STUDY OF INDIVIDUAL TERMS IN THE BOUSSINESQ EQUATION - Natasha Haloho, Desy
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.