In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretizati...In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretization.The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables.Meanwhile,a switch function is used in LBFS to adjust the magnitude of the numerical viscosity.Thus,it is more beneficial to capture both strong shock waves and thin boundary layers.Moreover,the viscous flux is computed according to the local discontinuous Galerkin method.Some typical compressible viscous problems,including manufactured solution case,lid-driven cavity flow,supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil,are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.展开更多
Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied...Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.展开更多
In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions conta...In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number Re, thus allows one to simulate high Reynolds number flows with relatively larger Re, or coarser grids for a fixed Re. On the other hand, Re cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the viscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-Stokes equations. We demonstrate that, for the second order scheme, Re ≤ 3 is an appropriate constraint for numerical resolution of the viscous profile, while for the fourth-order schemes the constraint can be relaxed to Re ≤ 6.0ur study indicates that the fourth order scheme is preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.展开更多
Some implicit time-marching finite-difference solutions of time-averaged Navier-Stokes equations for two dimensional compressible internal flows are presented.Five numerical examples including subsonic,Transonic,Super...Some implicit time-marching finite-difference solutions of time-averaged Navier-Stokes equations for two dimensional compressible internal flows are presented.Five numerical examples including subsonic,Transonic,Supersonic and hypersonic flow flelds with steady and unsteady phenomena show validity and flexibility of the present calcuation code.The TVD scheme suggested by Harten et al is used to improve the shock resolution,and an algebraic turbulenca model suggested by Baldwin and Lomax is introduced to evaluate the viscous effect in the turbulent flows,It is found that the computational results show fairly good agreement with the experimental data.展开更多
The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study o...The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.展开更多
受限于计算机的计算能力与计算的成本,实际的计算过程中,往往要对流体做出一些物理假设,如无粘流体、不可压缩流体等,但是这将给计算带来不同程度的误差.为解决此问题,提出了一种对弱可压缩粘性流动问题进行求解的数值方法.该方法不仅...受限于计算机的计算能力与计算的成本,实际的计算过程中,往往要对流体做出一些物理假设,如无粘流体、不可压缩流体等,但是这将给计算带来不同程度的误差.为解决此问题,提出了一种对弱可压缩粘性流动问题进行求解的数值方法.该方法不仅可以对计算域内包含静止固体的流场进行计算,也适用于包含运动固体的弱可压缩粘性流场的求解.该方法从水的状态方程开始,对弱可压缩粘性流体运动的速度与压力方程进行了严格推导.考虑到流场中固体的影响,使用边界数据浸入法(Boundary Data Immersion Method, BDIM)将流体子域与固体子域之间耦合,而所使用的BDIM可将流体及水下声学计算中的运动物体准确地表示出来.因此,本文首次将弱可压缩粘性流动计算与BDIM结合起来,并解决了考虑流体的弱可压缩性与粘性的流场求解问题.为验证所提方法的有效性及准确性,计算了3个二维经典算例,并将计算结果与采用其他方法所得数据结果进行比较.对比结果表明,在考虑流体的弱可压缩性与粘性的前提下,本文所提出的新算法可对运动流体中存在静止或运动固体的流场进行准确有效的计算.展开更多
基金supported by the National Natural Science Foundation of China(No.12072158)the Natural Science Foundation of Jiangsu Province(No.BK20191271)+1 种基金the Research Fund of Key Laboratory of Computational AerodynamicsAVIC Aerodynamics Research Institute(No.YL2022XFX0402)。
文摘In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretization.The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables.Meanwhile,a switch function is used in LBFS to adjust the magnitude of the numerical viscosity.Thus,it is more beneficial to capture both strong shock waves and thin boundary layers.Moreover,the viscous flux is computed according to the local discontinuous Galerkin method.Some typical compressible viscous problems,including manufactured solution case,lid-driven cavity flow,supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil,are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.
基金Supported by the National Natural Foundation of China (Grant Nos.40874077,40504020,and 40536029)the National Basic Research Program of China (Grant No.2006CB806304)
文摘Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.
基金Research supported by the National University of Singapore grant No. R-151-000-016-112. Email address: bao@cz3.nus.edu.sg.
文摘In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number Re, thus allows one to simulate high Reynolds number flows with relatively larger Re, or coarser grids for a fixed Re. On the other hand, Re cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the viscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-Stokes equations. We demonstrate that, for the second order scheme, Re ≤ 3 is an appropriate constraint for numerical resolution of the viscous profile, while for the fourth-order schemes the constraint can be relaxed to Re ≤ 6.0ur study indicates that the fourth order scheme is preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.
基金Project Supported by the National Natural Science Foundation of China
文摘Some implicit time-marching finite-difference solutions of time-averaged Navier-Stokes equations for two dimensional compressible internal flows are presented.Five numerical examples including subsonic,Transonic,Supersonic and hypersonic flow flelds with steady and unsteady phenomena show validity and flexibility of the present calcuation code.The TVD scheme suggested by Harten et al is used to improve the shock resolution,and an algebraic turbulenca model suggested by Baldwin and Lomax is introduced to evaluate the viscous effect in the turbulent flows,It is found that the computational results show fairly good agreement with the experimental data.
基金supported by the National Natural Science Foundation of China(11722104,11671150)supported by the National Natural Science Foundation of China(11571280,11331005)+3 种基金supported by the National Natural Science Foundation of China(11331005,11771150)by GDUPS(2016)the Fundamental Research Funds for the Central Universities of China(D2172260)FANEDD No.201315
文摘The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.
文摘受限于计算机的计算能力与计算的成本,实际的计算过程中,往往要对流体做出一些物理假设,如无粘流体、不可压缩流体等,但是这将给计算带来不同程度的误差.为解决此问题,提出了一种对弱可压缩粘性流动问题进行求解的数值方法.该方法不仅可以对计算域内包含静止固体的流场进行计算,也适用于包含运动固体的弱可压缩粘性流场的求解.该方法从水的状态方程开始,对弱可压缩粘性流体运动的速度与压力方程进行了严格推导.考虑到流场中固体的影响,使用边界数据浸入法(Boundary Data Immersion Method, BDIM)将流体子域与固体子域之间耦合,而所使用的BDIM可将流体及水下声学计算中的运动物体准确地表示出来.因此,本文首次将弱可压缩粘性流动计算与BDIM结合起来,并解决了考虑流体的弱可压缩性与粘性的流场求解问题.为验证所提方法的有效性及准确性,计算了3个二维经典算例,并将计算结果与采用其他方法所得数据结果进行比较.对比结果表明,在考虑流体的弱可压缩性与粘性的前提下,本文所提出的新算法可对运动流体中存在静止或运动固体的流场进行准确有效的计算.
