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.