Date of Award
8-1-1993
Document Type
Thesis
Degree Name
M.S. in Engineering Science
Department
Mechanical Engineering
First Advisor
Dr. Tyrus A. McCarty
School
University of Mississippi
Relational Format
Dissertation/Thesis
Abstract
Despite every effort being made to produce a completely problem-free computational model, no breakthrough has yet been made. When a numerical model is used to solve a real world problem, there is a tendency for the non-physical spurious waves to creep in. If these waves are not checked, they can lead to serious instability problems. Once these waves are removed, the model should be able to simulate physical phenomenon like circulation, separation, flow reversal in the vertical plane, mixing/transport, convection/diffusion, etc.
When a numerical mode] is made to run for a certain period of time, node-to-node oscillations may arise and have an adverse effect on the stability of the numerical model. It has been found that these osci1lations are inherent in the numerical technique applied contrary to the previous belief that it was due to round-off errors although they do represent an added complexity to the problem. The primary approach was to use a high eddy viscosity to obtain a stable solution but the literature reveals that this approach introduced too much artificial damping.
The River model uses the Finite Vicinity Method which is a combination of Finite Element Method and Finite Difference Method. It uses the fourth order Runge Kutta scheme for time-marching. In the absence of strong physical damping to smooth out the errors, these errors accumulate and lead to serious instability problems. The River model was found to be unstable at low eddy viscosity. Therefore, there is a great need for a smoothing technique which can filter out the oscillations without affecting the accuracy of the solution. Care needs to be taken to insure that this technique does not overdamp the solution. Sheng et. al. applied spatial smoothing for one-dimensional convection dominated problems at the end of every time step and found that smoothing improves the accuracy and stability of the solution. The drawback of this method is that it is applicable only to uniform grids. In the present study, this approach has been modified so that smoothing can be also applied to non-uniform grid cases. Thus, Sheng's approach becomes a special case of this approach. Application of smoothing should allow the computational time step to be more than the one that corresponds to the Courant-Friedrichs-Lewy Condition (CFL).
It was possible to increase the maximum time step by a factor of 4. 75. It was found that when smoothing is applied, solutions obtained with the larger time step were better. Reduction of the frequency of smoothing also helped in getting a better solution. For each test case, conservation of mass was checked and was found to be satisfied. The test cases were run on a CRAY-XMP2/216 Supercomputer at the Mississippi Center for Supercomputing Research.
Recommended Citation
Abraham, Thomas P., "Proposed Smoothing Technique to avoid Numerical Instabilities in a Hydrodynamic Numerical Model" (1993). Electronic Theses and Dissertations. 8787.
https://egrove.olemiss.edu/etd/8787
Accessibility Status
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