Multi-physics Simulations in Continuum Mechanics

The era of commodity computing brings a profound change in the use of numerical analysis of continuum mechanics problems in science and engineering. Teraflop-rate computing facility, until recently available only to chosen few is becoming commonplace in an industrial setting. Range and complexity of problems where numerical methods are applied is also expanding. Here, massive reduction in the cost of solution allows the empirical or simplified models to be replaced by fundamental sets of equations. Numerical simulation is also expanding beyond its traditional realm of structural analysis and fluid flow. In the first phase, this covers real material properties, chemically reacting flows, multiphase and free surface flows, radiative heat transfer, electromagnetics etc. A natural extension of the above is coupled analysis of engineering components, covering a number of interacting phenomena. For example, a Fluid-Structure Interaction (FSI) simulation covers the physics of fluid flow and stress analysis, but the emphasis is on dynamic interaction between the two. Coupled nature of the problem brings its own challenges beyond the realm of “bread-and-butter” fluid flow or structural dynamics simulations. In this paper, expanded role of numerical solvers in Computational Continuum Mechanics (CCM) will be examined from the point of view of solver development. We shall present a new way of implementing partial differential equations of continuum mechanics in numerical simulation software through the use of object-oriented programming. Desirable consequences of objectorientation include data protection and encapsulation, layered development and code re-use and facilitate side-to-side implementation of various physical models and discretisation methods. This will be followed by an overview of complex geometry support and model to model coupling framework. The paper is concluded with examples of coupled multi-model simulations. OpenFOAM [6, 10], an Open Source object-oriented C++ library for numerical simulations in continuum mechanics is the basis of the review and source of examples.