Unified Flow Solver Research Articles

Kinetic Methods for Solving Unsteady Problems with Jet Flows

The study of nonstationary rarefied gas flows is currently paid much attention. Such interest to these problems is caused by the creation of pulsed jets used for the deposition of thin films and special coatings on solid surfaces. However the problems of nonstationary rarefied gas flows have not been studied sufficiently fully because of their large computational complexity. In this paper the computational aspects of investigating the nonstationary flows of a reflected gas from a wall and flowing through a suddenly formed gap is considering. The objective of this study is to analyze the possible numerical kinetic approaches for solving such nonstationary problems and to identify the difficulties encountered in solving.When studying the gas flows in strong rarefaction regimes one should consider the Boltzmann kinetic equation, but its numerical implementation is rather laborious. In order to use more simple approaches based for example on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference of the solutions of the model equations and the Boltzmann equation. For this purpose two auxiliary problems are considered: reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas. Numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but a strong dependence on the velocity grid step . The detailed velocity grid is necessary to avoid non-monotonous behavior of macroparameters caused by the “ray effect”. To reduce numerical costs on detailed grid a hybrid method based on the synthesis of model equation and the Boltzmann equation is proposed. Such approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The results presented in this paper were obtained using two different software packages Unified Flow Solver (UFS) [13] and Nesvetay 3D [14-15]. Note that UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility of calculating both the Boltzmann equation and model equations is realized. The Nesvetay 3D complex was created to solve the Shakhov model equation, (S-model) and makes it possible to calculate on non-structured non uniform grids in velocity and physical spaces.Translated from Russian. Original text: Mathematics and Mathematical Modeling. 2018. no. 4. Pp. 27-44.

Kinetic Methods for Solving Non-stationary Jet Flow Problems

The study of non-stationary rarefied gas flows is, currently, attracting a great deal of attention. Such an interest arises from creating the pulsed jets used for deposition of thin films and special coatings on the solid surfaces. However, the problems of non-stationary rarefied gas flows are still understudied because of their large computational complexity. The paper considers the computational aspects of investigating non-stationary movement of gas reflected from a wall and flowing through a suddenly formed gap. The study objective is to analyse the possible numerical kinetic approaches to solve such problems and identify the difficulties in their solving. When modeling the gas flows in strong rarefaction one should consider the Boltzmann kinetic equation, but its numerical implementation is rather time-consuming. In order to use more simple approaches based, for example, on approximation kinetic equations (Ellipsoidal-Statistical model, Shakhov model), it is important to estimate the difference between the solutions of the model equations and of the Boltzmann equation. For this purpose, two auxiliary problems are considered, namely reflection of the gas flow from the wall and outflow of the free jet into the rarefied background gas.A numerical solution of these problems shows a weak dependence of the solution on the type of the collision operator in the rarefied region, but at the same time a strong dependence of a behavior of the macro-parameters on the velocity grid step. The detailed velocity grid is necessary to avoid a non-monotonous behavior of the macro-parameters caused by so-called ray effect. To reduce computational costs of the detailed velocity grid solution, a hybrid method based on the synthesis of model equations and the Boltzmann equation is proposed. Such an approach can be promising since it reduces the domain in which the Boltzmann collision integral should be used.The article presents the results obtained using two different software packages, namely a Unified Flow Solver (UFS) [13] and a Nesvetay 3D software complex [14-15]. Note that the UFS uses the discrete ordinate method for velocity space on a uniform grid and a hierarchical adaptive mesh refinement in physical space. The possibility to calculate both the Boltzmann equation and the model equations is realized. The Nesvetay 3D software complex was created to solve the Shakhov model equation (S-model) for calculations based on non-structured non-uniform grids, both in velocity space and in physical one.

Adaptive Kinetic-Fluid Models for Expanding Plasmas

We describe gas dynamic and plasma effects for transient plasma jets under different conditions. Our Unified Flow Solver (UFS) is evaluated for simulations of mixed continuum-rarefied flows, transient gas expansion dynamics and collisionless plasma expansion. We identify further advances that are required for hybrid fluid-kinetic simulations of laser-ablation and EEE-induced plasma jets.

Electrostatic PIC with adaptive Cartesian mesh

We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU–GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24×24×24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.

Complex nonequilibrium flows with slow and fast chemical reactions for simulation processes in open systems

Simulations of flows on the basis of kinetic equations for mixtures with chemical reactions are performed. The nonuniform relaxation problems are solved for different variants. The numerical methods of unified flow solver are used for simulation of 1D and 2D flows with nonequilibrium boundary conditions. The kinetic approach provides results, which are beyond the traditional theory of macroscopic phenomena based on the Navier-Stokes equations. Nonequilibrium flows with anomalous transport properties in relaxation zones are described. A special attention is paid to study of behavior of the nonequilibrium entropy for 1D and 2D cases both for slow and fast chemical reactions and to investigation of it as a measure of complexity of open systems.

