tailieunhanh - On some numerical methods for solving the 1-D saint-venant equations of general flow regime

This Part of the paper presents the results of verification by various test problems, covering all of three flow regimes: sub-, trans-, and super-critical. The results show that the mixed approach (between pointwise and upwind) for source terms is better than the pointwise one and any mathematical transformation of source terms must be careful, since that can lead to nonphysical solutions. The Roe's approximation with the mixed technique for the source terms is used for a preliminary evaluation of the Son La - Hoa Binh dambreak problem. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 25, 2003, No 1 (26 - 38) ON SOME NUMERICAL METHODS FOR SOLVING THE 1-D SAINT-VENANT EQUATIONS OF GENERAL FLOW REGIME Part 2: Verification and application NGUYEN VAN HANH 1 , NGUYEN VAN DIEP 2 AND NGO HUY CAN 2 1 Institute for Water Resources Research, 271 Tay son street, Hanoi, Vietnam 2 Institute of Mechanics, 264 Doi can street, Hanoi, Vietnam ABSTRACT. In the Part 1 of this paper [l], some numerical methods for solving the 1-D Saint-Venant equations of general flow regime have been described. This Part of the paper presents the results of verification by various test problems, covering all of three flow regimes: sub-, trans-, and super-critical. The results show that the mixed approach (between pointwise and upwind) for source terms is better than the pointwise one and any mathematical transformation of source terms must be careful, since that can lead to nonphysical solutions. The Roe's approximation with the mixed technique for the source terms is used for a preliminary evaluation of the Son La - Hoa Binh dambreak problem. 1. Verification of the numerical methods by Test-Cases To evaluate the general flow simulation capacity and the advantages of every numerical method presented in the Part 1 of this paper some test cases newly developed by European Hydraulic Laboratories [2, 3] will be used. The results of testing will be shown in figures (1-14, 16-21). In these figures the following notations are used: - Z 9 t, Q 9 t , V9 t - analytical water level , discharge , velocity - Zu , Qu , Vtt - numerical water level, discharge, velocity - zb - bed level - H - Water depth . Schemes with the pointwise source term integral . Steady fiow through a bump In this case all 4 schemes are used to calculate the steady flow through a bump in a rectangular channel with a constant width [2]. Depending on the boundary and the initial conditions the flow may be sub-critical, super-critical, trans-critical or at rest.