A 1/3 Pure Subharmonic Solution and Transient Process for by Xu Y., Bao W.

By Xu Y., Bao W.

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Extra info for A 1/3 Pure Subharmonic Solution and Transient Process for the Duffings Equation

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SHEN Table I. 1 density, velocity and pressure L 1 errors for the Godunov scheme with the exact Riemann solver and the new solver in different scales of grids. 321964E−3 Table II. 2 density, velocity and pressure L 1 errors for the MUSCL scheme with the exact Riemann solver and the new solver in different scales of grids. 808145 Table III. 3 density, velocity and pressure L 1 errors for the MUSCL scheme with the exact Riemann solver and the new solver in different scales of grids. 182284 Table IV.

These equations express conservation of mass and momentum. In conservative form, they are as follows: Ut + F(U )x = S U= h hu , F(U ) = hu hu 2 + 12 gh 2 , S= 0 (1) gh(s0 − sf ) where U is the conservative variables vector in which, h and u are flow depth and velocity, respectively; F(U ) the flux vector; S the source term vector, consist of bed slope S0 and friction slope Sf . 33 where n is the empirical Manning resistance coefficient. The governing equations are based on the assumptions of hydrostatic pressure distribution, incompressibility of water and a sufficiently small channel slope.

The source term consists of two parts, the bed slope and the friction slope. Treatment of each part will be explained separately. 1. Bed slope treatment The main subject in dealing with the bed slope is to balance it with the convection flux in each cell at stationary flow field. This will be explained in more detail under the C-property preposition [29]. The C-property will be explained and approved for the proposed algorithm later on, but first the details of the source term discretization are presented below.

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