Extending EB3 scheme for the differential conservation law from node-centered to cell-centered control volumes I: Basic formula on regular cells

Abstract

The third-order edge-based (EB3) scheme for the differential conservation law is widely used on node-centered control volumes. It is much efficient and easy to implement, since the second derivatives for both fluxes and solutions are not required to compute and store, and the single quadrature point at per edge is enough to preserve the third-order solution accuracy on triangular grids. In this paper, the scheme is extended to the regular cell-centered control volume in two dimensions, and by analogy, it is named FB3, where “F” denotes the face of cell-centered elements. Compatible source term discretization is carefully derived, and based on the “collapsing-cell” idea, accuracy preserving boundary scheme is developed. More importantly, within the scope of FB3 scheme, the regularity of triangular grids is specifically discussed from the analytical and numerical perspectives. Numerical experiments based on the linear convective and Euler equations are implemented, and results indicate that the third-order solution accuracy is achieved at both internal and boundary fields, as long as the control volumes consist of regular triangles.