Nonlinear difference approximations for evolutionary PDEs

摘要

The authors describe a procedure to improve both the accuracy and computational efficiency of finite difference schemes used to simulate nonlinear PDEs. The underlying idea is that of enslaving, which is the estimation of the small unresolved scales in terms of the larger resolved scales. They discuss details of the procedure and illustrate them in the context of the forced Burgers' equation in one dimension. They present computational examples that demonstrate the predicted increases in accuracy and efficiency.