Derivation of computational kinetic models to include new physics:
PonD formulation of kinetic theory was extended to compressible non-ideal fluids. This enabled, for the first time, simulation of compressible multiphase flow, including supersonic regimes, such as droplet-shock wave interaction and supercritical flow at high pressure.
This line of research has led us to a rigorous formulation of kinetic models for multiphase flows with phase transitions, starting with the fundamental statistical mechanics picture of particles interaction and performing meaningful steps of reduction to a model with a finite number of discrete speeds. This approach enabled simulations with realistic density contrast between liquid and its vapor, for the first time performing dynamic simulations of droplets coalescence of heavy liquid as mercury.
Multi-component model for fully compressible flow, enabling the realistic Stefan-Maxwell diffusion for the first time in the discrete velocities setting was first proposed.
This model was extended to include detailed chemical reactions, and was realized with nontrivial benchmarks such as various flame regimes in a microchannel.
Simulations of detonation at high Mach numbers were demonstrated within the PonD framework.
Compressible flow models with the standard (minimal) number of discrete velocities enabling mildly supersonic flow simulations were developed. These models were designed with the idea of high computational efficiency that parallels the classical lattice Boltzmann model. The success of the new kinetic model has led to utilizing it with the aforementioned multi-component and multi-phase formulations.
Realization of fluid-solid interaction with moving rigid bodies was also achieved.
Particles-on-Demand method development:
In contrast to the conventional lattice Boltzmann method, PonD operates with discrete velocities that do not, in general, form a regular lattice.
The reason for this is that, in PonD, discrete velocities are constructed relative to a local reference frame of the flow rather than with respect to a global fixed reference frame as in the lattice Boltzmann model.
The necessity of the adaptive (on-demand) discrete velocities is the feature of PonD enabling arbitrary large flow speeds.
Hence, as with any off-lattice velocities, PonD realization was performed in a variety of settings of particles propagation (semi-Lagrangian, finite difference and finite volume) in order to optimize performance.
In particular, a robust finite-volume formulation was adopted for the consequent exploration thanks to its rigorous conservative properties, stability and efficiency.
With this, simulations of hypersonic flows, such as astrophysical jet at Mach number 80 (see figure for illustration) were achieved.
Extensive testing of performance was conducted on a number of benchmark problems including Richtmyer-Meshkov instability of shock wave, near-vacuum flows, shock diffraction at a corner and others.
Moreover, PonD has been realized within a multi-scale simulation strategy using an adaptive number of discrete velocities in a single simulation.
This sets up yet another degree of freedom in optimization of PonD applications, especially for the rarefied gas nonequilibrium flows
