Simulation Of Dam-break Flows Based On Finite Volume HWENO Schemes

People build dams among the rivers in order to irrigate with water, generate electricity and prevent the flood. They can protect human beings against disasters such as the flood, but also has tremendous potential danger. If the dams break because of human reasons or the natural power, the flood wave cause by sudden released water will cause catastrophic disasters to the downstream area. Therefore to predict the discharge and water level lines besides the dam and to insure the discharge, water level and velocity along the downstream area are important. The problem has called the attention of researchers as well as practicing engineers for several decades.The idea of HWENO reconstruction is coming from the original WENO scheme, it was presented by Qiu J X and Shu C W as a limiter of RKDG schemes for solving hyperbolic conservation law equations. Comparing with the WENO scheme, HWENO scheme has fewer stencils, higher precision, fewer computation load, and so on merits. Many method had been utilized to simulate dam-break flow, but HWENO scheme for simulating dam-break flow have not been presented, this paper has done some work in this aspect, mainly includes:1. The one-dimensional shallow water wave equations which were utilized to model the dam-break flow have many characteristics such as clear concept, simple computation and reliable results and so on. They are widely used on the projection particularly applied on the simulation of long section of river and large scale. this paper solve the one-dimensional shallow water wave equations with the finite volume HWENO scheme, and simulate the Stoker problem. the results based on HWENO scheme are compared with the theorical solution and the results based on WENO scheme, and show that the finite volume HWENO scheme could restrains oscillation effectively and the results fits the theory solution well.2. Two-dimensional dam-break flow simulation mainly based on two-dimensional shallow water wave equations. This paper applies the finite volume method to spatial discretiation, reconstructs the left and right function values of the variables with the HWENO scheme, and uses the four steps Runge-Kutta method to time discretiation. The solving form for two-dimensional shallow water wave equations are presented, the 2D partial dam-break flow and circle dam-break flow are simulated. All results conform to the actual physical phenomenon, fit the results well reported before, and prove the validity and applicability of our model.