The objective of the presented work is to formulate a computationally accurate and efficient shape sensitivity analysis method, called Continuum Sensitivity Analysis (CSA), for optimizing shape of the next-generation vehicle systems in high-speed flow involving discontinuities, such as, shock boundaries and rarefaction waves. Examples of such systems include high-speed aircraft, satellite launch systems, turbomachinery components, automobiles, wind turbine blades, etc. CSA is based on the premise of "first differentiate (the governing equations) and then discretize" that results in more accurate shape sensitivities than the most present-day discrete approaches which are based on "first discretize then differentiate." CSA enjoys the benefit of having to solve linear sensitivity equations to get the local shape derivatives, and thus is more efficient than the contemporary discrete approaches. The novelty of the proposed work will be (a) establishing the first formulation of CSA for accurate computation of two- and three-dimensional shape derivatives of high-speed flow having discontinuities such as shocks, (b) calculation of derivatives with respect to multiple shape variables at a fraction of the flow or structural analysis cost, and (c) nonintrusive application of the proposed sensitivity method, that is, using black-box programs such as FLUENT to compute high-fidelity sensitivities, better than those currently provided by these software. The broader impact of this work is the ability to gauge effectiveness of multiple designs using the efficient and accurate sensitivity analysis approach. Generally, decisions regarding the shape of high performance systems, such as aircraft structures, are made in the conceptual design phase with use of low to medium fidelity tools. Use of CSA is expected to help avoid late detection of such design flaws that otherwise costs millions of dollars.
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