A Concept to Eliminate the Meshing Bottleneck During the Design and Analysis of Fluid Systems

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The proper function of many systems vital to the United States' economy, defense, and national health depend on fluid flow (i.e., the flow of a liquid or gas). Examples of such systems include commercial and military aircraft, automobile engines, wind turbines, and heart pumps. Fluid systems are characterized by unintuitive physics, which makes them exceptionally difficult to design. This difficulty is particularly acute during the conceptual design of unconventional fluid systems, for which experimental data and engineering experience is lacking. In principle, engineers could use numerical simulations to analyze innovative fluid systems, but high-fidelity simulations have found limited use during conceptual design. Why? Flow simulations typically rely on meshes, which divide the region occupied by the fluid into many smaller volumes, and generating high-quality meshes for complex geometries remains a time-consuming, human-in-the-loop process. This research will investigate a fundamentally new approach to mitigate the meshing bottleneck and thereby improve the fluid system design process. Project outcomes will include novel algorithms and prototype implementations of the algorithms that will be made available in an online repository. The research project will study a novel immersed-boundary method and its application to design optimization. The key insight is to frame the immersed-boundary method as an inverse problem. The idea is to introduce a body force, or surface flux, interior to the geometry that acts like a control variable to impose the boundary conditions. The optimal value for this control is determined by solving a partial-differential-equation constrained inverse problem. This approach is attractive for the analysis of fluid systems during conceptual design, because the computational mesh does not need to conform to the geometry. Furthermore, unlike most immersed-boundary methods, this project's approach remains accurate and is compatible with high-order discretizations. To assess the potential of the concept, the project will investigate several critical questions: among alternative inverse-problem formulations, which one is the best? How should the problem be regularized? How do we solve the inverse problem efficiently? How robust and accurate is the concept when applied to imperfect CAD geometries? And, how can the method be used to advance shape optimization algorithms?This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.