含源项双曲守恒方程的保平衡 HLL 格式

A new finite volume scheme was proposed for hyperbolic conservation systems with source terms. The classical finite volume schemes could not accurately simulate the dynamic problems caused by the balance between flux terms and source terms. To deal with this problem, an approximate Riemann solver with source terms was designed in accordance with the classical HLL approximate Riemann solver. The well-balanced HLL scheme (WB-HLL) was obtained through modification of the flux calculation schemes for 1D Euler equations and ideal MHD equations with gravity source terms, and a proof for the well-balanced property of the new scheme was presented. Two numerical examples of 1D Euler equations and ideal MHD equations demonstrate that the proposed WB-HLL scheme has higher accuracy and faster convergence than the classical HLL ones.