The chapters presented in this volume correspond to lectures given during the course “Efficient High-Order Discretizations for Computational Fluid Dynamics” that was held at the CISM in Udine, Italy, July 16–20, 2018.
High-order methods have been gaining a lot of momentum during the last decades and are being increasingly deployed in new-generation fluid dynamics solvers. As compared to low-order finite volume methods predominant in today’s production codes, higher order discretizations significantly reduce dispersion and dissipation errors, the main source of error in long-time simulations of flows at higher Reynolds numbers. Furthermore, high-order methods have the potential to better use modern computer hardware by doing more arithmetic operations on cacheable data. Combined with a reduced number of unknowns, they promise to relax the memory transfer and communication limits in well-optimized low-order simulators. This combination makes previously intractable problems accessible to simulation in an increasingly wide range of applications. However, high-order methods are no silver bullet, requiring a careful selection of algorithmic ingredients and implementations.