CAREER: Simulation-Enhanced Virtual Design Environments for Fluid Systems

这项教师早期职业发展（Career）资助旨在使流体系统的设计更直观、更容易获得、更便宜。流体系统，如飞机、生物医学泵或涡轮机，在美国经济的许多部门发挥着至关重要的作用。由于流体流动的复杂物理特性，这些系统通常设计困难且成本高昂。这对寻求开发涉及如此复杂流体流动的产品的初创公司构成了障碍。流体流动的复杂性也给工程教育带来了障碍，学生往往很难对流体流动产生直觉。为了消除这些障碍，该奖项设想了一个沉浸式的虚拟现实设计环境，在这个环境中，工程师可以与飞机或心脏泵互动，就像艺术家与粘土互动一样。这一愿景的一个关键要求是能够在工程师塑造虚拟设计时为他们提供即时的性能预测。该奖项将有助于建立复杂流体流动实时预测所需的知识，从而为沉浸式计算机辅助设计和工程教育提供下一代工具。由于控制方程的非线性和高保真仿真的高成本，快速准确地预测流体系统的初步设计性能仍然是一个挑战。降阶模型提供了一种合适的替代方法，因为它们有可能显著降低计算成本，而准确性只会有很小的降低。该奖项所探索的创新是创建降阶模型，以实现工程师通常感兴趣的边界量（例如升力和阻力）的高精度，而不是对整体流量的高精度。具体而言，研究小组将研究基于伴随的基函数来构建适合于预测此类边界积分的降阶模型。在利用降阶模型找到初步设计方案后，可采用基于高保真度模型的数值优化来细化设计参数。在这里，数值误差估计和控制尤其重要，因为优化算法可能利用数值误差而不是物理来优化感兴趣的数量。本研究将探索同时使用几何和网格优化作为解决误差控制的一种手段。最后，在优化之后，工程师可能需要探索设计空间，以满足定性约束或考虑权衡。研究团队将测试无矩阵谱方法可以重新参数化和近似设计空间的假设，这样工程师就可以在不显著影响最优性和可行性的情况下进行实时更改。

This Faculty Early Career Development (CAREER) grant aims to make the design of fluid systems more intuitive, accessible, and inexpensive. Fluid systems, such as aircraft, biomedical pumps, or turbines, play a vital role in many sectors of the U.S. economy. Due to the complex physics of fluid flow, these systems are often difficult and costly to design. This presents a barrier to start-up companies seeking to develop products that involve such complex fluid flows. The complicated nature of fluid flows also poses a barrier in engineering education, where students often struggle to achieve intuition regarding fluid flows. To mitigate these barriers, this award envisions an immersive, virtual-reality design environment in which engineers can interact with aircraft or heart pumps in the same way artists interact with clay. A key requirement of this vision is the ability to provide engineers with instantaneous performance predictions as they shape their virtual designs. This award will help build the knowledge necessary for real-time prediction of complex fluid flows, thereby enabling the next generation of tools for immersive computer-aided design and engineering education.Predicting the performance of fluid systems quickly and accurately for preliminary design remains a challenge due to the nonlinearity of the governing equations and the large cost of high-fidelity simulations. Reduced-order models provide a suitable alternative approach, since they have the potential to significantly reduce computational cost with only a small reduction in accuracy. The innovation explored in this award is to create reduced-order models that achieve high accuracy for boundary quantities that engineers are typically interested in, e.g., lift and drag, rather than high accuracy for the overall flow. Specifically, the research team will investigate adjoint-based basis functions to construct reduced-order models suitable for prediction of such boundary integrals. After using the reduced-order model to find a preliminary design, a numerical optimization based on a high-fidelity model can be applied to refine the design parameters. Here, numerical error estimation and control is especially important, because an optimization algorithm may exploit numerical errors rather than physics to optimize the quantity of interest. This research will explore the use of simultaneous geometry and mesh optimization as a means of addressing error control. Finally, after optimization, an engineer may need to explore the design space in order to meet qualitative constraints or consider tradeoffs. The research team will test the hypothesis that matrix-free spectral methods can re-parameterize and approximate the design space in such a way that engineers can make real-time changes without significantly impacting optimality and feasibility.