有限体积法中面积分离散格式的精度分析

讨论了应用顶点中心格式对欧拉方程进行有限体积离散时的精度,详细推导了顶点中心格式在平滑网格和扭曲网格上的截断误差,同时与中心格式和顶点格式进行了比较.格式精度分析采用泰勒级数展开的方法.分析结果表明:顶点中心格式和顶点格式类似,总能达到至少是一阶的精度,并且可以通过加密网格的办法减少误差,而且顶点中心格式更适合于分区计算.通过圆弧亚音速绕流和NACA0012翼型绕流流场的数值计算,验证了分析的结论.

Analysis of the Accuracy of the Spatial Discretization Schemes for Surface Integrals in Finite Volume Method

The order of accuracy of Vertex Centered finite volume scheme for the unsteady Euler equations is investigated and compared with that of cell centered and cell vertex schemes. An error analysis using Taylor series expansion is applied. It shows that the accuracy of the vertex centered scheme, similar to the cell vertex scheme, is at least first order on skewed meshes and the error terms can be reduced by a mesh refinement and is suitable for multiblock computation. On smooth grids all three schemes exhibit an accuracy of almost second order. Subsonic internal flow over circular arc and transonic flow around NACA0012 airfoil are calculated by using the three different spatial discretization schemes. Numerical results confirm the technique statement.