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 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...
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...
The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...
The purpose of this paper is to apply particle methods to the numerical solution of the
EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry
momentum so that wavefront interactions represent collisions in which momentum is
exchanged. This behavior allows for the description of many rich physical applications,
but also introduces difficult numerical challenges. We present a particle method for the
EPDiff equation that...
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