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Numerical Solution of Incompressible Viscous Flow Problems Using High-Order Schemes

Thesis Info

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Author

Rizwan, Muhammad

Supervisor

Abdullah Shah

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2016

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9844/1/Muhammad_Rizwan_Maths_2016_CIIT_Main%20pt%20with%20ref..pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726780031

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Numerical Solution of Incompressible Viscous Flow Problems Using High-order Schemes Numerical solution of the Navier-Stokes equations that describe incompressible viscous fluids has been a very active research field due to the rapid development of computational techniques and availability of high speed computers. It has motivated a very large number of researchers whose work provide an invaluable source of solution methods and test problems. Numerous computational methods have been developed and are in used today for steady and time-accurate computation of these equations. The motivation of this thesis is also a desire to develop an efficient, accurate and simple method for the numerical solution of incompressible viscous flow problems in primitive variables. For this purpose, a numerical method based on high-order compact finite difference schemes is developed in conjunction with the well-known artificial compressibility approach for solving incompressible Navier-Stokes equations. By adding pseudo time derivative terms to each equation, the coupled system becomes hyperbolic in time and the artificial compressibility method becomes applicable. We have also focused on the extension of the method for simulating two-phase flow by coupling phase-field model to the incompressible Navier-Stokes solver. This research work is divided into three steps in which each step focuses on an aspect of the development of a numerical method. In the first step, a third-order upwind compact finite difference scheme based on the fluxdifference splitting is developed and implemented with the implicit Beam-Warming approximate factorization scheme for solving the incompressible Navier-Stokes equations. The upwind compact scheme for the convective terms is preferred because of its high resolving efficiency with less numerical dissipation and truncation errors. The numerical scheme is applied to compute the flow inside the two sided lid driven cavity flow and compared with the finite difference alternating direction implicit scheme. In the second step, we implemented higher-order central compact finite difference scheme along with filtering procedure for steady and unsteady incompressible Navier- Stokes equations. The central compact scheme is also implemented under the framework of the artificial compressibility method in which convective terms of the governing x equations are approximated by using the high-order central compact schemes with filtering procedure and the viscous terms are discretized with a sixth-order central compact finite difference scheme. Dual-time stepping technique is employed for unsteady solutions at each physical time step. Computational efficiency and accuracy of the method is compared with upwind compact schemes by computing several benchmark flow problems. In the third step, the central compact scheme is applied successfully to incompressible two-phase flows both in two and three space dimensions. For this purpose, the modified Allen-Cahn type phase-field model is coupled with the incompressible Navier-Stokes equations. In the phase-field formulation, the classical infinitely thin boundary of separation between two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one or two fluids changes continuously. The effectiveness of the method is demonstrated by computing several benchmark twophase incompressible flow problems. Finally, advantages and difficulties in solving incompressible viscous flow problems are discussed and future directions of the effort are proposed.
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انور نعمانی

انور نعمانی مرحوم
علامہ شبلیؒ نعمانی نے اپنے بھائی مولوی محمد اسحاق مرحوم وکیل الہ آباد ہائی کورٹ کی موت پر اپنے ایک پر درد نوحہ میں یہ فرمایا تھا۔
مرنے والے کو نجات ابدی کی ہو نوید
خوش و خرم رہے چھوٹایہ مرا بھائی جنید
ان ہی جناب جنید نعمانی کے مرحوم کے اکلوتے بیٹے انور نعمانی مرحوم تھے، جنھوں نے لگ بھگ اسّی۸۰ سال کی عمر میں کراچی میں مئی ۱۹۸۶؁ء کے آخری ہفتہ میں وفات پائی، مرحوم اپنے والد بزرگوار کے سایۂ عا طفت میں بڑے لاڈ پیار اور ناز ونعمت سے پلے، تعلیم مسلم یو نیو رسٹی علی گڑھ میں پائی، گھر میں دولت تھی، اس لئے ان کو نوکری کرنے کی ضرورت نہیں پڑی، کچھ دنوں مرزا پور میں فارم کیا، چھوٹی موٹی تجارت بھی کی، پھر حضرت مولانا اشرف علی تھانویؒ کے خلیفہ مولانا عبدالغنی پھولپوری کے ایسے گرویدہ اور فریضتہ ہوئے کہ وہ نقل وطن کرکے کراچی چلے گئے تو یہ بھی اپنا گھربار سب کچھ چھوڑ کر ان ہی کے ساتھ وہاں رہنے لگے، جب تک اعظم گڑھ میں رہے دارالمصنفین والوں کے یار وفادار اور غم گسار بن کر ان کے لئے اپنی محبت کا دم بھرنا زندگی کا شعار بنائے رکھا۔ کراچی میں ان کے اکلوتے لڑکے سرکاری نوکر ہیں، اچھے حال میں ہیں ،پھر ان کے اور قریبی اعزہ بھی وہاں بہت خوش حال ہیں، مگر انھوں نے کسی کے یہاں رہنا پسند نہیں کیا، اپنے مرشد کی ایک پسند یدہ مسجد سے ملحق ایک کٹیا ان ہی کے نام پر ایک عبادت گاہ کے گوشے میں رہ کر اپنی بقیہ زندگی گذاردی، کراچی جب جب گیا، ان سے جاکر ضرور ملا، اور ان کی پرانی زندگی کی یادوں کی قندیل روشن کی، کسی زمانے میں صاحب کی طرح زندگی بسر کرنے والے کو ان...

