含源项双曲守恒方程的保平衡HLL格式

A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms

针对含源项的双曲守恒方程给出了一种新的有限体积格式.经典的有限体积格式不能正确地模拟对流通量项和外力之间的平衡所产生的动力学问题.为解决这个问题,仿照经典的HLL近似Riemann求解器设计思路设计了含源项的近似Riemann求解器.针对含重力源项的一维流体Euler方程和理想磁流体方程,通过对通量计算格式的修正得到了保平衡HLL格式(WB-HLL),并给出了保平衡的证明.针对一维Euler方程和理想磁流体给出了两个算例,比较了传统HLL格式和提出的WB-HLL格式的计算精度.计算结果表明,WB-HLL格式精度更高,收敛更快.

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.