A FINITE VOLUME SEMI-IMPLICIT SEMI-LAGRANGIAN SCHEME ON THE YIN-YANG MESH

Designed for grid point systems, the traditional semi-Lagrangian semi-implicit scheme is not mass-conserving and can lead to significant solution errors. In the present study, a finite-volume semi-Lagrangian semi-implicit scheme (hereafter “FVSLSI”) is designed for the Yin-Yang mesh and tested in a barotropic shallow water model in the spherical coordinate system. Three test cases, i.e. the advection of a solid body, a steady state nonlinear zonal geostrophic flow and the deformation flow, are simulated to compare the performance of the FVSLSI with that of the traditional semi-Lagrangian scheme (hereafter “SL”) from perspectives of shape preservation, mass conservation, normalized bias, and convergence rate. Results indicate that the FVSLSI performs better than the SL in mass conservation and shape preservation. The bias by the FVSLSI is smaller than that by the SL, while the rate of convergence by the FVSLSI is larger than that by the SL. The FVSLSI also allows large time step. Therefore, the FVSLSI is suggested to be distributed to communities that are developing atmospheric/oceanic models.     

带岛屿约束的三角形空间剖分算法的改进方法

本文针对数值模拟中三角形有限元网格的具体要求，对经典的Bowyer-watson算法作了局部改进，利用具有岛屿约束的Delaunay剖分方法来构建三角形网格，使其适用于有岛屿、关键点和特征线约束的区域剖分的要求。此方法在（苏州，无锡，常州）以下简称苏锡常地区地下水流数值模拟中得到了应用，结果表明此方法自动生成带岛屿约束的三角形网格是可行的。     

三维I型超长管线阴极保护的数值模拟

研究超长管线阴极保护设计问题的数学模型和数值模拟,并将介质电阻、金属面电阻及金属自身电阻作了系统处理。通过数值试验与实验结果的对比,肯定了所提出的数学模型及所用边界元法在处理此类问题时的合理性及有效性。     

三维有限元位移场插值问题的研究和应用

对三维有限元位移场的插值问题进行了研究,提出基于Delaunay三角剖分的二次细分网格法。该法首先建立2个模型--整体模型和局部二次细分模型,对整体模型进行有限元计算和反分析得到初始地应力场和位移场;然后,基于Delaunay三角剖分,对整体模型的三维有限元位移场进行插值,插值结果作为局部模型的边界位移,局部二次细分模型再在此基础上进行有限元分析。最后,将该方法应用于工程实践,证明能提高计算效率,是切实可行的。