arXiv subjects

Kun Xu

Publications and source records attributed to Kun Xu.

355 records · Page 20Linked to original sources

arXiv2016

A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows IV: full Boltzmann and Model Equations

Fluid dynamic equations are valid in their respective modeling scales. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the flow study in this regime. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.

math.NA↗

arXiv2015

An indirect magnetic approach for determining entropy change in first-order magnetocaloric materials

Taking into account the phase fraction during transition for the first-order magnetocaloric materials, an improved isothermal entropy change determination has been put forward based on the Clausius-Clapeyron (CC) equation. It was found that the isothermal entropy change value evaluated by our method is in excellent agreement with those determined from the Maxwell-relation (MR) for Ni-Mn-Sn Heusler alloys, which usually presents a weak field-induced phase transforming behavior. In comparison with MR, this method could give rise to a favorable result derived from few thermomagnetic measurements. More importantly, we can eliminate the isothermal entropy change overestimation derived from MR, which always exists in the cases of Ni-Co-Mn-In and MnAs systems with a prominent field-induced transition. These results confirmed that such a CC-equation-based method is quite practical and superior to the MR-based ones in eliminating the spurious spike and reducing measuring cost.

cond-mat.mtrl-sci↗

arXiv2015

Semantic Relation Classification via Convolutional Neural Networks with Simple Negative Sampling

Syntactic features play an essential role in identifying relationship in a sentence. Previous neural network models often suffer from irrelevant information introduced when subjects and objects are in a long distance. In this paper, we propose to learn more robust relation representations from the shortest dependency path through a convolution neural network. We further propose a straightforward negative sampling strategy to improve the assignment of subjects and objects. Experimental results show that our method outperforms the state-of-the-art methods on the SemEval-2010 Task 8 dataset.

cs.CL↗

arXiv2015

Discrete unified gas kinetic scheme on unstructured meshes

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for deterministic solution of the Boltzmann model equation with asymptotic preserving property. In DUGKS, the numerical flux of the distribution function is determined from a local numerical solution of the Boltzmann model equation using an unsplitting approach. The time step and mesh resolution are not restricted by the molecular collision time and mean free path. To demonstrate the capacity of DUGKS in practical problems, this paper extends the DUGKS to arbitrary unstructured meshes. Several tests of both internal and external flows are performed, which include the cavity flow ranging from continuum to free molecular regimes, a multiscale flow between two connected cavities with a pressure ratio of 10000, and a high speed flow over a cylinder in slip and transitional regimes. The numerical results demonstrate the effectiveness of the DUGKS in simulating multiscale flow problems.

physics.flu-dyn↗

arXiv2015

Cartesian Grid Method for Gas Kinetic Scheme

A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. The boundaries are represented by a set of direction-oriented boundary points. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We also propose a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux function. The reconstruction scheme for recovering the boundary conditions of compressible viscous and heat conducting flow with a Cartesian mesh can provide a smooth distribution of physical quantities at solid boundary, and present an accurate solution for the flow study with complex geometry.

physics.flu-dyn↗

arXiv2014

A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations

In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only neighboring cells, is due to the use of a high-order gas evolution model. Besides the evaluation of the time-dependent flux function across a cell interface, the high-order gas evolution model also provides an accurate time-dependent solution of the flow variables at a cell interface. Therefore, the current scheme not only updates the cell averaged conservative flow variables inside each control volume, but also tracks the flow variables at the cell interface at the next time level. As a result, with both cell averaged and cell interface values the high-order reconstruction in the current scheme can be done compactly. Different from using a weak formulation for high-order accuracy in the Discontinuous Galerkin (DG) method, the current scheme is based on the strong solution, where the flow evolution starting from a piecewise discontinuous high-order initial data is precisely followed. The cell interface time-dependent flow variables can be used for the initial data reconstruction at the beginning of next time step. Even with compact stencil, the current scheme has third-order accuracy in the smooth flow regions, and has favorable shock capturing property in the discontinuous regions. Many test cases are used to validate the current scheme. In comparison with many other high-order schemes, the current method avoids the use of Gaussian points for the flux evaluation along the cell interface and the multi-stage Runge-Kutta time stepping technique.

