The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theor...The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
A new physical structure of vortical flow, i.e., tubular limiting stream surface(TLSS), is reported. It is defined as a general mathematical structure for the physical flow field in the neighborhood of a singularity, ...A new physical structure of vortical flow, i.e., tubular limiting stream surface(TLSS), is reported. It is defined as a general mathematical structure for the physical flow field in the neighborhood of a singularity, and has a close relationship with limit cycles.The TLSS is a tornado-like structure, which separates a vortex into two regions, i.e., the inner region near the vortex axis and the outer region further away from the vortex axis.The flow particles in these two regions can approach to(or leave) the TLSS, but never could reach it.展开更多
Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and ...Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and their evolutions.However,like many other high-order shock capturing schemes,WENO schemes also suffer from the problem that it can not easily converge to a steady state solution if there is a strong shock wave.This is a long-standing difficulty for high-order shock capturing schemes.In recent years,this non-convergence problem has been studied extensively for WENO schemes.Numerical tests show that the key reason of the non-convergence to steady state is the slight post shock oscillations,which are at the small local truncation error level but prevent the residue to settle down to machine zero.Several strategies have been proposed to reduce these slight post shock oscillations,including the design of new smoothness indicators for the fifth-order WENO scheme,the development of a high-order weighted interpolation in the procedure of the local characteristic projection for WENO schemes of higher order of accuracy,and the design of a new type of WENO schemes.With these strategies,the convergence to steady states is improved significantly.Moreover,the strategies are applicable to other types of weighted schemes.In this paper,we give a brief review on the topic of convergence to steady state solutions for WENO schemes applied to Euler equations.展开更多
In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suita...In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions.We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes.The method is an extension of the inverse Lax-Wendroff(ILW)procedure in our works(Cheng et al.,Appl Math Mech(Engl Ed)42:841-854,2021;Liu et al.)for 2D problems.Different from the 2D case,the local coordinate rotation in 3D required in the ILW procedure is not unique.We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation,ensuring the method is feasible and valid.Both translation and rotation of the body are taken into account in this paper.In particular,we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition,which plays a key role in the proposed algorithm.Numerical simulations on the cylinder and sphere are given,demonstrating the good performance of our numerical boundary treatments.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11372340 and 11732016)
文摘The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
基金Project supported by the National Natural Science Foundation of China(Nos.11372340 and 11732016)
文摘A new physical structure of vortical flow, i.e., tubular limiting stream surface(TLSS), is reported. It is defined as a general mathematical structure for the physical flow field in the neighborhood of a singularity, and has a close relationship with limit cycles.The TLSS is a tornado-like structure, which separates a vortex into two regions, i.e., the inner region near the vortex axis and the outer region further away from the vortex axis.The flow particles in these two regions can approach to(or leave) the TLSS, but never could reach it.
基金The work of the first author was supported by NSFC grant 11732016The research of the second author was supported by NSFC grant 11872210The research of the third author was supported by NSF grant DMS-1719410.
文摘Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and their evolutions.However,like many other high-order shock capturing schemes,WENO schemes also suffer from the problem that it can not easily converge to a steady state solution if there is a strong shock wave.This is a long-standing difficulty for high-order shock capturing schemes.In recent years,this non-convergence problem has been studied extensively for WENO schemes.Numerical tests show that the key reason of the non-convergence to steady state is the slight post shock oscillations,which are at the small local truncation error level but prevent the residue to settle down to machine zero.Several strategies have been proposed to reduce these slight post shock oscillations,including the design of new smoothness indicators for the fifth-order WENO scheme,the development of a high-order weighted interpolation in the procedure of the local characteristic projection for WENO schemes of higher order of accuracy,and the design of a new type of WENO schemes.With these strategies,the convergence to steady states is improved significantly.Moreover,the strategies are applicable to other types of weighted schemes.In this paper,we give a brief review on the topic of convergence to steady state solutions for WENO schemes applied to Euler equations.
基金National Numerical Windtunnel project(No.NNW2019ZT4-B10)National Natural Science Foundation of China(Nos.11901555,11901213,11871448,11732016).
文摘In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions.We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes.The method is an extension of the inverse Lax-Wendroff(ILW)procedure in our works(Cheng et al.,Appl Math Mech(Engl Ed)42:841-854,2021;Liu et al.)for 2D problems.Different from the 2D case,the local coordinate rotation in 3D required in the ILW procedure is not unique.We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation,ensuring the method is feasible and valid.Both translation and rotation of the body are taken into account in this paper.In particular,we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition,which plays a key role in the proposed algorithm.Numerical simulations on the cylinder and sphere are given,demonstrating the good performance of our numerical boundary treatments.
