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Center for Nonlinear Studies |
A common element in the compressible CFD analysis problem and the design optimization problem is that the nonlinear aspects of the problem are the most challenging. A commonly used solution method for both problems is Newton's method. Often in discussions of these methods, the emphasis has been on methods for computing the required derivatives rather than on the perhaps equally important issue of the globalization strategy. In fact, the globalization strategy can be more important in cases where there are bifurcations or complex interactions with grid refinement. In this talk, we will discuss some globalization strategies based on nonlinear elimination and their application to incease the reliability of CFD computations. In this algorithmic context, we will describe some applications of optimization in aerodynamic design and consider the algorithmic implications of the engineering requirements.