| Author | Das, Himangshu Shekhar |
| Call Number | AIT Thesis no. WM-95-14 |
| Subject(s) | Hydraulic engineering--Mathematical models
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| Note | A thesis submitted in partial fulfillment of the requirement for the degree of Master of Engineering, School of Civil Engineering |
| Publisher | Asian Institute of Technology |
| Series Statement | Thesis ; no. WM-95-14 |
| Abstract | A stable numerical scheme is one for which errors from any source (round-off, truncation, mistakes) are not permitted to grow in the sequence of numerical procedures as the calculation proceeds from one. marching step to the next. In solving hydrodynamic partial differential equations over marehing steps, the problem of instability is a greatly concerned phenomenon as it disrupts the solution progress. The study of stability limits for generalized hydrodynamic models is necessary as an earlier detection of this limit can save our computer time and effort. In this work, efforts are given to develop a workable method to establish the stability limits for two dimensional hydrodynamic models with linear and constant coefficients. Principally, there are three methods which can be applied for stability analysis, namely, (i) Discrete Perturbation Stability Analysis, (ii) Hirt' s Stability Analysis, and (iii) Von Neumann Stability Analysis. In summary, all these methods provide information of value. In our present work, Von Neumann stability analysis is used as the method is the simplest, the most straight forward and most dependable. Starting with the most simplified cases of governing equations, stability is checked and gradually more and more terms are being added in the simplified governing equations to establish the additional stability criteria due to the additional terms in the partial differential equations for two dimensional flows. At present, eight different cases (Four for one dimensional cases and another four for two dimensional cases) are being worked with and it is found from this study that for simplified model equations, stability criteria can be achieved solely by analytical method ; but for complicated partial differential equations a hybrid method which is partly analytical and partly numerical, should be used to detect stability limits. It is found from this study of two dimensional flow that the dimensionless parameters namely Courant Number, Advective, Bottom friction and Coriolis force control stability criteria. |
| Year | 1995 |
| Corresponding Series Added Entry | Asian Institute of Technology. Thesis ; no. WM-95-14 |
| Type | Thesis |
| School | School of Civil Engineering |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Water Engineering and Management (WM) |
| Chairperson(s) | Suphat Vongvisessomjai; |
| Examination Committee(s) | Sutat Weesakul;Harumichi, Kyotoh; |
| Scholarship Donor(s) | Asian Institute of Technology Partial Scholarship; |
| Degree | Thesis (M. Eng.) - Asian Institute of Technology, 1995 |