Associate Professor
Shanghai Jiaotong University, School of Aeronautics & Astronautics
Associate Professor in the School of Aeronautics & Astronautics at Shanghai Jiao Tong University and Honorary Research Fellow at Imperial College London. Before I joined Shanghai Jiao Tong University, I was a Rolls-Royce researcher in the Department of Aeronautics and a researcher in the Department of Mathematics at Imperial College London. My research interests span applied/computational mathematics and fluid mechanics: hydrodynamic instability (laminar-turbulent transition), aeroacoustics, turbulence, kinetic theory-based modelling/method, numerical analysis and methods. I am currently working on broadband noise modelling and prediction, laminar-turbulent transition. Especially, I have been working on spectral/hp element methods and am a developer of the opensource software Nektar++. I was also one of the pioneering porotype designers of ProLB (LaBS) and a developer of Palabos. My researches are being/were supported by NSF, EPSRC, Rolls-Royce, Airbus, Bombardier, McLaren, Renault and so on. My research papers were mainly published in Journal of Fluid Mechanics, SIAM Journal on Scientific Computing, Journal of Computational Physics and so on.
Shanghai Jiaotong University, School of Aeronautics & Astronautics
Imperial College London, Department of Aeronautics & Department of Mathematics
University of Nottingham, Department of Mechanical, Materials and Manufacturing Engineering
University Pierre and Marie CURIE, Institut Jean Le Rond d'Alembert
Leadership in Research
Imperial College London
Power Engineering & Engineering Thermophysics
Xi'an Jiaotong University
Mathematics
Xi'an Jiaotong Unversity
Mathematics
Xi'an Jiaotong Unversity
My research interests are in the area of Applied/Computational Mathematics & Fluid Mechanics. Specifically, I have been working on asymptotic theories, high precision numerical computations, instabilities/transition in a laminar boundary layer, multiscale methods/modelling, kinetic theory and parallel computations in disciplines of fluid mechanics and numerical analysis/computations of partial differential equations.
During the past several years, my research target has been aiming at hydrodynamic instability ( laminar-turbulent transition ) for understanding influence of surface imperfection on instability of a boundary layer and exploring optimal paths to turbulence. One of the key focuses is to see how asymptotic theory and computational modelling can be used to address this challenge. The task is in bridging this challenging interface of asymptotic theory and direct numerical modelling. Whilst another task is to understand effect of a 3D surface localised/random imperfection on the primary mode in a boundary layer and address global instability induced by the imperfection. I am now working on laminar-turbulent transition, turbulence and broadband noise mechanisms in both fundamental and applied aspects.
If you have any interest in these aspects, please don't hesitate to contact me for either pursuing degrees or collaborations (or discussions).
I have been and will be working with world-leading experts in the fields of applied/computational mathematics and fluid mechanics.
I here show my selected papers which are published in Journal of Fluid Mechanics, Journal of computational Physics, SIAM Journal on Scientific Computing and so on, with selected conference presentations.
A topic of fundamental interest from the viewpoint of flow destabilisation, in that a localised surface imperfection generally leads to flow destabilisation; if the surface imperfection is significantly large enough bypass transitional mechanisms arise. The interest in the aeronautical industry is significant, from viewpoint of developing robust engineered surfaces which can maintain laminarity, due to steps, gaps and changes to surface quality due to impact damage. The role of a smooth isolated three-dimensional (3D) bump on laminar-turbulent transition in a flat-plate boundary layer is numerically studied. The main concern lies with the recent discovery of the significant difference between a surface indentation and a bump intruding into the main boundary layer. The study aims at comprehensively elucidating the observed differences, which is a follow-up to Xu et. al. (2017, doi.org/10.1017/jfm.2017.193) where the role of a localised 3D dimple intruding into the surface was investigated numerically by linear and nonlinear analysis, together with complementary experiments. Here, it is shown that if only modification and destabilisation of Tollmien-Schlichting disturbances are assessed in a similar parameter regime as used by Xu et. al. (2017), the transition induced by an isolated bump is more catastrophic than that induced by a surface indentation. In both cases, with deep (or high) enough indentations (or bumps), fully 3D laminar separation bubbles arise, which lead to strongly destabilising behaviour. Based on concepts of the critical Reynolds number and global linear stability theory (LST), in the parameter regime, capturing the transition pathway behind an isolated bump depends on the mechanism of both convective and absolute instabilities -- our findings will be presented in the conference paper. Results from an equivalent PSE3D will also be discussed, in relation to its ability to deal with localised 3D separation bubbles formed by the surface feature. Comparisons of the PSE3D derived analysis with more higher fidelity direct numerical simulations will also be covered.