math.NA↗

arXiv2014

Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case

This paper is a continuation of our earlier work [Z.L. Guo {\it et al.}, Phys. Rev. E {\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the fluxes at cell interfaces, so that the nice asymptotic preserving (AP) property is retained, such that the time step is limited only by the CFL number, the distribution function at cell interface recovers to the Chapman-Enskog one in the continuum limit while reduces to that of free-transport for free-molecular flow, and the time and spatial accuracy is of second-order accuracy in smooth region. These features make the DUGKS an ideal method for multiscale compressible flow simulations. A number of numerical tests, including the shock structure problem, the Sod tube problem with different degree of non-equilibrium, and the two-dimensional Riemann problem in continuum and rarefied regimes, are performed to validate the scheme. The comparisons with the results of DSMC and other benchmark data demonstrate that the DUGKS is a reliable and efficient method for multiscale compressible flow computation.

physics.flu-dyn↗

arXiv2013

A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit

Asymptotic preserving (AP) schemes are targeting to simulate both continuum and rarefied flows. Many AP schemes have been developed and are capable of capturing the Euler limit in the continuum regime. However, to get accurate Navier-Stokes solutions is still challenging for many AP schemes. In order to distinguish the numerical effects of different AP schemes on the simulation results in the continuum flow limit, an implicit-explicit (IMEX) AP scheme and the unified gas kinetic scheme (UGKS) based on Bhatnagar-Gross-Krook (BGk) kinetic equation will be applied in the flow simulation in both transition and continuum flow regimes. As a benchmark test case, the lid-driven cavity flow is used for the comparison of these two AP schemes. The numerical results show that the UGKS captures the viscous solution accurately. The velocity profiles are very close to the classical benchmark solutions. However, the IMEX AP scheme seems have difficulty to get these solutions. Based on the analysis and the numerical experiments, it is realized that the dissipation of AP schemes in continuum limit is closely related to the numerical treatment of collision and transport of the kinetic equation. Numerically it becomes necessary to couple the convection and collision terms in both flux evaluation at a cell interface and the collision source term treatment inside each control volume.

physics.flu-dyn↗

arXiv2013

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S-model) are constructed for the correction of Prandtl number of the original BGK model through the modification of stress and heat flux. Even though in the continuum flow regime, both models can give the same Navier-Stokes equations with correct Prandtl number, their modification of the collision term may have different dynamic effect in the non-equilibrium transition flow regimes. With the introduction of one free parameter, a generalized kinetic model with the combination of the ES-model and S-model can be developed, and this new model can get the correct Navier-Stokes equations in the continuum flow regime as well, but with abundant dynamic effect through the adjustment of the new degree of freedom. In order to validate the generalized model, a numerical method based on the unified gas kinetic scheme (UGKS) has been developed for the new model. The physical performance of the new model with the variation of the free parameter has been tested, where the ES-model and S-model become the limiting cases. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. The overall conclusion is that the S-model predicts more accurate numerical solutions in most tough test cases presented in this paper than the ES-model, while ES-model performs better in the cases when the flow is mostly driven by heat, such as a channel flow with large boundary temperature variations at high Knudsen number. The numerical study demonstrates the necessity of developing such a generalized model. With the inclusion of one more freedom, in the transition regime the new kinetic model may provide more accurate solution than the ES and Shakhov models.

physics.flu-dyn↗

arXiv2012

The Integration of High-k Dielectric on Two-Dimensional Crystals by Atomic Layer Deposition

We investigate the integration of Al2O3 high-k dielectric on two-dimensional (2D) crystals of boron nitride (BN) and molybdenum disulfide (MoS2) by atomic layer deposition (ALD). We demonstrate the feasibility of direct ALD growth with trimethylaluminum(TMA) and water as precursors on both 2D crystals. Through theoretical and experimental studies, we found that the initial ALD cycles play the critical role, during which physical adsorption dominates precursor adsorption at the semiconductor surface. We model the initial ALD growth stages at the 2D surface by analyzing Lennard-Jones Potentials, which could guide future optimization of the ALD process on 2D crystals.

