Adaptive Moving Grid Method for One-Dimensional Systems of Partial Differential Equations

摘要

A fully adaptive, moving grid method was developed for solving initial-boundary value problems for systems of one-space dimensional partial differential equations (PDE) whose solutions exhibit rapid variations in space and time. The method, based on finite differences, is of the Lagrangian type and was derived through a coordinate transformation which leads to equidistribution in space of the second derivative. The technique is intermediate between static regridding methods, where nodes remain fixed for intervals of time, and continuously moving grid methods, where the node movement and the PDE integration are fully coupled. The computation of the moving grids and the solution on these grids are carried out separately, while the nodes are moved at each time-step. Two error monitors were implemented, one to govern the time step selection and the other to adapt the number of moving nodes. The method allows the use of different moving grids for different components in the PDE system. Numerical experiments are presented for a set of five sample problems from the literature, including two problems from combustion.