Abstract. This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization.The paper has three goals. First, it is an expository introduction to MDO aimed at those who do research on optimization algorithms, since the optimization community has much to contribute to this important class of computational engineering problems. Second, this paper presents to the MDO research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems. Third, the "individual discipline feasible" (IDF) approaches introduced here make use of existing specialized analysis codes, and they introduce significant opportunities for coarse-grained computational parallelism particularly well suited to heterogeneous computing environments.The key distinguishing characteristic of the three fundamental approaches to MDO formulation discussed here is the kind of disciplinary feasibility that must be maintained at each optimization iteration. Other formulation issues, such as the sensitivities required, are also considered. This discussion highlights the trade-offs between reuse of existing software, computational requirements, and probability of success.
In this paper we examine the mathematical structure of a model for three-phase, incompressible flow in a porous medium. We show that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic. We present an example in which there is an elliptic region in saturation space for reasonable relative permeability data. A linearized analysis shows that in nonhyperbolic regions solutions grow exponentially. However, the nonhyperbolic region, if present, will be of limited extent which inherently limits the exponential growth. To examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method. These experiments indicate that the solutions of Riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space. In particular, when initial states are outside the elliptic region the Riemann problem solution appears to stay outside the region. Furthermore, stable shocks are formed connecting states inside the nonhyperbolic regions with states outside.
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