Abstract
This paper presents new finite volume schemes for hyperbolic conservation system with source terms. The classical finite volume schemes could not accurately simulate the dynamic problems caused by the balance between flux term and source terms. In order to deal with this problem, an approximate Riemann solver with source terms was designed in accordance with the classical HLL approximation Riemann solver. The well-balanced HLL schemes (WB-HLL) was obtained by modifying the flux calculation schemes for one-dimensional Euler equations and ideal MHD with gravity source terms, and a proof for well-balanced property of the new schemes has been presented.Two numerical examples of one-dimensional Euler equation and ideal MHD demonstrated that the WB-HLL scheme has higher accuracy and faster convergence than the classical HLL.
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