Numerical Simulation On Two-Dimensional Shallow-Water Flows Based On Finite Volume Method

With the rapid pace of economic development, the environmental pollution problems have become increasingly serious. People have been aware of the environmental problems which brought a series of social problems related to human survival. In recent years, the pace of global industrialization accelerated lead to more serious rivers, lakes and other water resources pollution. How to clean up the contamination of water pollutants, as well as to explore the wider marine energy has become the need for today’s socio-economic development. Because of this, shallow water flow problems have been focus on the domestic and international Computational Fluid Dynamics by the hydrodynamic scholars. Several scholars have put forth many related calculation methods.This article focuses on how to simulate the movement of two-dimensional shallow water flow based on the finite volume method. We develop a new finite volume method Riemann solver of two-dimensional shallow water equations numerical calculation on the basis of the previous development. We established the new Riemann solver finite volume model for two-dimensional shallow water equations, and discussed finite volume discretization process and the basic format.In this paper, the new finite volume Riemann solving format that we proposed is implemented on triangular unstructured meshes. The proposed approach consists of a predictor stage and a corrector stage on time integration. A predictor-corrector stepping is used for time integration. In the predictor step, a non-conservative approach is used to determine the intermediate values whereas in the corrector step, a fully conservative solution is achieved by solving a series of local Riemann problems based on data from the predictor step.In the past, the majority of scholars often ignore the source term when they using finite volume method to simulate the shallow water movement. With the continuous improvement of the depth of theory and technology in recent years, many scholars focus on the processing of source terms when they studied the finite volume method. In this paper, the proposed approach which is a new finite volume method Riemann solver we developed on the basis of the previous development focused on the source term approach when using for two-dimensional shallow water equations numerical calculation. Numerical simulation of shallow water flow movement is more accuratly, more realistic.Finally, we simulated the typical cases of two-dimensional water movement, two-dimensional partial dam break flow, two-dimensional obstacles dam break flow and two-dimensional circular dam break flow, by the proposed finite volume Riemann format. Several types of two-dimensional dam-break flow simulation results verified the high accuracy and resolution of the new proposed finite volume method Riemann solver in solving two-dimensional shallow water equations.