Supersonic Flows with Nontraditional Transport Described by Kinetic Methods

AbstractA new class of supersonic nonequilibrium flows is studied on the basis of solving the Boltzmann and model kinetic equations with the aim to consider new non-linear structures in open systems and to study anomalous transfer properties in relaxation zones. The Unified Flow Solver is applied for numerical simulations. Simple gases and gases with inner degrees of freedom are considered. The experimental data related to the influence of the so-called optical lattices on the supersonic molecular beams are considered and numerical analysis of the nonequilibrium states obtained on this basis is made. The nonuniform relaxation problem with these distributions is simulated numerically and anomalous transport is confirmed. The conditions for strong changes of the temperature in the anomalous transfer zones are discussed and are realized in computations.

Simulations of pressure-driven flows through channels and pipes with unified flow solver

The aim of this paper is to demonstrate the benefits of direct methods of solving kinetic equations and adaptive kinetic-fluid solvers for vacuum science and technology. We consider pressure-driven flows through short channels for a wide range of gas rarefaction degrees. Our Unified Flow Solver combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic and fluid solvers in different parts of computational domain. The discrete velocity method is used for direct numerical solution of Boltzmann and model kinetic equations. The advantages of adaptive hybrid method are demonstrated for compressible flows at large pressure gradients. For small pressure drops, direct solutions of the Boltzmann equation provide accurate solutions of rarefied flows not achievable by the traditional direct simulation Monte Carlo methods.

Evaluation of a Hybrid Boltzmann-Continuum Method for High-Speed Nonequilibrium Flows

A series of monatomic gas flows over a cylinder, with a freestream Mach number of 4 and a range of Knudsen numbers, are used to evaluate the unified flow solver (UFS) code. The UFS code combines several compressible gas flow simulation schemes for application to flow problems involving a wide range of Knudsen number (Kn) regimes, and features capabilities for strong coupling between low-Kn and high-Kn schemes along with automatic tree-based grid adaptation. UFS simulation results are compared with results from simulations which employ other codes intended for the same class of problems, and good agreement is generally found. Areas identified for improvement in UFS include calculation of surface quantities and numerical performance of the UFS Boltzmann equation solver.

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang–Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.

Numerical Analysis of Spacecraft Rocket Plume Impingement Under Lunar Environment

A numerical investigation is presented for hypersonic rocket exhaust plume flow over lunar surface, a problem offering limited experimental data and significant challenges to computational models in practice. In this paper, examinations on the accuracy of a hybrid continuum-rarefied flow simulation method (unified flow solver) demonstrated close agreements against experimental data for plume shock structures under vacuum conditions and the associated force exerted on the impingement surface. The unified flowmodeling approach is then used to resolve the physics of plume expansion under lunar environment, seamless flow transition from continuum to rarefied regime, and the corresponding plume–surface interactions. Analysis of the lander descent action or the plume impingement height revealed significant consequences on the characteristics of supersonic boundary layer, and resulting surface force distributions ranging from near-plume to the far-field observations.

Entropy-Shock Interactions Using the Unified Flow Solver

The unified flow solver, a hybrid continuum-rarefied code, is used to investigate the structure of a normal shock wave as an entropy perturbation is introduced upstream of the shock and allowed to propagate through the shock. The entropy spot is introduced into a two-dimensional domain over a range of Knudsen numbers (Kn = 0.01, 0.1, and 1.0) for Mach 2.0 in argon. Previous work on entropy-shock interactions has only been reported with an Euler-solution-method scheme. Here, results are presented in argon, using coupled Bhatnagar-Gross-Krook and Navier-Stokes solvers, using the hybrid nature of the unified flow solver code for a better examination and understanding of the propagation of entropy disturbances. Density, pressure, and temperature profiles, as well as the profiles of their gradients, are reported at discrete intervals after the entropy spot convects through the shock.

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.

Construction of a Unified Continuum/Kinetic Solver for Aerodynamic Problems

We describe our progress toward the development of a unified flow solver (UFS) that can automatically separate nonequilibrium and near-equilibrium domains and switch between continuum and kinetic solvers to combine the efficiency of continuum models with the accuracy of kinetic models. Direct numerical solution of the Boltzmann transport equation is used in kinetic regions, whereas kinetic schemes of gas dynamics are used elsewhere. The efficiency and numerical stability of the UFS is attained by using similar computational techniques for the kinetic and continuum solvers and by employing intelligent domain decomposition algorithms. Different criteria for identifying kinetic and continuum areas and two different mechanisms of coupling Boltzmann and Euler solvers are explored. Solutions of test problems with small Knudsen number are presented to illustrate the capabilities of the UFS for different conditions. It is shown that the UFS can automatically introduce and remove kinetic patches to maximize the accuracy and efficiency of simulations. To our knowledge, this is the first attempt to use direct Boltzmann and continuum flow solvers for developing a hybrid code with solution adaptive domain decomposition.