A TWO-STEP PREDICTIVE-CORRECTIVE SCHEME FOR 2D POISSON EQUATION

Since the classic 4th order compact scheme requires ninepoints for 2D Poisson equation, the boundary conditions make the schemedifficult to be implemented, especially when the equations need to be solved bya multi-grid method. A new 4th order accurate scheme is derived. First, a predictive solution is obtained by using the classic 2ndorder five-point scheme. Then, the solution is corrected by considering theresidual term. Finally, the scheme combines the predictive and thecorrective solutions to achieve 4th order accuracy. In each step, theclassical 2nd order scheme is used and the boundary conditions areeasy to be treated. Although the scheme costs twice of the computationaltime ascompared with the 2nd order scheme, it is much more accurate than the2nd order scheme. Moreover, the boundary conditions are quite simpleand it is easier to code for this new scheme. The numerical simulationsconfirm that the new scheme has the same accuracy as the classic 4th ordercompact scheme. This provides a new approach to turn a lower orderscheme in to a high order scheme.