We are concerned about the role of a smooth localised three-dimensional (3D) roughness on instability of an incompressible boundary layer by linear and nonlinear analysis. Widths of roughness elements are comparable to wavelength of instability waves and depths/heights are less than the 99% local boundary layer thickness. We are interested in the roughness element which gives rise to a local thin separation bubble. Accordingly, two problems are numerically investigated, one of which is complemented by an experimental study. The first concerns the interaction between the local thin separation bubbles and oncoming instability waves, by which spanwise-uniform Tollmien-Schlichting (TS) waves are destabilised and the TS modes’ shapes are modified by a gradual switchover into an inviscid inflectional instability mechanism. The second problem concerns the nonlinear effect induced by a localised roughness element by which laminar-turbulent transition is prompted. Direct numerical simulations are employed to address the process of disturbance breakdown to turbulence. The traditional N-factors are used to assess instability of 3D disturbances, which is a general indication of development of strongly nonlinear behaviour, although N-factor, based on linear models, can only be used to provide indications and severity of the destabilisation. As an extension, we finally discuss the likelihood of generating absolute instabilities in the thin separation bubble.
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
We consider the influence of a smooth three-dimensional (3-D) indentation on the instability of an incompressible boundary layer by linear and nonlinear analyses. The numerical work was complemented by an experimental study to investigate indentations of approximately 𝛿 and 𝛿 width at depths of 45 %, 52 % and 60 % of 𝛿, where 𝛿 indicates 99% boundary layer thickness. For these indentations a separation bubble confined within the indentation arises. Upstream of the indentation, spanwise-uniform Tollmien–Schlichting (TS) waves are assumed to exist, with the objective to investigate how the 3-D surface indentation modifies the 2-D TS disturbance. Numerical corroboration against experimental data reveals good quantitative agreement. Comparing the structure of the 3-D separation bubble to that created by a purely 2-D indentation, there are a number of topological changes particularly in the case of the widest indentation; more rapid amplification and modification of the upstream TS waves along the symmetry plane of the indentation is observed. For the shortest indentations, beyond a certain depth there are then no distinct topological changes of the separation bubbles and hence on flow instability. The destabilising mechanism is found to be due to the confined separation bubble and is attributed to the inflectional instability of the separated shear layer. Finally for the widest width indentation investigated ( 𝛿 ), results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using -factors to assess instability of properly 3-D disturbances reveals that a general indication of flow destabilisation and development of strongly nonlinear behaviour is indicated as values are attained. However -factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdown to turbulence is inherently nonlinear and dependent on the magnitude and scope of the initial forcing.
We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %–30 % and four times the width of the local boundary layer thickness 𝛿. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien–Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency (𝜔 𝜈, where 𝜔 and denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and 𝜈 denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.
A fully discrete second‐order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second‐order decoupled implicit/explicit scheme is used for time discretization, and a finite element method based on the P1(P1) − P1−P1(P1) elements for velocity, pressure and density is used for spatial discretization of these primitive equations. Optimal H1−L2−H1 error estimates for numerical solution and an optimal L2 error estimate for are established under the convergence condition of 0 ......
This paper is concerned with the behaviour of Tollmien–Schlichting (TS) waves experiencing small localised distortions within an incompressible boundary layer developing over a flat plate. In particular, the distortion is produced by an isolated roughness element located at . We considered the amplification of an incoming TS wave governed by the two-dimensional linearised Navier–Stokes equations, where the base flow is obtained from the two-dimensional nonlinear Navier–Stokes equations. We compare these solutions with asymptotic analyses which assume a linearised triple-deck theory for the base flow and determine the validity of this theory in terms of the height of the small-scale humps/indentations taken into account. The height of the humps/indentations is denoted by , which is considered to be less than or equal to (corresponding to for our choice of ). The rescaled width of the distortion is of order and the width is shorter than the TS wavelength ( ). We observe that, for distortions which are smaller than 0.1 of the inner deck height ( ), the numerical simulations confirm the asymptotic theory in the vicinity of the distortion. For larger distortions which are still within the inner deck ( $0.4\,\% ) and where the flow is still attached, the numerical solutions show that both humps and indentations are destabilising and deviate from the linear theory even in the vicinity of the distortion. We numerically determine the transmission coefficient which provides the relative amplification of the TS wave over the distortion as compared to the flat plate. We observe that for small distortions, , where the width of the distortion is of the order of the boundary layer, a maximum amplification of only 2 % is achieved. This amplification can however be increased as the width of the distortion is increased or if multiple distortions are present. Increasing the height of the distortion so that the flow separates ( $7.2\,\% ) leads to a substantial increase in the transmission coefficient of the hump up to 350 %.
