Based on shallow-water approximations the governing equations for twodimensional two-phase gravity currents over a porous substrate and some appropriate boundaryconditions were introduced. With on characteristic inter...Based on shallow-water approximations the governing equations for twodimensional two-phase gravity currents over a porous substrate and some appropriate boundaryconditions were introduced. With on characteristic interpolations the numerical boundary conditionswere introduced and a series of exact solutions were constructed. Numerical a-nalysis were made byusing the two-step Lax scheme, second-order TVD scheme, third-order ENO scheme and fifth-order WE NOscheme combined with second- and third-order TVD-Runge-Kutta method is given. It is found that forpractice applications the second-order TVD scheme combined with the second-order TVD- Runge- Kuttamethod is an economical and suitable choice.展开更多
文摘Based on shallow-water approximations the governing equations for twodimensional two-phase gravity currents over a porous substrate and some appropriate boundaryconditions were introduced. With on characteristic interpolations the numerical boundary conditionswere introduced and a series of exact solutions were constructed. Numerical a-nalysis were made byusing the two-step Lax scheme, second-order TVD scheme, third-order ENO scheme and fifth-order WE NOscheme combined with second- and third-order TVD-Runge-Kutta method is given. It is found that forpractice applications the second-order TVD scheme combined with the second-order TVD- Runge- Kuttamethod is an economical and suitable choice.
