We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (, it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are
separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied
by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious
oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell...
This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed.
This paper concerns numerical methods for two-phase flows.
The governing equations are the compressible 2-velocity,
2-pressure flow model. Pressure and velocity relaxation
are included as source terms. Results obtained by a
Godunov-type central scheme and a Roe-type upwind scheme
are presented. Issues of preservation of pressure equilibrium,
and positivity of the partial densities are addressed.
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