求解渗流问题的高精度差分格式

在求解渗流问题的传统差分格式中 ,只有Crank Nicolson格式具有对时间t的二阶精度。本文在导数超收敛点概念的基础上 ,提出 1种求解渗流问题的三阶精度差分格式 ,并将其与显式差分格式叠加形成组合差分格式以改善格式的稳定、收敛条件。算例计算结果表明 ,该组合格式具有精度高、稳定收敛限制宽松、易于编程等优点。

Difference Scheme with High Accuracy to Solve Seepage Flow

Among the classical difference schemes to solve seepage flow only the Crank-Nicolson scheme is of the 2-order accuracy in t.Based on the concept of the ultra-convergence of derivative,a new difference scheme that is of the 3-order accuracy in t is proposed.To improve the stable and convergence conditions the composite difference scheme is formed based on the linear superposition of 3-order accuracy scheme and explicit scheme.The calculation results show that the advantages of the composite difference scheme are high accuracy,loose limitation for the stability and convergence and easy to program.