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We study a general approach to solving conservation laws of the form qt+f (q, x)x = 0, where the flux function f (q, x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function f i (q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A(More)
An extension of the wave propagation algorithm first introduced by LeVeque [J.] is developed for hyperbolic systems on a general curved manifold. This extension is important in a variety of applications, including the propagation of sound waves on a curved surface, shallow water flow on the surface of the Earth, shallow water magnetohydrodynamics in the(More)
In this paper we are concerned with the limiting behavior of gas flow in a thin channel as described by the Broadwell model. The Broadwell model is a simplified kinetic description for gas dynamics where the main assumption is that the particle distribution function can be represented by a discrete number of velocities. Starting from the Broadwell model and(More)
We study magnetic reconnection in electron-positron plasma using a collisionless two-fluid model with isotropic pressure, in which only the inertial term of the generalized Ohm's law is present. Our simulations indicate that the inertial term alone from Ohm's law is not sufficient to give reconnection. We contrast this result with other simulations where(More)