Introduction

The past several decades have witnessed impressive successes in the ability of scientists and engineers to accurately simulate physical phenomena on computers. In engineering, it would now be unimaginable to design complex devices such as aircraft engines or skyscrapers without detailed numerical modeling playing an integral role. In science, computation is now recognized as a third mode of inquiry, complementing theory and experiment. As the steady march of progress in individual spheres of interest continues, the focus naturally turns toward leveraging efforts in previously separate domains to advance one's own domain or in combining old disciplines into new ones. Such work falls under the umbrella of multiphysics modeling.

Overcoming the physical, mathematical, and computational challenges of multiphysics modeling comprises one of the central challenges of 21st-century science and engineering. In one of its three major findings, the National Science Foundation Blue Ribbon Panel on Simulation-Based Engineering Science (SBES) cited “open problems associated with multiscale and multi-physics modeling” among a group of “formidable challenges [that] stand in the way of progress in SBES research.” As the juxtaposition of “multiphysics” and “multiscale” in the panel's report implies, multi-physics problems often involve dynamics across a broad range of lengths and times.

At the level of the physics and mathematics, integrating the disparate dynamics of multiple fields poses significant challenges in simulation accuracy, consistency, and stability.