Mold Filling Simulation by Finite Difference Method with High Order Scheme in Regular Cartesian Grid

Finite difference methods in the regular Cartesian grid are often used for mold filling simulations. The main advantages of these methods are memory and CPU saving and ease of grid generation compared to other unstructured methods. However, representation accuracy of casting shape is very poor; for example, slopes or curves are represented as stair-steps. Therefore, in such cases, calculated results are rarely consistent with the actual phenomena. However, these disagreements are not only caused by poor shape representation but also by the numerical error of the upwind scheme. In other words, high order schemes are expected to provide more accurate solutions without improving stair-step representation of the casting shape. The aim of this work was to investigate the stair-step representation, and to improve the accuracy of numerical analysis by the CIP CConstrained Interpolation Profile) method as high order scheme. By speculating the problems of stair-step approximation, it was found that inappropriate pressures are caused by numerical deterioration of fIow velocity. The decay is proportional to the n-th power of the Courant number, ifthe accuracy of the scheme is in the time-space n-th order. In general , the Courant number is less than 1. So the error of stair-step representation can be reduced by using the high order scheme. Some problems were solved by the upwind scheme and CIP method. In the simulated results by the upwind scheme, the error of stair-step generated strongly. On the other hand, itwas found that CIP method reduces the error.