج با نتایج روش تحلیلی.. 99

4-3-2-3- مقایسه ی نتایج با نتایج روش عددی RBF. 102

4-4- انتشار موج ایجاد شده توسط موج ساز در مخزن آزمایشگاهی.. 102

عنوان                                                                                                                      صفحه

 

4-4-1- بررسی عوامل موثر بر غیرخطی شدن موج.. 105

 

فصل پنجم: نتیجه گیری و پیشنهادات

5-1- مقدمه. 109

5-2- جمع بندی و نتیجه گیری.. 109

5-3- پیشنهادات.. 110

 

مراجع.. 111

 

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