A. A. Frolova

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.

Analysis of Compressible Viscous Flow Solvers with Adaptive Cartesian Mesh

This paper reports an analysis of compressible Navier-Stokes (NS) solvers with adaptive Cartesian mesh. A particular focus is on performance and grid requirements for these solvers for problems of viscous flows past blunt bodies under different conditions. We find that the immersed boundary method (IBM) for the treatment of embedded solid surfaces offers great improvements for calculation of skin friction and heat fluxes for external flows in comparison with the cut-cell methods. To improve the performance of the implemented NS solvers, we propose special methods of automatic meshing around the solid objects. The methods include building layered meshes around the surfaces and employing meshes whose solid refinement levels increase during a simulation. We find that to obtain grid converged results similar grid resolution is required for the implemented NS solvers and those using body-conforming meshes and that this resolution can be determined in terms of cell Reynolds number. We compare the traditional NS schemes, gas-kinetic and hybrid traditional-kinetic schemes for different flow regimes. Comparison with analytical solutions, experimental data and results obtained NS solvers with body-conforming meshes show that compressible viscous flow solvers with adaptive Cartesian mesh offer viable alternative to the conventional CFD methods.

Boltzmann Solver with Adaptive Mesh in Velocity Space

We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow‐kernel distributions.

Immersed Boundary Method for Boltzmann and Navier‐Stokes Solvers with Adaptive Cartesian Mesh

Adaptive Cartesian mesh methods have demonstrated unique abilities for automated mesh generation and dynamic mesh adaptation to flow solution and moving boundaries. However Navier‐Stokes (NS) solvers with Cartesian mesh often produce large fluctuations of surface quantities (pressure, skin friction, and heat flux) at solid boundaries. We show that the Immersed Boundary Method (IBM) with adaptive octree Cartesian mesh allows one to eliminate unphysical fluctuations of skin friction and heat flux at solid boundaries for viscous flow simulations. Implementation of IBM for deterministic Boltzmann solvers with adaptive Cartesian mesh is described.

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.

Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.