Periodic Reporting for period 2 - PonD (Particles-on-Demand for Multiscale Fluid Dynamics)
Période du rapport: 2021-03-01 au 2022-08-31
Whether predicting the turbulent motion of boiling water, next week’s weather, or future energy production technologies, the varied consequences of fluid motions on human activity are undeniable.
Computational fluid dynamics strives to predict the flow behavior on the basis of mathematical formulations of their laws of motion, and has achieved undeniable success in many sectors of flowing matter. However, with the variety of different physical phenomena involved, the computational methods have specialized and a uniform platform for high-quality simulations has long been pursued.
The lattice Boltzmann method was conceived as an alternative paradigm for fluid dynamics. With its basis in kinetic theory and statistical physics, the lattice Boltzmann method realizes the complex flow dynamics such as turbulence with a simple representation of designer particles, with only a handful of discrete velocities, streaming and colliding on a lattice. The lattice Boltzmann computations received wide acceptance by fluid dynamics community, including industrial applications such as automotive design. However, the lattice Boltzmann method has been successful only in the domain of slow flows, with characteristic speeds well below the speed of sound. The reasons for that are structural: fixed velocities of particles in the traditional approach impose rigid constraints on Mach number, temperature and pressure in the simulations, and these can only be mitigated at a cost of ever-increasing number of particles. Therefore, applications such as super- and hyper-sonic flows, constituting important sector of industrial applications, remained essentially out of reach for the otherwise promising lattice Boltzmann methods.
A novel formulation of fluid dynamics as a kinetic theory with a small number of tailored, on-demand constructed discrete velocities removes the restrictions on flow speed and temperature when compared to the lattice Boltzmann methods and their modifications. The Particles-on-Demand method (PonD) is a complete 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 and hypersonic 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. Particles on demand shall deliver new solutions to hypersonic flows involving fluid-structure interaction and will make it easy to incorporate chemical reactions and multiple phases. The strength and universality of the 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.
Computational fluid dynamics strives to predict the flow behavior on the basis of mathematical formulations of their laws of motion, and has achieved undeniable success in many sectors of flowing matter. However, with the variety of different physical phenomena involved, the computational methods have specialized and a uniform platform for high-quality simulations has long been pursued.
The lattice Boltzmann method was conceived as an alternative paradigm for fluid dynamics. With its basis in kinetic theory and statistical physics, the lattice Boltzmann method realizes the complex flow dynamics such as turbulence with a simple representation of designer particles, with only a handful of discrete velocities, streaming and colliding on a lattice. The lattice Boltzmann computations received wide acceptance by fluid dynamics community, including industrial applications such as automotive design. However, the lattice Boltzmann method has been successful only in the domain of slow flows, with characteristic speeds well below the speed of sound. The reasons for that are structural: fixed velocities of particles in the traditional approach impose rigid constraints on Mach number, temperature and pressure in the simulations, and these can only be mitigated at a cost of ever-increasing number of particles. Therefore, applications such as super- and hyper-sonic flows, constituting important sector of industrial applications, remained essentially out of reach for the otherwise promising lattice Boltzmann methods.
A novel formulation of fluid dynamics as a kinetic theory with a small number of tailored, on-demand constructed discrete velocities removes the restrictions on flow speed and temperature when compared to the lattice Boltzmann methods and their modifications. The Particles-on-Demand method (PonD) is a complete 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 and hypersonic 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. Particles on demand shall deliver new solutions to hypersonic flows involving fluid-structure interaction and will make it easy to incorporate chemical reactions and multiple phases. The strength and universality of the 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.
Within the period covered by this report, the work was performed in two main direction.
Derivation of computational kinetic models to include new physics:
PonD formulation of kinetic theory was extended to two-phase nonideal 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.
First simulations of simplified models of detonation at high Mach numbers were also 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 optimization:
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
Derivation of computational kinetic models to include new physics:
PonD formulation of kinetic theory was extended to two-phase nonideal 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.
First simulations of simplified models of detonation at high Mach numbers were also 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 optimization:
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
Particles-on-demand method, as a novel formulation of computational fluid dynamics, has already demonstrated its capabilities beyond state-of-the-art lattice Boltzmann method by enabling simulations at very high flow speeds, temperature and pressure variations. Until the end of the project, PonD shall also be highly optimized to bring its performance as close as possible to that of the lattice Boltzmann standards. Current work in this direction is supplemented with the development of the full fluid-structure interaction in the framework of the immersed boundary approach. We shall also explore modern optimization techniques based on artificial intelligence in order to train particles-on-demand to find optimal flow reference frames.
The new kinetic models, which were introduced in the first half of the project in the multi-component reactive and multi-phase sectors of flow physics shall be used both in the PonD and the more familiar lattice Boltzmann settings to study phenomena such as detonation and atmospheric re-entry problem, detailed simulation of diffusive transport of species in a fuel cell and liquid droplets interaction with non-wettable surfaces.
Finally, the third avenue of research is the nonequilibrum rarefied gas flow. PonD is closely related to the models of the Boltzmann equation, and has already shown good performance in the simulation of the nonequilibrium shock waves. On this line, we shall perform a rigorous study of the hydrodynamic limit of kinetic models related to the Boltzmann equation in order to achieve a wider application domain of the PonD method, targeting not only continuum flows but also highly rarefied gas flows pertinent to upper atmosphere.
The new kinetic models, which were introduced in the first half of the project in the multi-component reactive and multi-phase sectors of flow physics shall be used both in the PonD and the more familiar lattice Boltzmann settings to study phenomena such as detonation and atmospheric re-entry problem, detailed simulation of diffusive transport of species in a fuel cell and liquid droplets interaction with non-wettable surfaces.
Finally, the third avenue of research is the nonequilibrum rarefied gas flow. PonD is closely related to the models of the Boltzmann equation, and has already shown good performance in the simulation of the nonequilibrium shock waves. On this line, we shall perform a rigorous study of the hydrodynamic limit of kinetic models related to the Boltzmann equation in order to achieve a wider application domain of the PonD method, targeting not only continuum flows but also highly rarefied gas flows pertinent to upper atmosphere.