Second-Order Particle-in-Cell (PIC) Computational Method in the One-Dimensional Variable Eulerian Mesh System

摘要

As part of an effort to incorporate the variable Eulerian mesh into the second-order PIC computational method, a truncation error analysis was performed to calculate the second-order error terms for the variable Eulerian mesh system. The results that the maximum mesh size increment/decrement is limited to be alpha ( delta r/sub i/) exp 2 where delta r/sub i/ is a non-dimensional mesh size of the ith cell, and alpha is a constant of order one. The numerical solutions of Burgers' equation by the second-order PIC method in the variable Eulerian mesh system wer compared with its exact solution. It was found that the second-order accuracy in the PIC method was maintained under the above condition. Additional problems were analyzed using the second-order PIC methods in both variable and uniform Eulerian mesh systems. The results indicate that the second-order PIC method in the variable Eulerian mesh system can provide substantial computational time saving with no loss in accuracy. (ERA citation 06:024525)