مقاله انگلیسی تجزیه و تحلیل مجانبی جریان یک لایه مایع نازک بین دو سطح متحرک
ترجمه نشده

مقاله انگلیسی تجزیه و تحلیل مجانبی جریان یک لایه مایع نازک بین دو سطح متحرک

عنوان فارسی مقاله: تجزیه و تحلیل مجانبی جریان یک لایه مایع نازک بین دو سطح متحرک
عنوان انگلیسی مقاله: Asymptotic analysis of a thin fluid layer flow between two moving surfaces
مجله/کنفرانس: مجله تحلیل و برنامه های کاربردی ریاضی - Journal of Mathematical Analysis and Applications
رشته های تحصیلی مرتبط: ریاضی، مهندسی مکانیک
گرایش های تحصیلی مرتبط: آنالیز عددی، محاسبات نرم، مکانیک سیالات
کلمات کلیدی فارسی: مکانیک سیالات، روغن کاری، آب های کم عمق، تجزیه و تحلیل بدون علامت
کلمات کلیدی انگلیسی: Fluid mechanics - Lubrication - Shallow waters - Asymptotic analysis
نوع نگارش مقاله: مقاله پژوهشی (Research Article)
نمایه: Scopus - Master Journals List - JCR
شناسه دیجیتال (DOI): https://doi.org/10.1016/j.jmaa.2021.125735
دانشگاه: گروه ریاضیات، دانشکده معماری دانشگاه فنی عالی، اسپانیا
صفحات مقاله انگلیسی: 28
ناشر: الزویر - Elsevier
نوع ارائه مقاله: ژورنال
نوع مقاله: ISI
سال انتشار مقاله: 2022
ایمپکت فاکتور: 1.983 در سال 2020
شاخص H_index: 142 در سال 2021
شاخص SJR: 0.951 در سال 2020
شناسه ISSN: 0022-247X
شاخص Quartile (چارک): Q1 در سال 2020
فرمت مقاله انگلیسی: PDF
وضعیت ترجمه: ترجمه نشده است
قیمت مقاله انگلیسی: رایگان
آیا این مقاله بیس است: خیر
آیا این مقاله مدل مفهومی دارد: ندارد
آیا این مقاله پرسشنامه دارد: ندارد
آیا این مقاله متغیر دارد: ندارد
آیا این مقاله فرضیه دارد: ندارد
کد محصول: E15689
رفرنس: دارای رفرنس در داخل متن و انتهای مقاله
فهرست مطالب (انگلیسی)

Abstract

Keywords

1. Introduction

2. Derivation of the model

2.1. Original domain

2.2. Construction of the reference domain

2.3. Navier-Stokes equations

2.4. Asymptotic analysis

3. A new generalized lubrication model

4. A new thin fluid layer model

5. Conclusions

Appendix A. Change of variable

Appendix B. Coefficients definition

Appendix C. Derivation of equations to calculate 

References

بخشی از مقاله (انگلیسی)

Abstract

In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water model, depending on the boundary conditions imposed. Finally, we discuss under what conditions each of the models would be applicable.

 

1. Introduction

The asymptotic analysis method is a mathematical tool that has been widely used to obtain and justify reduced models, both in solid and fluid mechanics, when one or two of the dimensions of the domain in which the model is formulated are much smaller than the others.

After the pioneering works of Friedrichs, Dressler and Goldenveizer (see [28] and [30]) the asymptotic development technique has been used successfully to justify beam, plate and shell theories (see, for example, [43], [16], [17], [15], [5], [54], and many others).

This same technique has also been used in fluid mechanics to justify various types of models, such as lubrication models, shallow water models, tube flow models, etc. (see, for example, [25], [24], [18], [3], [37], [55], [36], [31], [6], [2], [29], [26], [32], [33], [9], [23], [45], [46], [47], [48], [49], [50], [21], [22], [34], [35], [40], [41], [42], [10], [11], and many others).

In this work, we are interested in justifying, again using the asymptotic development technique, a lubrication model in a thin domain with curved mean surface. Following the steps of [3], but with a different starting point, we devote sections 2 and 3 to this justification. During the above process we have observed that, depending on the boundary conditions, other models can be obtained, which we show in section 4. In this section we derive a shallow water model changing the boundary conditions that we had imposed in section 3: instead of assuming that we know the velocities on the upper and lower boundaries of the domain, we assume that we know the tractions on these upper and lower boundaries.

Thus, two new models are presented in sections 3 and 4 of this article. These models can not be found in the literature, as far as we know. In addition, the method used to justify them allows us to answer the question of when each of them is applicable. In section 5 we discuss the models yielded, as well as the difference between one model and another depending on the boundary conditions, reaching the conclusion that the magnitude of the pressure differences at the lateral boundary of the domain is key when deciding which of the two models best describes the fluid behavior.