改进的二维三阶半离散中心迎风格式

对二维三阶半离散中心迎风格式中的权函数给出了简化改进.在保持格式精度的基础上,改进后的权函数在二维情况下具有更加简单直接的结构而且严格非负.该改进方法得到的格式仍然具有半离散中心迎风格式的优点,同时保持了重构函数的非振性.时间离散采用保持强稳定性的三阶Runge-Kutta方法,并利用四阶Lax-Wendroff(L-W)格式计算磁流体算例中的磁场散度.用该修正格式计算了二维磁流体数值算例,得到高精度无振荡的结果,验证了此方法的有效性.

Modified Two Dimensional Third-order Semi-discrete Central-upwind Scheme

The semi-discrete central-upwind scheme is a new Godunov type numerical method which is developed in 1990s.The scheme is widely used in the computational fluid dynamics and its advantages include the simple calculation process,the high calculation precision and so on.But for the third-order scheme,the positivity of the weight function and the non-oscillation of the WENO type reconstruction function in every direction cannot be preserved in two dimensional problems. In this article,a simple,direct modification is taken to the weight function of the two dimensional third-order semi-discrete central-upwind scheme.The modified weight function will keep the positivity all the time while the accuracy of the semi-discrete central-upwind method is preserved.The revised scheme still has the advantages of central-upwind schemes and it keeps the non-oscillation of reconstruction.To explore the potential capability of application of this reformation of weight function, two Magnetohydrodynamics(MHD) problems are simulated.In simulations,the third order Runge-Kutta method is used to solve the time evolution and the divergence of magnetic field was calculated by fourth-order Lax-Wendroff(L-W) scheme.All the numerical results demonstrate the modified scheme can solve the MHD equations stably,get high resolution and non-oscillatory results, keep the positivity of the weight function and the reconstruction is non-oscillatory in each direction.