Studies on Solution Methods for Nonlinear, Multiple-Time-Scale, PDE Simulations: Examples from Diffusion / Reaction Systems (1)

John N. Shadid(2)

Curt C. Ober(2)

Roger P. Pawlowski(2)

David L. Ropp(3)

Sandia National laboratories MS 1111 PO Box 5800 Albuquerque NM, 87185


Abstract

In this talk we consider issues related to the solution of large-scale, nonlinear, multiple-time-scale, PDE systems. We begin by reviewing a number of solution strategies for such systems, including time-integration techniques based on time-step lagging and linearization of nonlinear terms, various operator-splitting methods and fully-implicit techniques. These techniques have been applied to a set of diffusion/reaction problems: thermal-wave propagation, chemical dynamics and radiation/diffusion. We will comment on the time accuracy, the nonlinear consistency and the apparent stability of these methods. We will also describe some difficulties of completing order-of-accuracy studies between solution methods due to differences in the behavior of the effective spatial discretization of the PDEs. -------------------------- (1) This work was partially supported by the DOE office Science MICS effort and the ASCI Algorithms effort at Sandia National Laboratory under contract DE-AC04-94AL85000 (2) Computational Sciences Department (3) Computational Mathematics and Algorithms Department --