Academic Positions

  • Present 2018

    Associate Professor

    Shanghai Jiaotong University, School of Aeronautics & Astronautics

  • Present 2012

    Honorary Research Fellow

    Rolls-Royce Researcher

    Research Associate

    Imperial College London, Department of Aeronautics & Department of Mathematics

  • 2018 2017

    Visiting Researcher

    University of Nottingham, Department of Mechanical, Materials and Manufacturing Engineering

  • 2012 2010

    Postdoctoral Research Fellow

    University Pierre and Marie CURIE, Institut Jean Le Rond d'Alembert

Education & Training

  • Leadership 2017

    Leadership in Research

    Imperial College London

  • Ph.D. 2009

    Power Engineering & Engineering Thermophysics

    Xi'an Jiaotong University

  • M.Sc.2006


    Xi'an Jiaotong Unversity

  • B.Sc.2003


    Xi'an Jiaotong Unversity

Honors, Awards and Grants

  • 2019 - 2021
    (PI) Transition, turbulence & broadband noise (Training Program of the Major Research Plan of the National Natural Science Foundation of China)
  • 2019 - 2022
    (Co-PI) Platform of high-fidelity simulations of combustion chambers for aeronautical engines
  • 2017 - 2018
    Specifications of the work on high-order methods for noise prediction and supported by Rolls-Royce
  • 2016 - 2017
    Nonlinear optimisation strategies for understanding optimal paths to transition and supported by EPSRC PRISM platform grant
  • 2014 - 2018
    System Advances In Nacelle Technology Aerodynamics (SANTANA)
    SANTANA is a collaborative programme focused on the development of aerodynamic technologies for the design of advanced, Ultra High Bypass Ratio (UHBR) power plant nacelles. The nacelle on a modern high bypass ratio engine is a significant contributor to power weight, and owing to its size, can also have a marked impact on aircraft fuel burn performance. Targeting nacelle components for next generation aircraft, this programme exploits new lower weight structural designs, to reduce performance losses associated with installed nacelle systems. The programme also develops advanced aerodynamic testing methods, improvements to laminar-turbulence modelling and improves testing facilities within the UK. These advancements are essential to achieve the global ACARE (Advisory Council for Aeronautics Research in Europe) 2020 and 2030 entry-into-service emissions targets for noise and fuel burn. SANTANA’s partners comprise UK industrial organisations: Bombardier, Belfast; Aircraft Research Association Ltd (ARA), Bedford; and S&C Thermofluids Ltd, Bath; and aerodynamics research teams at City University, London and Imperial College, London.
  • 2012-2016
    Development of underpinning technology for laminar flow control (EPSRC)
    The development of viable LFC designs requires sophisticated mathematical, computational and experimental investigations of the onset of transition to turbulence and its control. Existing tools are too crude to be useful and contain little input from the flow physics. Major hurdles to be overcome concern:
    • How do we specify generic input disturbances for flow past a wing in a messy atmosphere in the presence of surface imperfections, flexing, rain, insects and a host of other complicating features
    • How do we solve the mathematical problems associated with linear and nonlinear disturbance growth in complex 3D flows
    • How do we find a criterion for the onset of transition based on flow physics which is accurate enough to avoid the massive over-design associated with existing LFC strategies yet efficient enough to be useable in the design office
    • How can we use experiments in the laboratory to predict what happens in flight experiments
    • How can we devise control strategies robust enough to be used on civilian aircraft
    • How can we quantify the manufacturing tolerances such as say surface waviness or bumps needed to maintain laminar flow
    The above challenges are huge and can only be overcome by innovative research based on the mathematical, computational and experimental excellence of a team like the one we have assembled. The solution of these problems will lead to a giant leap in our understanding of transition prediction and enable LFC to be deployed. The programme is based around a unique team of researchers covering all theoretical, computational, and experimental aspects of the problem together with the necessary expertise to make sure the work can be deployed by industry. Indeed our partnership with most notably EADS and Airbus UK will put the UK aeronautics industry in the lead to develop the new generation of LFC wings.
  • 2010 - 2012
    Aerodynamics & aeroacoustics and supported by FUI project (France)
    • Development of a numerical tool for computational fluid dynamics based on Lattice Boltzmann Method and optimized for massively parallel computing.
    • Target applications: aerodynamic simulations (calculation and optimization of aerodynamic drag and lift coefficients), aeroacoustic simulations (aerodynamic noise sources reduction) and acoustic simulations (porous materials modeling).
    • Application fields: automotive, railway and aeronautic industries.
  • 2010 - 2012
    Dimension splitting method for the 3D rotating incompressible and compressible Navier-Stokes equations (NSF Grant)
  • 2005 - 2007
    High performance numerical algorithms of solving Navier-Stokes equations based on inertial manifolds (NSF Grant)