Attitude Towards Science: A Case Study of Higher Secondary Level Students of Sindh Province

This research is conducted, in order to perceive the attitude of higher secondary level students of Sindh towards science. Students (Male = 448, Female = 648) belonging to higher-secondary level (Class-XI & XII) from Hyderabad division were surveyed. Students were divided in Urban (N=455) and Rural (N=641) groups accordingly. “Test of Science Related Attitudes” known as TOSRA, initially developed by (Fraser, 1978) was adapted and translated in Urdu as well, was used as the attitude measurement instrument. Internalk consistancey was checked with Cronbach’s alpha reliability test. After pilot study the test was administrated. Significant difference of the attitude towards science across the students was noticed based on their gender and their locale. The results show that, with small effect size, male students significantly scored higher on almost all of the attitude sub-scales of TOSRA as compared to female students. Interestingly, students belonging to rural areas significantly scored higher with medium effect size on all the attitude sub-scale towards science as compare to students from urban areas.

Pharmacovigilance and Patients’ Awareness Studies Towards Antihypertensive Therapy in Hospitals of Hyderabad, Sindh, Pakistan

Pharmacovigilance is well defined by an internationally accepted health organization i.e. WHO, it is a study about finding, evaluation, understanding and avoidance of adverse effects or any other possible drug-related problems. The study of Adverse drug reactions (ADRs) have a major role in regulatory processes of each medicine and ultimately impact on patients lives. Moreover it is an integral part between the patient and health care for better management of disease. Hypertension is one among the several chronic illnesses which is now the principal foundation of cardiovascular diseases worldwide. However, if remains uncontrolled, it can lead to various life threatening complications. The objectives of the study are to evaluate the prescribing trend of antihypertensive therapy among all three hospitals of Hyderabad, to assess the occurrence of ADRs due to antihypertensive drugs in Hyderabad city, to identify the most common adverse drug reactions of different classes of antihypertensive drugs, to assess the knowledge/awareness of patients regarding hypertension and appropriate use of antihypertensive drugs, to compare the ADRs between the hospitals of Hyderabad, to compare the Patient awareness between the hospitals of Hyderabad and to assess the perception of health care professionals regarding Pharmacovigilance. A descriptive cross-sectional study was conducted to evaluate the ADRs associated with antihypertensive therapy and patient’s awareness by collecting the patient’s feedback and health care professionals feedback via purposive and random sampling respectively from medicine and cardiac outpatient departments (OPD) of three major hospitals of Hyderabad, Sindh on predesigned questionnaire based on WHO monitoring guidelines for a period of three years and then data has been evaluated. Out of 3000 patients, maximum numbers of patients were enrolled from GTCH and the percentage was 42.37%. Majority of the patients were belonged to male gender with 57.33%. Further it was also observed that most of the patients were from urban areas with 79.77%. There were two out-patient departments (OPD) from where the patients enrolled i.e. medical as well as cardiac, 64.07% of the patients were reported from cardiac OPD and 35.93% from medical OPD. 30.63% of the patients were aged between 49 to 58 years i.e. maximum. About family history, 20.97% of the patients had positive history as 1 parent, 10.07% of the patients had two parents history while 55.23% of the patients had no any history of hypertension. The maximum number of patients was on combinations therapy i.e. 64.6% as compared to monotherapy patients i.e. 35.4%. Among combinations therapy the dual therapy was most commonly prescribed and the percentage was 65.02% as compared to triple (21.41%) and quadruple therapy (13.57%). In Government tertiary care hospital the most common prescribed antihypertensive drug as monotherapy was Atenolol and the percentage was 16.33%. In Private tertiary care hospital the most common prescribed antihypertensive drug as monotherapy was Telmisartan and the percentage was 15.84%. In Government secondary care hospital the most common prescribed antihypertensive drug as monotherapy was Atenolol and the percentage was 12.24%. In Government tertiary care hospital the most common prescribed antihypertensive drug as dual therapy was Telmisartan + hydrochlorothiazide and the percentage was 14.76%. In Private tertiary care hospital the most common prescribed antihypertensive drug as dual therapy was Valsartan+Amlodipine and the percentage was 13.21%. In Government secondary care hospital the most common prescribed antihypertensive drug as dual therapy was Lisinopril+hydrochlorothiazide and the percentage was 10.66%. In Government tertiary care hospital the most common prescribed antihypertensive drug as triple therapy was Atenolol + Chlorthalidone + Telmisartan and the percentage was 15.30%. In Private tertiary care hospital the most common prescribed antihypertensive drug as triple therapy was Enalapril + hydrochlorothiazide+Atenolol and the percentage was 21.48%. In Government secondary care hospital the most common prescribed antihypertensive drug as triple therapy was Valsartan+ hydrochlorothiazide+Amlodipine and the percentage was 18.56%. In Government tertiary care hospital the most common prescribed antihypertensive drug as quadruple therapy was Atenolol + Chlorthalidone + Telmisartan+αMD and the percentage was 26.44%.In Private tertiary care hospital the most common prescribed antihypertensive drug as quadruple therapy was Valsartan + Amlodipine+Atenolol+Chlorthalidone and the percentage was 35.29%. In Government secondary care hospital the most common prescribed antihypertensive drug as quadruple therapy was Amlodipine+Telmisartan+ Enalapril + hydrochlorothiazide and the percentage was 25.93%.