cond-mat.mes-hall↗

arXiv2010

A Symplecticity-preserving Gas-kinetic Scheme for Hydrodynamic Equations under Gravitational Field

A well-balanced scheme for a gravitational hydrodynamic system is defined as a scheme which could precisely preserve a hydrostatic isothermal solution. In this paper, we will construct a well-balanced gas-kinetic symplecticity-preserving BGK (SP-BGK) scheme. In order to develop such a scheme, we model the gravitational potential as a piecewise step function with a potential jump at the cell interface. At the same time, the Liouville's theorem and symplecticity preserving property of a Hamiltonian flow have been used in the description of particles penetration, reflection, and deformation through a potential barrier. The use of the symplecticity preserving property for a Hamiltonian flow is crucial in the evaluation of the high-order moments of a gas distribution function when crossing through a potential jump. As far as we know, the SP-BGK method is the first shock capturing Navier-Stokes flow solver with well-balanced property for a gravitational hydrodynamic system. A few theorems will be proved for this scheme, which include the necessity to use an exact Maxwellian for keeping the hydrostatic state, the total mass and energy (the sum of kinetic, thermal, and gravitational ones) conservation, and the well-balanced property to keep a hydrostatic state during particle transport and collision processes. Many numerical examples will be presented to validate the SP-BGK scheme.

physics.comp-ph↗

arXiv2010

Valid Physical Processes from Numerical Discontinuities in Computational Fluid Dynamics

Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting from the discontinuity, a Riemann problem in the Godunov method is solved for the flux evaluation across the cell interface in a finite volume scheme. With the increasing of Mach number in the CFD simulations, the adaptation of the Riemann solver seems introduce intrinsically a mechanism to develop instabilities in strong shock regions. Theoretically, the Riemann solution of the Euler equations are based on the equilibrium assumption, which may not be valid in the non-equilibrium shock layer. In order to clarify the flow physics from a discontinuity, the unsteady flow behavior of one-dimensional contact and shock wave is studied on a time scale of (0~10000) times of the particle collision time. In the study of the non-equilibrium flow behavior from a discontinuity, the collision-less Boltzmann equation is first used for the time scale within one particle collision time, then the direct simulation Monte Carlo (DSMC) method will be adapted to get the further evolution solution. The transition from the free particle transport to the dissipative Navier-Stokes (NS) solutions are obtained as an increasing of time. The exact Riemann solution becomes a limiting solution with infinite number of particle collisions. For the high Mach number flow simulations, the points in the shock transition region, even though the region is enlarged numerically to the mesh size, should be considered as the points inside a highly non-equilibrium shock layer.

math-ph↗

arXiv2008

Generalized Gas Dynamic Equations for Microflows

n an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids {\bf 19}, 016101 (2007)], to simulate non-equilibrium flows. In this paper, instead of using three temperatures in $x-$, $y-$, and $z$-directions, we are going to further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives the 10 moment closure equations of Levermore [C.D. Levermore, J. Stat. Phys {\bf 83}, pp.1021 (1996)]. To the 1st-order expansion, the derived gas dynamic equations can be considered as a regularization of Levermore's 10 moments equations. The new gas dynamic equations have the same structure as the Navier-Stokes equations, but the stress strain relationship in the Navier-Stokes equations is replaced by an algebraic equation with temperature differences. At the same time, the heat flux, which is absent in Levermore's 10 moment closure, is recovered. As a result, both the viscous and the heat conduction terms are unified under a single anisotropic temperature concept. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier-Stokes equations. The current gas dynamic equations are natural extension of the Navier-Stokes equations to the near continuum flow regime and can be used for microflow computations. Two examples, the force-driven Poiseuille flow and the Couette flow in the transition flow regime, are used to validate the model. Both analytical and numerical results are encouraging.

physics.flu-dyn↗