Spencer J. Sherwin, FREng, FRAeS

Professor at Imperial College London

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Philip Hall

Professor at Monash University

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Wenquan Tao, CAS Member

Professor at Xi'an Jiaotong University

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Xuesong Wu

Professor at Imperial College London

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Pierre Sagaut

Professor at Aix-Marseille Université

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Gianmarco Mengaldo

Senior Researcher at California Institute of Technology

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Great People

I have been and will be working with world-leading experts in the fields of applied/computational mathematics and fluid mechanics.

Research Projects

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    Wake turbulence & broadband noise

    A brief description

  • image

    DG/FR high-fidelity computations for viscous compressible flows

    A continuous development task in Nektar++ for stabilisation of implementing calculations of compressible flows.

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Pathway to laminar-turbulent transition in a three-dimensional bump distorted boundary layer

H. Xu, S. Mughal, H. Liu, S. Sherwin
Conference PapersIUTAM Transition 2019, London


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, 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.

The role of a localised three-dimensional roughness element on instability waves in a boundary layer

H. Xu, S. Sherwin
Conference Papers ECCN-ECFD 2018


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.

Spectral/hp element methods: Recent developments, applications, and perspectives (Invited paper)

H. Xu, C. D.Cantwell, C. Monteserin, C. Eskilsson, A. P. Engsig-Karup, S. Sherwin
Journal Paper Journal of Hydrodynamics, Volume 30, Issue 1, February 2018, Pages 1-22


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.

Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation

H. Xu, S. Mughal, E. R. Gowree, C. J. Atkin, S. Sherwin
Journal Paper Journal of Fluid Mechanics, Volume 819, May 2017, Pages 592-620


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.

Influence of localised smooth steps on the instability of a boundary layer

H. Xu, J. E. Lombard, S. Sherwin
Journal Paper Journal of Fluid Mechanics, Volume 817, April 2017, Pages 138-170


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 second‐order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

Y. He, H. Xu*, Z. Chen
Journal Paper International Journal for Numerical Methods in Engineering, Volume 108, Issue 7, February 2016, Pages 750-789


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 ......

The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions

H. Xu, S. Sherwin, P. Hall, X. Wu
Journal Paper Journal of Fluid Mechanics, Volume 792, April 2016, Pages 499-525


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 %.

Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods

H. Xu, P. Sagaut
Journal Paper Journal of Journal of Computational Physics, Volume 245, July 2013, Pages 14-42


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.

Sensitivity analysis and determination of free relaxation parameters for the weakly-compressible MRT–LBM schemes

H. Xu, O. Malspinas, P. Sagaut
Journal Paper Journal of Computational Physics, Volume 231, Issue 21, August 2012, Pages 7335-7367


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.

Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics

H. Xu, P. Sagaut
Journal Paper Journal of Computational Physics, Volume 230, Issue 13, August 2011, Pages 5353-5382


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.

Currrent Teaching

  • Present 2018

    Numerical Analysis

    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.

Teaching Materials

  • 2019 2018

    Numerical Analysis (Fall-term)

    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

At My Office

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.