Practical Aspects in Comparing Shock-Capturing Schemes for Dam Break Problems

Abstract

The results of a survey aimed at comparing the performances of first-order and total variation diminishing (TVD) second-order upwind flux difference splitting schemes, first-order space-centered schemes, and second-order space-centered schemes with the TVD artificial viscosity term are reported here. The schemes were applied to the following dam-break wave cases: in a dry frictionless horizontal channel; in a dry, rough and sloping channel; and in a nonprismatic channel. Among first-order schemes, the diffusive scheme provides only slightly less accurate results than those obtained by the Roe scheme. For TVD second-order schemes, no significant difference between the upwind scheme and central schemes are reported. In the case of a dam break in a dry frictionless horizontal channel, the second-order schemes were two- to five-fold more accurate than the diffusive scheme and Roe’s scheme. These differences in scheme performances drastically reduce when the results obtained for the rough sloping channel test and for the nonprismatic channel test are analyzed. In particular, the accuracy of the diffusive and Roe’s schemes is similar to second-order schemes when such features of dam break wave, relevant from an engineering viewpoint, like wave peak arrival time and maximum water depths, are considered.