An Adaptively-Moving-Grid Finite-Volume Scheme with Boundary-Grid Elimination/Addition

摘要

One of interesting problems in CFD is an interaction between fluid motion and body/wall boundary motion. To simulate accurately such a problem with moving boundary, we often encounter two problems. For achieving sufficient resolution of a solution, we have to use enough number of grid points. The increase of grid points, however, means the increase of CPU time. One of the techniques to overcome this problem is to develop an adaptive grid method for moving grid system. Another one accompanying moving-boundary problem appears when the size of the flow region changes excessively according to the wall-boundary motion. It is, for example, typically seen for the moving piston inside a closed cylinder. As the piston moves toward the end of the cylinder, the flow region becomes narrower and the grid becomes excessively fine. Then the numerical stability becomes worse and results in the use of smaller time step accordingly. On the contrary, for the case that the piston moves away from the end of the cylinder the flow region becomes wide and the grid spacing becomes far wider than the original state. In that case, the accuracy of the computation becomes worse. If we can remove or add the grid points from or to the region, the computation becomes more efficient, numerically stable and accurate.