We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the...
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 introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes,
proposed in [A. Kurganov , submitted to ],
whose construction is based on the maximal one-sided local speeds of propagation.
We also present a recipe, which helps to improve the resolution of contact waves.
This is achieved by using the , suggested
by Nessyahu and Tadmor [
(1990) 408-463],...
We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant
propagation is described by a transport equation.
This paper is an extension of our previous work [Chertock, Kurganov and Petrova,
(to appear)], where the one-dimensional finite-volume-particle method has been proposed.
The core idea behind the finite-volume-particle...
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 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...
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
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.
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that
the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied
to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its
high resolution and robustness in a number of numerical examples.
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