Particles-On-Demand for multiscale fluid dynamics
Computational fluid dynamics achieved undeniable success in many sectors of flowing matter. However, with the variety of different physical phenomena involved, also the computational methods have specialized and a uniform platform for high-quality simulations has long been in pursuit. With its roots in kinetic theory and statistical mechanics, the lattice Boltzmann method was conceived as an alternative paradigm for fluid dynamics but only partially succeeded in a subclass of incompressible flows. The reasons for that are structural: fixed particles’ velocities in traditional approaches imply rigid constraints on Mach number and temperature in the simulations, and which can only be mitigated at a price of ever increased number of particles’ speeds. A novel formulation of fluid dynamics as a kinetic theory with a small number of tailored, on-demand constructed particles removes any restrictions on flow speed and temperature as compared the lattice Boltzmann methods and their modifications. Particles-on-Demand method is a disruptive change of perspective on computational fluid dynamics through kinetic theory that opens up an unprecedented wide domain of applications, and for the first time delivers a seamless and universal computing of any type of flow, from high Knudsen number rarefied gas to supersonic flow and turbulence. Our approach is inherently physical and rigorous, with kinetic theory translated onto a fully discrete framework in position, momentum, time and space system. Particle-on-Demand shall deliver new solutions to hypersonic flows involving fluid-structure interaction and makes it easy to incorporate mixing and chemical reactions. The strength and universality of PonD method shall be demonstrated with simulations of a wide spectrum of multiscale problems such as atmospheric reentry, geostrophic turbulence, micro-flows and multiphase flow.