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We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...
We present one- and two-dimensional central-upwind schemes
for approximating solutions of the Saint-Venant system
with source terms due to bottom topography.
The Saint-Venant system has steady-state solutions
in which nonzero flux gradients are exactly balanced by
the source terms. It is a challenging problem to preserve
this delicate balance with numerical schemes.
Small perturbations of these states are also very difficult
to compute. Our approach is based on extending semi-discrete central...
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.
Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.
We present and analyse in this paper a novel cell-centered collocated finite volume scheme for incompressible flows.
Its definition involves a partition of the set of control volumes; each element of this partition is called a cluster and consists in a few neighbouring control volumes.
Under a simple geometrical assumption for the clusters, we obtain that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is inf-sup...
This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [J. Evol. Eq. 3 (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). Therefore, we propose an implicit Finite Volume method based on an equivalent formulation of the initial...
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