A NUMERICAL FRAMEWORK FOR THE DAM BREAK PROBLEM FOR SHALLOW WATER EQUATIONS USING MOVING-GRID FINITE VOLUME METHOD
Keywords:
shallow water equations, dam break problem, grid technique, finite volume methodDOI:
https://doi.org/10.17654/0975045223005Abstract
In this paper, we present numerical methods for the dam break problem for shallow water equations. The particular method we considered here is the adaptive moving-grid finite volume approach, based on the equidistribution of compute nodes using a control (or monitor) function. It is one of the moving-grid methods proposed by Huang et al. [22]. Since the computational accuracy of such methods strongly depends on the choice of the control function, we propose a well-suited control function allowing to obtain a better convergence rate. Motivated by efficiency considerations for problems in one or more spatial dimensions, we will apply the proposed numerical approach for the solution of the dam break problem for the shallow water equations, widely used for modeling the flow of water rivers, lakes, reservoirs, coastal areas and other situations in which the water depth is much smaller than the horizontal length scale of the flow. The performance of this framework is illustrated for numerical experiments that support the main theoretical results.
Received: December 21, 2022
Accepted: January 27, 2023
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