A unified treatment of steady-state shallow water and two-dimensional navier-stokes equations — finite element penalty function approach

摘要: Abstract The objectives of this paper are threefold: 1. (a) To introduce new generalized formulation shallow water equations which permits taking into account the effect return current distribution in depth direction. 2. (b) a penalty steady state solution equations. 3. (c) test validity various arbitrary approximations introduced simplified by different investigators. In development first objective we start, as is common practice, introducing only approximation necessary formulations, i.e. neglect vertical acceleration terms. essential variables remaining surface elevation and two horizontal velocities. problem thus still three dimensional albeit with velocity components to be represented an expansion coordinate reduced set space dimensions but finite k parameters defining distributions. This permits, when ⩾ 2, obtain currents have been included general given other authors at expense omitting viscosity convective second objective, that developing “penalty” form for resulting accomplished manner previously used Navier-Stokes results elimination variable from final discrete imposing approximate simultaneous satisfaction continuity constraint number. last section third addressed study several examples full well its used. One concerns lake circulation driven wind forces another wave generated near shore obstacle.