The primary goal of the 2021 International Symposium on High-Order Methods for Computational Fluid Dynamics (ISHOMCFD-2021) is to enable discussions among the international community of computational mechanics about pacing items of high-order methods for computational fluid dynamics. High-order methods in computational fluid dynamics still face algorithmic and numerical challenges on various levels that prevent their widespread use. The focus of this symposium is on theoretical advances in numerical methods aimed at overcoming these challenges, as well as application demonstrations that stress the limits of high order and identify new challenges. The symposium is organized as a sub-field of the 16th U.S. National Congress (USNCCM16) to be held July 25-29, 2021 in Chicago, CA. The NSF support will cover the conference registration cost for 15 students and 4 postdoc participants. <br/><br/>The proposed international symposium will have strong technological and educational impacts. The symposium will promote scientific discussions among two different scientific communities (engineering CFD and computational mathematics) and potentially create new ideas and new collaborative opportunities. Moreover, the promise of quantum computing will be discussed in this symposium. The NSF funding will promote fruitful discussions among young research students/postdocs and invited senior speakers. We also plan to use the NSF funding to select three outstanding student presenters, and to inspire young researchers of high-order methods for becoming future leaders of computational fluid dynamics and solving real-world problems. In 2015, the PI co-organized a similar symposium and featured 22 outstanding speakers from USA, UK, Japan, China, France, Italy, Germany, and Spain. The 2021 conference is expected to host at least 24 speakers for the ISHOMCFD-2021. In addition, selected presentations will be included in a special issue of Computers & Fluids, an Elsevier journal following the rigorous review process of this journal for all invited manuscripts related to the ISHOMCFD-2021.<br/><br/>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.