非结构有限体积法海洋模式垂向计算的一种改进方法

Improved vertical algorithm for finite volume coastal and ocean model with unstructured-grid

多维正定平流输运算法(MPDATA)通过迭代计算反向虚拟平流,在达到二阶精度的同时保证保守量正定性。基于非结构有限体积法的海岸和海洋模型(FVCOM),设计了一个耦合MPDATA和通量修正格式(FCT)的方法,并与水平方向有限体积法兼容。通过两个数值试验,将新方法FVCOM模型与原始FVCOM模型计算结果进行了比较。结果表明,MPDATA方法在一定程度上消除了FVCOM海洋模型原有格式引起的振荡,而MPDATA和FCT耦合方法严格保证了FVCOM计算结果正定性,同时保留了原有计算精度。

The iterative method was used to calculate anti-diffusion flux in multidimensional positive definite advection transport algorithm（MPDATA）,which guarantees the positive definite of flux and has a second order accuracy.A method combining MPDATA and flux-corrected transport method（FCT） was incorporated into the unstructured-grid finite-volume coastal and ocean model（FVCOM）,which has the horizontal flux calculated from finite volume method and vertical flux calculated from finite difference method.The simulations of the FVCOM with the new method were compared with those of the original FVCOM by testing two idealized setups.The results indicate that the MPDATA method,in some extent,inhibits the numerical oscillation brought by FVCOM original scheme,and the method coupling MPDATA and FCT guarantees the positive definiteness of simulation of FVCOM without sacrificing the accuracy.