Numerical approaches for Boussinesq type equations with its application in Kampar River, Indonesia

In this study, we examine numerous numerical approaches for solving the 1-Dimensional Boussinesq problem. 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 modified two-four finite difference scheme and staggered finite volume scheme has a shorter computational time than the Mohapatra–Chaudhry scheme, which reduces the computational cost. We compare the performance of each numerical scheme against the analytical solutions and approximate solutions using different type of numerical method that is called the MUSCL4 scheme. Furthermore, the calculated results are compared and utilized to assess the contribution of each individual Boussinesq term. Each Boussinesq term was evaluated to examine its affect on the Boussinesq equation’s calculated result. Further, we also implement the numerical schemes that we formulate to investigate the undular bore phenomena in Kampar River. This finding may be useful to those who use the Boussinesq equation to study fluid or wave phenomena.