Survey on Modeling and Simulation of Multiphysics Systems John G. Michopoulos ¤ Center for Computational Material Science Special Projects Group Computational Multiphysics Systems Laboratory U.S. Naval Research Laboratory Washington DC, 20375 [email protected] ASME member Charbel Farhat Mechanical Engineering and Institute for Computational and Mathematical Engineering Stanford University Stanford, CA, 94305 [email protected] ASME fellow Jacob Fish Dept. of Civil, Mechanical and Aerospace Engineering Rensseleaer Polytechnic Institute Troy, NY, 12180 ¯[email protected] ASME member April 15, 2005 Abstract This paper presents a retrospective on the evolution of modeling and simulation (M&S) as they relate to multiphysics systems. The context space of M&S is de¯ned in terms of number of ¯elds, number of domains, length scale, and computational technologies involved. Representative past and the present e®orts on each one of these contexts and some of their combinations are described and their relationship to the product development e®orts of ASME's Computer and Information in Engineering (CIE) division is identi¯ed. The general procedures for developing multi-¯eld formulations are given ¯rst. Then the multi-domain progress is given with an emphasis on fluid-structure interaction problems pertaining to linear and non-linear aeroelasticity and aerothermoelasticity. Multi-scale methodologies follow, and the computational technologies associated with model generation and simulation is also presented. Potential future anticipated trends and directions are identi¯ed and conclude this survey. ¤Address all correspondence to this author. 1 INTRODUCTION The main goal of the present e®ort is to present an overview of the past, present and potentially the future evolution in the ¯eld of modeling and simulation (M&S) of multiphysics systems from a product development perspective. On one hand, the extensive pluralism of the ever evolving computational technologies and on the other hand the sharp private focus of individual researchers onto their own subject of interest sometimes prevent an up-to-date comprehensive understanding of how private e®orts relate to global history and trends. Thus, besides its ceremonial character relative to honoring the 25th anniversary of the Computer and Information in Engineering (CIE) division of the ASME, the technical component of the motivation for the present work is to provide a reality check reference point for all practitioners of M&S methodologies and technologies as they apply to product development. Here it should be underlined that while utilitarian and economic pressures push for the development of inexpensive complex products under complex operational conditions, the computational technology evolution provides an ever improving realm of reducing to practice applied science and engineering knowledge. These two factors provide us with the opportunity to anticipate fast, e±cient and economically viable development of complex products, the models of which correspond to real-life applications with less simpli¯cations and assumptions than those used in the past. It is imperative that for the sake of clarity and disambiguation we provide the operational de¯nitions of the fundamental terms associated with our topic. Today's product development requires the exercise of M&S not only in terms of product appearance and shape but also in terms of the systemic behavior of a product. The ¯rst aspect of M&S for shape and appearance deals with what traditionally has been associated with Computer Aided Design (CAD) and and Manufacturing (CAM). However, these are areas explored by another article on the same issue of JCISE []. Our present e®ort focuses on examining the evolution of M&S in terms of behavioral models for multiphysics systems. In particular, by \modeling" here we imply the activity of forming a mathematical representation (and its algorithmic and computational implementation) of the behavior of the system that captures the relation between input (stimulus) and response (output) state variables or/and parameters characterizing this behavior of the system. By the term \simulation" we imply the computational exercise of the model produced by the \modeling" activity, for the sole purpose of predicting the behavior of the system at hand. Clearly, since this behavior is in many cases given in terms of contour, vector and color intensity artifacts painted on the surface or in the volume of the associated systems, the geometric model of them is implicitly but inextricably associated with the behavioral models. The usage of the term \multiphysics" has been often used liberally during the past ¯ve years by various 2 researchers. However, it has been used in more than one undeclared contexts not always allowing the occasional consumers of the term to be able to isolate the meaning intended by the originators of the term. Some of the frequently attributed meanings of the term have been those of: \multi-¯eld" to denote the simultaneous excitation and response of the system by multiple physical ¯elds; \multi-domain" to denote the interaction among continuum representations of systems with drastically di®erent properties (e.g. fluid- structure interaction, moving solidi¯cation boundary problems e.t.c.) through sharable boundaries; \multi- scale" to denote the consistent bridging of various behavioral models of the system at hand, at various length scales as required by a multitude of scopes ranging from manufacturing process perspective to macro- behavioral utilization. In addition, any combination of these three semantic possibilities generates four more meanings of the term \multiphysics" including the one that reflects the co-existence of all three of them. This suggests the de¯nition of a conceptual attribute space (see Fig. 1) spanned by the three basis attributes namely, \multi-¯eld", \multi-domain" and \multi-scale". All other cases for the potential meaning of the term \multi-¯eld" are embedded implicitly in this space and can be thought of as linear combinations of the three base-cases. In addition, the \multi-¯eld" and \multi-domain" bases are endowed with a measure de¯ned in terms of two discrete increments for \one" and \many". The \multi-scale" base is similarly endowed by a measure de¯ned in terms of the discrete increments in the term set f\nano", \micro", \macro"g roughly corresponding to applying these as pre¯xes to the term \meter" when used as a length unit. Any discrete volume in this discrete space as shown in Fig. 1, is de¯ned by a triplet of coordinates originating from each one of these attribute axes, and represents a region encompassing certain classes of physical problems. This signi¯es that these problems can be modeled in a multiphysics sense as de¯ned by their corresponding coordinates. Our description of the M&S retrospective will be based on references in this space in a manner that corresponds to the authors' individual experiences as they correspond to these base cases of this space. There are many more attributes of the M&S activities as they relate to the interests of the various stake- holders associated with the production and consumption of M&S methodologies, processes, and products, that can de¯ne their own spaces (e.g. implementation technology, manufacturing, business, human factors, technology transfer, direction of modeling, maintainability, software engineering etc.) in a manner similar to the one used above for describing the term \multiphysics". Example base cases for the economical business subspace would be the total cost of ownership, the return on investment and the production cost. Example base cases for the manufacturing subspace would be total production time, yield and e±ciency. Examples base cases for the human factors subspace would be con¯dence measures such as quali¯cation, veri¯cation and validation, and usability measures such as slope and length of learning curve etc. However, it falls outside the scope of this paper to address these and the rest of the subspaces mentioned in more detail. 3 Figure 1: Multiphysics attribute space. In addition to the three base cases described for the de¯ning the therm \multiphysics", here we will focus only on one of these additional subspaces. This will be the \computational technology implementation" subspace. Activities in this subspace are intimately associated with the progress on M&S as a discipline in its own right because they often provide a motivational pulling mechanism for reducing to practice advances of the associated methodologies and implementations. Space limitations do not allow further decomposition of this attribute space to base cases (e.g. distributed technologies, semantic technologies, data exchange technologies etc.) Product development e®orts based on the research activity e®orts on multiphysics systems are far less compared to the \single" physics system modeling, mainly due to the inherent complexity associated with them. Therefore, this paper will be focusing less on the history and more on the available methodologies and technologies as opportunities for future product development via the catalytic leveraging of the independent progress of the computational technologies. Therefore, this paper contains descriptions of the evolution of M&S in terms of the four base cases of multi-¯eld, multi-domain, multi-scale formulations and computational technologies. We initially de¯ne the abstract formulation context for these cases in order to facilitate the development of their retrospective