STUDY OF INDIVIDUAL TERMS IN THE BOUSSINESQ EQUATION
In this final project, we examine numerous numerical approaches for solving the 1-Dimensional Boussinesq problem with third order Boussinesq terms. The proposed methods to be discussed include Mohapatra and Chaudhry’s two-four finite difference scheme, the modified two-four finite difference sche...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/64939 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this final project, we examine numerous numerical approaches for solving
the 1-Dimensional Boussinesq problem with third order Boussinesq terms. The
proposed methods to be discussed include Mohapatra and Chaudhry’s two-four
finite difference scheme, the modified two-four finite difference scheme, and the
staggered finite volume scheme. The calculation results of the numerical scheme
will then be validated by comparing them to the analytical solution of the Shallow
Water Equation (SWE) and we will also compared the computational time of each
numerical scheme. The dam-break flow with a non-hydrostatic pressure distribution
will then be simulated using each scheme in two scenarios: the wet-wet
dam-break problem and the wet-dry dam-break problem. Furthermore, the calculated
results are compared and utilized to assess the contribution of each individual
Boussinesq term. The numerical scheme solution reveals that in the wet-wet dambreak
problem, the first Boussinesq term forms a larger amplitude of undulation than
the other Boussinesq terms. Meanwhile, it is discovered that in the wet-dry dambreak
problem, the solution without the first Boussinesq term of the finite volume on
a staggered grid scheme generates a rarefaction zone that occurs earlier than other
numerical schemes. Both dam-break simulations show that the first Boussinesq
term significantly affects the results of the Boussinesq equation calculation. An
undular bore simulation was also performed to demonstrate the scheme’s ability
to account for dispersive effects, by comparing the computational results to the
MUSCL4 scheme by Soares-Fraz˜ao and Guinot. Afterward, the numerical scheme
will be used to simulate the Kampar River’s tidal bore. This finding may be useful
to those who use the Boussinesq equation to study fluid or wave phenomena. |
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