Research

Research plays a vital role in pushing the boundaries of our knowledge of a particular subject/field. Unlike homework for your coursework, research projects do not usually end when you reach their deadlines and do not have "true" answers that are known a priori. Furthermore, since the purpose of research is to extend our knowledge, you will run into roadblocks, and the process of overcoming these roadblocks might take months or even years. As a Ph.D. student, you will spend a significant portion of your daily life working on your research project(s). So, before you enroll in a doctoral program, make sure that you find your research interest and choose your doctoral research topic, research advisor, and research group wisely!!! From experience, I can tell you that working on something you love and getting along with people in your research group will make your doctoral study much more productive and enjoyable.

Here, you can find information on my research interests and background. Details on my research lab can be found here.

Computational Fluid Dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that harnesses computing power to analyze and study fluid flow problems. Strong background in mathematics, sciences, and computer programming is essential for the development and advancement of CFD. In aerospace engineering, CFD is known for significantly reducing the number of expensive wind tunnel tests required for new aircraft designs in the early 1990s. In recent years, CFD has become one of the core tools for multidisciplinary design optimization of new, unconventional aircraft configurations. Additionally, CFD enables us to analyze flows that are hard to produce or visualize experimentally, such as analysis of atmospheric contaminant transport and visualization of turbulent flows generated by small parts of a race car. Despite decades of CFD development and its prevalent use in industry, CFD is not yet mature. More in-depth understanding and various improvements in many aspects of CFD are necessary for CFD to make a broader impact on the overall aircraft development process.

High-order CFD methods

The emerging popularity of research in high-order CFD methods is primarily motivated by the prospect of obtaining more accuracy at a lower cost than low-order methods. In aerospace engineering, CFD methods with third-order accuracy or higher are high-order. Today, the industry standard for production-level CFD codes is second-order accurate, and high-order methods are still far from ready to become the new industry standard. Compared to second-order methods, high-order methods are inherently more complex and less robust, and they might require large memory when implicit time stepping is used. Thus, extra care is needed before we can take full advantage of high-order methods. Moreover, high-order methods require high-order meshes to perform at their best. Our research focuses on high-order, finite-element methods, namely the discontinuous Galerkin (DG) method.

Output-based error estimation

The ability to obtain accurate error estimates is crucial for improving the reliability and robustness of CFD. While error estimation is usually presented as a key ingredient in adaptive CFD, error estimates are valuable even when adaptation is not employed. These error estimates tell us how trustworthy and reliable our prediction is. Our research focuses on a posteriori error estimation, specifically the dual-weight residual (DWR) method for output-based error estimation.

Adaptive CFD framework

The idea of an adaptive CFD framework is adopted from control theory, in which a feedback loop gradually decreases the error between the process output and the desired output. A general adaptive CFD framework is illustrated below, with similarities to a closed-loop controller highlighted.

Our research focuses on improving current mesh adaptation methods, formulating novel mesh adaptation/refinement techniques, and developing automated mesh adaptation/optimization/generation strategies for high-performance computing.

High-Performance Computing (HPC)

The rapid advance of computing power and the growing accessibility of affordable HPC systems to a wider scientific community during the last several decades have motivated the vast development of computational sciences, including CFD. As HPC systems evolve, revolutionary algorithmic improvements are needed to efficiently use these HPC systems and to obtain more accurate solutions. Our research focuses on improving automation in the CFD workflow and developing fast, robust, and accurate CFD algorithms that take advantage of modern HPC architectures.

Past and Current Projects

High-Order Mesh Optimization Strategies

Our current state-of-the-art meshing procedures are unquestionably far from ideal. Human intervention and expert knowledge are almost always required, and even if this is acceptable by our current standard, it often causes robustness issues, jeopardizes the accuracy of the simulations, and is simply inadequate for high-performance computing. In this work, we consider solution-based mesh optimization, metric-based mesh optimization, and machine learning approaches to find the optimal locations of elements' vertices within the computational domain and adjust the locations of high-order geometry nodes within each mesh element accordingly without human intervention.

Warped-Element Refinement Method (q-adaptation)

This refinement/adaptation method aims to strategically place the high-order geometry nodes of a mesh element such that the errors in solution approximations, engineering output predictions, or metric approximations are minimized. Some clustering of the high-order geometry nodes within an element is permitted as long as the validity of the element is maintained. The resulting (adapted) mesh contains warped elements in the regions where complex geometries, important flow features, and/or high error estimates are present. Here, we refer to the warping of mesh elements as the changes in the inner shape of the elements; the edges (outer shape) of the mesh elements and the locations of the vertices in the initial mesh remain unchanged.

Supersonic (M=3) , inviscid flow past a cylinder

Flow (Re = 1000) in a moving and deforming cylinder [A test case presented in the High-Fidelity CFD Workshop 2022: Mesh Motion]

Global High-Order Mesh Optimization

This study aims to capture the global coupling between the vertex and high-order geometry node locations and gain full control of the shape and size of mesh elements. The new methodologies developed to solve global high-order mesh optimization will be embedded in an adaptive, CFD framework that can handle a variety of governing equations and engineering output (e.g., lift or drag) predictions.

Statistical Inversion of Atmospheric Contaminant Transport

Consider a scenario where a contaminant was accidentally released in an urban environment, and the contaminant diffuses and convects with the wind. In this stressful and life-threatening situation, real-time modeling and inversion of the contaminant release event are extremely valuable in assisting the decision-making process. The goal of this work is to formulate statistical algorithms based on Markov Chain Monte Carlo (MCMC) methods for efficiently solving large-scale contaminant source inversion problems. To significantly reduce the computational time, we consider two strategies: 1) discrete adjoint solutions are pre-computed in an offline stage and are used to directly evaluate samples, and 2) a Kriging forward emulator is used to calculate the individual forward solutions during the MCMC process. Furthermore, to address the deterioration of statistical sampling efficiency for anisotropic posteriors, we present an application of an ensemble MCMC method. Results for two- and three-dimensional problems demonstrate the feasibility of statistical inversion for large-scale problems and show the advantage of statistical results over single-point deterministic results.

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