Vladimir Aristov

Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

This paper describes a Unified Flow Solver (UFS) for rarefied and continuum gas flows. The UFS separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models. The direct numerical solution of the Boltzmann transport equation is used in rarefied regions, while kinetic schemes of continuum fluid dynamics are used elsewhere. Using similar computational techniques for the kinetic and continuum solvers, and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the UFS. Solutions of test problems are presented to illustrate the capabilities of the UFS for high and low speed flows. It is shown that the UFS can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed.

A steady state, supersonic flow solution of the Boltzmann equation☆

Abstract Nonclassical effects which appear in the supersonic nonequilibrium gas flow of a nonuniform relaxation described by the Boltzmann equation are studied. For such a flow, in particular, the heat flux and the temperature gradient have the same signs. Analytical and numerical results are presented. Possible experimental verification is discussed.

A new effect of the nongradient transport in relaxation zones

The nontraditional transfer properties in the spatially nonuniform relaxation regions are studied by the methods of kinetic theory applied to gas mixtures and gases with inner degrees of freedom. Direct numerical methods for solving the Boltzmann and kinetic model equations are used. The influence of the nonequilibrium boundary distribution functions and consequently of boundary fluxes of dissipative values on the gradients of some moments is studied. It is found that in the relaxation zones which are formed by the supersonic nonequilibrium boundary conditions the gradients of velocity and temperature can have the same signs as the appropriate component of the nonequilibrium stress tensor and heat flux, respectively, which is an example of the nongradient transport differing from the classic Stokes and Fourier transport. The physical sense of this formulation of the problem is discussed. 1D and 2D nonuniform relaxation problems are considered and examples of the anomalous transport are presented.

Nonequilibrium kinetic processes with chemical reactions and complex structures in open systems

The study of the nonequilibrium distributions in open systems with complex kinetic processes is performed. The nonuniform relaxation problems (NRP) are solved. Previous solutions of NRP have demonstrated nonclassical transfer properties in the relaxation zones for monatomic simple gases, for mixtures of simple gases and for molecular gases. In the present paper for the first time more complex structures for mixtures of four chemically reacting gases are investigated by means of kinetic model equations. Nonclassical effects are observed in simulations. It is discussed how this can allow us to simulate properties of complex nonequilibrium systems and, in particular, the role of the nonequilibrium entropy (−H-function) is also considered.

Acceleration of Deterministic Boltzmann Solver with Graphics Processing Units

GPU‐accelerated computing of the Boltzmann collision integral is studied using deterministic method with piecewise approximation of the velocity distribution function and analytical integration over collision impact parameters. The acceleration of 40 times is achieved compared to CPU calculations for a 3D problem of collisional relaxation of bi‐Maxwellian velocity distribution.

Parallel algorithms of direct solving the Boltzmann equation in aerodynamics problems

Publisher Summary This chapter describes the possibilities of parallel algorithms for directly solving Boltzmann equations with different numerical schemes. Two decomposition methods for parallelization in physical and velocity spaces are applied. Simulations of 2D and 3D jet flows with these parallel schemes are carried out on distributed memory parallel computers in a wide range of Knudsen numbers. The most interesting results concern the behavior at small Knudsen numbers, especially instability in a mixing layer. The main idea of the direct approach is to use the schemes of the kinetic equation, which are applied directly for aerodynamics complex flows with zones of different rarefaction. These parallel algorithms for multiprocessor computers with distributed memory allow resolving the fine structure of free jet flow. One can expect to study the unstable structure of supersonic jets from upstream Taylor-Goertler type vortices until a structure of small unsteady vortices downstream.

The possibility of anomalous heat transfer in flows with nonequilibrium boundary conditions

The kinetic Boltzmann equation has been solved for the boundary-value problem of heat transfer with boundary conditions in the form of nonequilibrium distributions. Modes with anomalous heat transfer have been revealed in the spatial zones where the signs of the heat flux and temperature gradient coincide (in the classical statement of the problem with equilibrium conditions, heat transfer conventionally occurs in the entire range of physical parameters). Possible experiments aimed at verifying these effects are discussed.

Unified flow solver for transient rarefied-continuum flows

A Unified Flow Solver (UFS) is demonstrated for simulations of transient rarefied-continuum flows. Three specific problems are considered: shock wave penetration into a narrow channel (pipe), propagation and attenuation of a large-scale initial pressure discontinuity inside a long channel (pipe), and gas evacuation though a short pipe from a small high-pressure chamber into a large chamber at initially low pressure. The benefits of Adaptive Mesh and Algorithm Refinement of the UFS are demonstrated for solving the considered class of problems in 2D and 3D geometries. Parallel capabilities of UFS are illustrated. A (partially) implicit scheme is implemented for model kinetic equation to enable acceleration of transient problems characterized by different time scales.

Kinetic Effects for Couette Flows with Oscillating Walls

Oscillating Couette flow problem is studied for a wide range of Knudsen, Mach and Stokes numbers. From analysis of the free molecular solution, we obtained collisionless boundary layer of thickness proportional to the mean thermal velocity of the gas particles and inversely proportional to frequency of the wall oscillations. This boundary layer is quite different from the viscous layer formed near oscillating wall in the collisional regime, which is described by the Navier‐Stokes equations. The velocity profiles in the boundary layers obtained from numerical solution of the Boltzmann and Navier‐Stokes equations deviate considerably from each other when the boundary layer thickness becomes comparable or smaller than the mean free path. Considerable gas heating occurs when the wall velocity becomes comparable or larger than thermal velocities of the gas particles. In this case, large heat fluxes in both normal and longitudinal directions with respect to the wall have been obtained in our free‐molecular solu...

Multi-scale Simulations of Gas Flows with Unified Flow Solver

The Boltzmann kinetic equation links micro- and macroscale descriptions of gases. This paper describes multi-scale simulations of gas flows using a Unified Flow Solver (UFS) based on the Boltzmann equation. A direct Boltzmann solver is used for microscopic simulations of the rarefied parts of the flows, whereas kinetic CFD solvers are used for the continuum parts of the flows. The UFS employs an adaptive mesh and algorithm refinement procedure for automatic decomposition of computational domain into kinetic and continuum parts. The paper presents examples of flow problems for different Knudsen and Mach numbers and describes future directions for the development of UFS technology.