Numerical Study of Three Moving Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines

摘要

Three Lagrangian-based moving grid methods for systems of 1-D time-dependent partial differential equations were compared to assess which method offers the best prospects for reliable, efficient, and robust method of lines (MOL) application, with as little user intervention as possible. Method 1 is the finite difference method of Petzold (1987). Method 2 is a finite difference method based on the semidiscrete Lagrangian form. Method 3 is the finite element method of Miller et al (1981, 1983). Method 2 is preferred. It is easier to work with and to implement than Method 3 and also more efficient. The grid movement of Method 2 is directly attached to equidistribution in space of a chosen monitor function. This approach provides a better and more unique way of automatically adjusting the grid to large spatial gradients. An important feature of the approach of Method 2 is the grid smoothing capability. Although this involves two method parameters, the choice of these parameters is not troublesome. Method 1 is not recommended for general use.