arXiv subjects

Tianbai Xiao

Publications and source records attributed to Tianbai Xiao.

24 records · Page 2Linked to original sources

arXiv2020

Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification

In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field solutions and real-world physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opportunities and challenges to develop both sound theories and reliable multi-scale algorithms. In this paper, we study the stochastic behavior of multi-scale gas dynamic systems, especially focusing on the non-equilibrium effects. The theoretical analysis is presented on the basis of kinetic model equation and its upscaling macroscopic system, with the reformulation from the stochastic Galerkin method. A newly developed stochastic kinetic scheme is employed to conduct numerical simulation of homogeneous relaxation, normal shock structure, shear layer and lid-driven cavity problems. Different kinds of uncertainties are involved in conjunction with the gas evolutionary processes. New physical observations, such as the synergistic propagation pattern between mean fields and uncertainties, sensitivity of different orders of uncertainties, and the influence of boundary effects from continuum to rarefied regimes, will be identified and analyzed theoretically. The paper serves as a heuristic study of quantifying the uncertainties within multi-scale flow dynamics.

physics.comp-ph↗

arXiv2020

A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification

In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type relaxation model of the multi-component Boltzmann equation, a scale-dependent kinetic central-upwind flux function is designed in both physical and particle velocity space, and the governing equations in the discrete temporal-spatial-random domain are constructed. By solving Maxwell's equations with the wave-propagation method, the evolutions of ions, electrons and electromagnetic field are coupled throughout the simulation. We prove that the scheme is formally asymptotic-preserving in the Vlasov, magnetohydrodynamical, and neutral Euler regimes with the inclusion of random variables. Therefore, it can be used for the study of multi-scale and multi-physics plasma system under the effects of uncertainties, and provide scale-adaptive physical solutions under different ratios among numerical cell size, particle mean free path and gyroradius (or time step, local particle collision time and plasma period). Numerical experiments including one-dimensional Landau Damping, the two-stream instability and the Brio-Wu shock tube problem with one- to three-dimensional velocity settings, and each under stochastic initial conditions with one-dimensional uncertainty, will be presented to validate the scheme.

physics.comp-ph↗

arXiv2020

A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification

Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opportunities and challenges to develop both sound theories and reliable multi-scale numerical algorithms. In this paper, a new stochastic kinetic scheme will be developed that includes uncertainties via a hybridization of stochastic Galerkin and collocation methods. Based on the Boltzmann-BGK model equation, a scale-dependent evolving solution is employed in the scheme to construct governing equations in the discretized temporal-spatial domain. Therefore typical flow physics can be recovered with respect to different physical characteristic scales and numerical resolutions in a self-adaptive manner. We prove that the scheme is formally asymptotic-preserving in different flow regimes with the inclusion of random variables, so that it can be used for the study of multi-scale non-equilibrium gas dynamics under the effect of uncertainties. Several numerical experiments are shown to validate the scheme. We make new physical observations, such as the wave-propagation patterns of uncertainties from continuum to rarefied regimes. These phenomena will be presented and analyzed quantitatively. The current method provides a novel tool to quantify the uncertainties within multi-scale flow evolutions.

physics.comp-ph↗

arXiv2018

A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows

In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow regions, particle distribution function is close to the Chapman-Enskog expansion and can be formulated with a continuous velocity space, where only macroscopic conservative variables are updated. With the emerging of non-equilibrium effects, the AUGKS automatically switches to a discrete velocity space to follow the evolution of particle distribution function. Based on the Chapman-Enskog expansion, a criterion is proposed in this paper to quantify the intensity of non-equilibrium effects and is used for the continuous-discrete velocity space transformation. Following the scale-dependent local evolution solution, the AUGKS presents the discretized gas dynamic equations directly on the cell size and time step scales, i.e., the so-called direct modeling method. As a result, the scheme is able to capture the cross-scale flow physics from particle transport to hydrodynamic wave propagation, and provides a continuous variation of solutions from the Boltzmann to the Navier-Stokes. Under the unified framework, different from conventional DSMC-NS hybrid method, the AUGKS does not need a buffer zone to match up kinetic and hydrodynamic solutions. Instead, a continuous and discrete particle velocity space is naturally connected, which is feasible for the numerical simulations with unsteadiness or complex geometries. Compared with the asymptotic preserving (AP) methods which solves kinetic equations uniformly over the entire flow field with discretized velocity space, the current velocity-space adaptive unified scheme speeds up the computation and reduces the memory requirement in multiscale flow problems, and maintains the equivalent accuracy. The AUGKS provides an effective tool for non-equilibrium flow simulations.

physics.comp-ph↗

arXiv2017

An investigation of non-equilibrium heat transport in a gas system under external force field

The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes equations, are valid in their respective modeling scales, and it is challenging for the modeling and computation of a multiple scale problem across different regimes and capture the corresponding non-equilibrium flow physics. Based on the direct modeling of conservation laws in the discretized space, a well-balanced unified gas-kinetic scheme (UGKS) for multiscale flow transport under external force field has been developed and is used in the current study of non-equilibrium gaseous flow under external force field. With the variation of modeling scale, i.e., the cell size and time step, the UGKS is able to recover cross-scale flow physics from particle transport to hydrodynamic wave propagation. Theoretical analysis based on the kinetic model equation is presented to conceptually illustrate the effects of external force on the non-equilibrium heat transport.

physics.flu-dyn↗

arXiv2016

A Well-Balanced Unified Gas-Kinetic Scheme for Multiscale Flow Transport Under Gravitational Field

The gas dynamics under gravitational field is usually associated with the multiple scale nature due to large density variation and a wide range of local Knudsen number. It is chal- lenging to construct a reliable numerical algorithm to accurately capture the non-equilibrium physical effect in different regimes. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for all flow regimes under gravitational field will be developed, which can be used for the study of non-equilibrium gravitational gas system. The well-balanced scheme here is defined as a method to evolve an isolated gravitational system under any initial condition to an isothermal hydrostatic equilibrium state and to keep such a solution. To preserve such a property is important for a numerical scheme, which can be used for the study of slowly evolving gravitational system, such as the formation of star and galaxy. Based on the Boltzmann model with external forcing term, an analytic time evolving (or scale-dependent) solution is constructed to provide the corresponding dynamics in the cell size and time step scale, which is subsequently used in the construction of UGKS. As a result, with the varia- tion of the ratio between the numerical time step and local particle collision time, the UGKS is able to recover flow physics in different regimes and provides a continuum spectrum of gas dynamics. For the first time, the flow physics of a gravitational system in the transition regime can be studied using the UGKS, and the non-equilibrium phenomena in such a grav- itational system can be clearly identified. Many numerical examples will be used to validate the scheme. New physical observation, such as the correlation between the gravitational field and the heat flux in the transition regime, will be presented. The current method provides an indispensable tool for the study of non-equilibrium gravitational system.

physics.comp-ph↗