It has been demonstrated that Lattice Boltzmann methods (LBMs) are very efficient for Computational Aeroacoustics (CAA). In order to address the issue of absorbing acoustic boundary conditions for LBM, three kinds of damping terms are proposed and added to the right hand side of the LBM governing equations. According to the classical theory, these terms play an important role to damp and minimize the acoustic wave reflections from computational boundaries. The corresponding macroscopic equations with the damping terms are recovered for analyzing the macroscopic behaviors of the these damping terms and determining the critical absorbing strength. The dissipative and dispersive properties of the proposed absorbing layer terms are then further analyzed considering the linearized LBM equations. They are explored in the wave-number spaces via the Von Neumann analysis. The related damping strength critical values and the optimal absorbing term are discussed. Finally, some benchmark problems are implemented to assess the theoretical results.
Lattice Boltzmann methods (LBMs) are very efficient for computational fluid dynamics, and for capturing the dynamics of weak acoustic fluctuations. It is known that multi-relaxation-time lattice Boltzmann method (MRT–LBM) appears as a very robust scheme with high precision. There exist several free relaxation parameters in the MRT–LBM. Although these parameters have been tuned via linear analysis, the sensitivity analysis of these parameters and other related parameters is still not sufficient for describing the behavior of the dispersion and dissipation relations of the MRT–LBM. Previous researches have shown that the bulk dissipation in the MRT–LBM induces a significant over-damping of acoustic disturbances. This indicates that the classical MRT–LBM is not best suited to recover the correct behavior of pressure fluctuations. In wave-number space, the first/second-order sensitivity analyses of matrix eigenvalues are used to address the sensitivity of the wavenumber magnitudes to the dispersion-dissipation relations. By the first-order sensitivity analysis, the numerical behaviors of the group velocity of the MRT–LBM are first obtained. Afterwards, the distribution sensitivities of the matrix eigenvalues corresponding to the linearized form of the MRT–LBM are investigated in the complex plane. Based on the sensitivity analysis and an effective algorithm of recovering linearized Navier–Stokes equations (L-NSEs) from linearized MRT–LBM (L-MRT–LBM), we propose some simplified optimization strategies to determine the free relaxation parameters of the MRT–LBM. Meanwhile, the dispersion and dissipation relations of the optimal MRT–LBM are quantitatively compared with the exact dispersion and dissipation relations. At last, some numerical validations on classical acoustic benchmark problems are shown to assess the new optimal MRT–LBM.
Lattice Boltmzann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier–Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved. And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM. Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.
I have strong interest in teaching. I have taught a variety of courses both on strictly mathematical topics and interdisciplinary topics (fluid mechanics). I have been developing my own teaching materials, methods and approaches. I am enthusiastic about being a mentor both graduate and undergraduate students. Currently, my teaching interest lies in:
Hydrodynamic stability, asymptotic analysis and singular perturbation theory, mathematical modelling in coninuum mechanics and so on
Numerical solution of partial differential equations, numerical analysis, numerical mathematics/computational methods and so on.
Mathematical analysis, functional analysis, real analysis, applied partial differential equations, probability theory & mathematical statistics and so on.
Fundamentals of fluid mechanics, fundamentals of heat & mass transfer, computational fluid mechanics & heat transfer, fundamentals of turbulence, theoretical fluid mechanics and so on.
I am also exploring possibilities in teaching interdisciplinary courses.
This course is offered to postgraduates for single term and give them an introduction of the formulation, methodology, and techniques used in obtaining numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis.
Referece books
1. Numerical Analysis for Engineers and Scientists, G. Miller, Cambridge University Press, 2014
2. Numerical Analysis, 2nd Edition, T. Sauer, Pearson, 2011
3. Numerical Analysis 10th Edition, R. L. Burden, Cengage Learning, 2015
4. An Introduction to Numerical Analysis, E. Suli, Cambridge University Press, 2003
Collections for my family and my academic activities. Here, I showed the pictures of my travel footprints around the world and the wonderful time enjoyed with my families, teachers, friends, colleagues, students......
I am and will be missing the time which I spent with you ......
I would be happy to talk to you if you need my assistance in your research or your learning no matter where you are from. Though I have limited time, I will try my best to get in touch with you.
You can find me at my office located at School of Aeronautics & Astronautics at Shanghai Jiao Tong University.
I am at my office every day from 7:00 until 10:00 am, but you may consider a call or an email to fix an appointment.