High-Speed Compressible Flows

Our group has been at the forefront of pioneering and actively developing two approaches in this field. The first approach focuses on a family of lattice Boltzmann models that preserve the on-lattice streaming, ensuring an efficient and numerically attractive implementation. By including additional populations, carefully designing equilibria, and employing stabilization techniques based on entropy arguments, these models enable the simulation of supersonic flows.

To push the boundaries even further and tackle higher speed and hypersonic flows, we have embarked on a drastic methodology change. Recently, we have successfully reformulated kinetic schemes with adaptive velocity sets, leading to an unprecedented range of achievable Mach numbers and temperature ratios. This innovative approach, known as the Particles on Demand (PonD) method, has undergone rigorous testing across various applications, including multiphase flows, combustion processes, and rarefied regimes, yielding promising results.