پایان نامه بررسی مدل های شبکه ای به عنوان روشی عددی برای حل معادلات آب های زیرزمینی

فهرست:

1. کلیات   1

1-1 مقدمه  1

1-2 هدف از انجام این تحقیق  2

1-3 روش انجام تحقیق  4

1-4 نوآوری تحقیق  5

1-5 ساختار پایان نامه  5

2. پیشینه‌ی تحقیق  7

2-1 مقدمه  7

2-2 انواع مدلها 9

2-2-1 مدلهای ریاضی (mathematical models) 9

2-2-1-1 طبقه ‌بندی مدلهای ریاضی  10

2-2-1-2 معادله‌ی حاکم بر آبهای زیر زمینی  10

2-2-2 مدلهای فیزیکی (physical models) 13

2-2-3 مدلهای تمثالی(analog models) 15

2-2-3-1 مدلهای شبکه‌ای Pore Network Models (PNMs) 16

2-2-3-2 مدلهای سیال لزج (viscous fluid models) 25

2-2-3-3 مدلهای غشایی (membrane models) 26

2-2-3-4 مدلهای حرارتی (thermal models) 26

2-2-3-5 مدلهای الکتریکی (electrical models) 27

َ2-3 روشهای عددی  28

2-3-1 روش تفاضل محدود (finite difference method) 29

2-3-2 روش حجم محدود (finite volume method) 32

2-3-3 روش عناصر محدود (finite element method) 34

2-3-4. روش عناصر مرزی (boundary element method) 36

2-3-5 روش عددی دیفرانسیل کوادراچر (differential quadrature method) 39

2-3-6 روشهای طیفی (spectral methods) 40

3. معرفی روش شبکه‌ای به عنوان روشی عددی برای حل معادله‌ی آبهای زیرزمینی  41

3- 1  مقدمه  41

3-2 مبانی تئوریکی روشهای شبکه‌ای  42

3-2-1 معادله‌ی حاکم بر روش شبکه‌ای  42

3-2-2 معادله‌ی جبری حاکم بر روش شبکه‌ای در حالت ماندگار 45

3-2-3 تأثیر ناهمگنی و ناهمسانی بر معادلات جبری حاکم  50

3-2-4 تزریق و برداشت   51

3-2-5 معادله‌ی جبری حاکم بر روش شبکه‌ای در حالت ناماندگار 51

3-2-6 آبخوان محصور و آزاد 52

3-2-7 اصلاح روش شبکه‌ای  53

3-2-7-1 بهبود با استفاده از افزایش اتصال گره‌ها 53

3-2-7-2 بهبود با استفاده از نحوه‌ی مدل کردن گره‌های مرزی  57

3-2-8 معادله‌ی حاکم در حالت کلی  59

3-2-9 تأثیر شکل هندسی مجاری بر روش شبکه‌ای  61

3-2-9-1شکل مجاری  61

3-2-9-2 معادله‌ی حاکم  62

3- 3 مدل آزمایشگاهی  70

3-3-1 مقدمه  70

3-3-2 نحوه‌ی ساخت مدل آزمایشگاهی  70

3-3-3 روش انجام آزمایش    71

3-3-3-1محیط همگن و همسان با هد ثابت   72

3-3-3-2 آزمایش آبخوان آزاد 72

3-3-3-3 آزمایش لایه‌ی غیر قابل نفوذ 72

3-3-3-4 آزمایش ناهمگن و ناهمسان بودن محیط متخلخل  73

3-3-3-5 آزمایش جریان ناماندگار 74

4. مثالهای عددی و آزمایشگاهی و بحث در نتایج به دست آمده 75

4-1 مقدمه  75

4-2 مثالهای عددی  76

4-1-1 مثال 1) مسأله‌ی حالت ماندگار در محدوده‌ی مربعی و شرایط                 مرزی شکل 4-1  76

4-1-2 مثال 2) مسأله‌ی حالت ماندگار در محدوده‌ی مربعی و شرایط مرزی          شکل 4-5  87

4-1-3 مثال 3) مسأله‌ی حالت ماندگار در محدوده‌ی مستطیلی و شرایط             مرزی شکل 4-8  91

4-1-4 مثال 4) مسأله‌ی حالت ماندگار در محدوده‌ی مثلثی و شرایط مرزی      شکل4-11  94

4-1-5 مثال 5) مسأله‌ی حالت ماندگار با وجود چاه در محدوده‌ی مستطیلی              و شرایط مرزی شکل 4-14  97

4-1-6 مثال 6) مسأله‌ی حالت ماندگار در دامنه‌ای L شکل و شرایط                  مرزی شکل 4-17  99

4-1-7 مثال 7) مسأله‌ی حالت ناماندگار یک بعدی  101

4-1-8 مثال 8) مسأله‌ی حالت ناماندگار دو بعدی  104

4-1-9 مثال 9) مسأله‌ی حالت ماندگار با شرایط مرزی منحنی  107

4-1-10 مثال 10) مسأله‌ی حالت ماندگار در محدوده‌ی مستطیلی و                 شرایط مرزی شکل 4-25  110

4-1-11 مثال 11) مسأله‌ی حالت ماندگار در محدوده‌ی مثلثی و شرایط             مرزی شکل 4-27  113

4-3 مثالهای آزمایشگاهی  116

4-3-1 آزمایش 1) جریان در اطراف یک مانع مستطیلی  117

4-3-2. آزمایش 2) جریان با شرایط مرزی مرکب   120

4-3-3 آزمایش 3) جریان از زیر پرده‌ی آب بند  122

4-3-4 آزمایش 4) جریان در آبخوان آزاد 124

4-3-5 آزمایش 5) جریان در آبخوانی ناهمگن و ناهمسان  127

5. نتیجه‌گیری و پیشنهادات   132

پیوستها 134

پیوست 1. حل تحلیلی مثال 1  134

پیوست 2. حل تحلیلی مثال 2  136

پیوست 3. حل تحلیلی مثال 3  137

پیوست 4. حل تحلیلی مثال 4  138

پیوست 5. حل تحلیلی مثال 5  140

پیوست 6. حل تحلیلی مثال 7  142

پیوست 7. حل تحلیلی مثال 8  144

پیوست 8. حل تحلیلی مثال 9  146

پیوست 9. حل تحلیلی آزمایش 4  146

فهرست منابع  148

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