Introduction to numerical methods in gas dynamics for fluid machinery

This course investigates the principles and applications of unsteady gas dynamics within the context of turbomachinery. The programme explores the behavior of compressible flow under the high-speed conditions characteristic of modern gas turbines and compressors, with a specific focus on unsteady flow phenomena and the numerical modeling techniques essential for performance optimization.

The curriculum provides a solid foundation in the theory of hyperbolic systems, specifically focusing on the Euler equations of gas dynamics and non-stationary compressible flows. Key topics include the theory of characteristics and its application to conservative systems, as well as the study of Riemann problems, jump relations, and the dynamics of shock waves and expansion fans. Furthermore, the course explores practical applications through a time-dependent gas dynamics problem specifically tailored to the turbomachinery sector. To support these analyses, students will receive advanced training in compiled programming languages, focusing on modern Fortran 90 for high-performance computing. This integration of theoretical gas dynamics and numerical implementation ensures that students are equipped to simulate and optimize high-speed compressible flows in professional and research environments.

By the end of the course, PhD candidates will be able to apply the principles of unsteady gas dynamics and hyperbolic systems of equations to fluid flows in turbomachinery. Participants will gain deep insights into the numerical modeling of complex flow phenomena and develop advanced skills in high-performance computing (HPC) using modern Fortran 90, enabling them to address contemporary engineering challenges in the field.

• De Vanna, F., et al. (2020). A sharp-interface immersed boundary method for moving objects in compressible viscous flows. Computers and Fluids, 201, 104415.
• De Vanna, F., et al. (2021). Unified wall-resolved and wall-modeled method for large-eddy simulations of compressible wall-bounded flows. Physical Review Fluids, 6(3), 034614.
• De Vanna F., et al. (2023). Effect of convective schemes in wall-resolved and wall-modeled LES of compressible wall turbulence, Computers and Fluids
• De Vanna, F., et al. (2023). URANOS: A GPU accelerated Navier-Stokes solver for compressible wall-bounded flows. Computer Physics Communications, 287, 108717.