A new cell-centred finite difference scheme for CFD simulations
The governing partial differential equations of fluid motion are usually numerically approximated using one of the three classical methods: Finite Difference (FD), Finite Volume (FV) or Finite Element (FE). In this thesis, a new cell-centred FD (CCFD) formulation is developed, in which the governing fluid flow equations are differenced over all the cell centres instead of grid points. The nodes (grid points) are then updated by averaging the property from all the cell centres that share that node. This feature, which is motivated by development of the FV method, allows the application of the proposed FD numerical formulation on unstructured grids. Several test cases are investigated here to illustrate this approach. To verify the results, the analytical solution for the test case is used if available. Otherwise, the numerical solution is compared to the traditional FD solution.