Dr Xin Kai Li

Job: Reader in Computational Fluid Dynamics

Faculty: Technology

School/department: School of Engineering and Sustainable Development

Research group(s): Centre for Engineering, Science and Advance Systems (CESAS)

Address: De Montfort University, The Gateway, Leicester, LE1 9BH

T: +44 (0)116 207 8695

Personal profile

A native of Jilin, China, Xin Kai Li was educated at the University of Jilin. He graduated with a first class honours degree in computational mathematics in 1982. He was awarded an MSc from Shenyang Institute of Computing Technology, Academia Sinica in 1984. He started his DPhil at Linacre College, the University of Oxford in 1987 and obtained a DPhil from Oxford University Computing Laboratory in 1990 for his work on mathematical modelling and numerical approximations for two-phase flow problems.

After PhD studies, he spent about two years as a Research Fellow at the Department of Engineering, University of Leicester, and then three years as a Shell Research Fellow at the Institute of Non-Newtonian Fluid Mechanics and Department of Mathematics, University of Wales, Aberystwyth. He joined Department of Mathematical Sciences as a senior research fellow at the De Montfort University in 1996 and was then awarded a readership in computational fluid dynamics in April, 2000. He has been at the Department of Engineering since 2004.

After leaving Oxford, he has gradually involved himself in the activities of industrial and engineering problems while maintaining his interests in the development of mathematical model and analysis of new numerical algorithms. These two research areas are complementary since the development of the correct mathematical modelling and efficient numerical algorithms is crucial in order that complicated industrial and engineering problems can be simulated on modern computers. Over the past years, he has undertaken research on mathematical modelling and numerical methods in industrial multiphase flows and metal forming processes. In recent years, he has been working on mathematical modelling and numerical simulation for non-Newtonian complex fluids, i.e., computational rheology, which is one of challenging research areas in computational fluid dynamics.

He has written over fifty research journal papers and over twenty conference articles in the areas of numerical analysis, computational rheology, multiphase flows, metal forming processes and journal bearings. He has been also involved in developing a series of software packages for solving industrial and engineering problems. He is a member of British Society of Rheology since 1995.

Research group affiliations

Centre for Engineering, Science and Advance Systems (CESAS)

Publications and outputs

A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation
A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation Liu, Jianming; Li, X. K.; Hu, X. Numerical simulation technique of two-dimensional variable-order time fractional advection-diffusion equation is developed in this paper using radial basis function-based differential quadrature method (RBF-DQ). To the best of the authors’ knowledge, this is the first application of this method to variable-order time fractional advection-diffusion equations. For the general case of irregular geometries, the meshless local form of RBF-DQ is used and the multiquadric type of radial basis functions is selected for the computations. This approach allows one to define a reconstruction of the local radial basis functions to treat accurately both the Dirichlet and Neumann boundary conditions on the irregular boundaries. The method is validated by the well documented test examples involving variable-order fractional modelling of air pollution. The numerical results demonstrate that the proposed method provides accurate solutions fortwo-dimensional variable-order time fractional advection-diffusion equations. The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.
Coherent structures and flow topology of transitional separated-reattached flow over two and three dimensional geometrical shapes
Coherent structures and flow topology of transitional separated-reattached flow over two and three dimensional geometrical shapes Diabil, H. A.; Abdalla, I. E.; Li, X. K. Large-scale organized motions (commonly referred to coherent structures) and flow topology of a transitional separated-reattached flow have been visualised and investigated using flow visualisation techniques. Two geometrical shapes including two-dimensional flat plate with rectangular leading edge and three-dimensional square cylinder are chosen to shed a light on the flow topology and present coherent structures of the flow over these shapes. For both geometries and in the early stage of the transition, two-dimensional Kelvin-Helmholtz rolls are formed downstream of the leading edge. They are observed to be twisting around the square cylinder while they stay flat in the case of the two-dimensional flat plate. For both geometrical shapes, the two-dimensional Kelvin-Helmholtz rolls move downstream of the leading edge and they are subjected to distortion to form three-dimensional hairpin structures. The flow topology in the flat plate is different from that in the square cylinder. For the flat plate, there is a merging process by a pairing of the Kelvin-Helmholtz rolls to form a large structure that breaks down directly into many hairpin structures. For the squire cylinder case, the Kelvin-Helmholtz roll evolves topologically to form a hairpin structure. In the squire cylinder case, the reattachment length is much shorter and a forming of the three-dimensional structures is closer to the leading edge than that in the flat plate case.
Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock
Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock Liu, Jianming; Qiu, Jianxian; Goman, M. (Mikhail G.); Li, X. K.; Liu, Meilin In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.
The Chebyshev spectral element approximation with exact quadratures
The Chebyshev spectral element approximation with exact quadratures Li, Yibiao; Li, X. K. A new Chebyshev spectral element method has been developed in this paper, in which exact quadratures are used to overcome a shortfall of the Gauss–Chebyshev quadrature in variational spectral element projections. The method is validated with the Stokes and the Cauchy–Riemann problems. It is shown that an enhancement of the approximation convergence rate is attained, and numerical accuracy is much better than that from the Gauss–Lobatto–Legendre spectral element method.
Non-Newtonian lubrication with the Phan-Thien–Tanner Model
Non-Newtonian lubrication with the Phan-Thien–Tanner Model Li, X. K. We readdress a classical and practical problem as to whether viscoelasticity can have a measurable and beneficial effect on lubrication performance in thin film flows. In this paper, the viscoelasticity of the fluid is described by general Maxwell–Oldroyd type models. More specifically, it is modeled by the Phan-Thien–Tanner constitutive equations. A perturbation analysis for all the primary variables is carried out with the Deborah number as the perturbation parameter. The sequence of governing equations that results from the perturbation procedure is solved analytically up to first order in the Deborah number. Despite the inherent limitations of the perturbation method, the approach presented here demonstrates a reasonable way to determine the viscoelastic effects on lubrication performance in thin film flows. Numerical solutions indicate that there is a significant enhancement of the viscoelastic pressure when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed enhance the lubricant pressure field and produce a beneficial effect on lubrication performance, which is consistent with experimental observations.
A new immersed boundary method for compressible Navier-Stokes equations.
A new immersed boundary method for compressible Navier-Stokes equations. Liu, J.; Zhao, N.; Hu, O.; Goman, M. (Mikhail G.); Li, X. K.
Adaptive runge-kutta discontinuous galerkin method for complex geometry problems on cartesian grid
Adaptive runge-kutta discontinuous galerkin method for complex geometry problems on cartesian grid Liu, Jianming; Qiu, Jianxian; Hu, Ou; Zhao, Ning; Goman, M. (Mikhail G.); Li, X. K. A Cartesian grid method using immersed boundary technique to simulate the impact of body in fluid has become an important research topic in computational fluid dynamics because of its simplification, automation of grid generation, and accuracy of results. In the frame of Cartesian grid, one often uses finite volume method with second order accuracy or finite difference method. In this paper, an h-adaptive Runge–Kutta discontinuous Galerkin (RKDG) method on Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is developed. A ghost cell immersed boundary treatment with the modification of normal velocity is presented. Themethod is validated versus well documented test problems involving both steady and unsteady compressible flows through complex bodies over a wide range of Mach numbers. The numerical results show that the present boundary treatment to some extent reduces the error of entropy and demonstrate the efficiency, robustness, and versatility of the proposed approach.
On non-Newtonian lubrication with the upper convected Maxwell model.
On non-Newtonian lubrication with the upper convected Maxwell model. Li, X. K.; Luo, Y.; Qi, Y.; Zhang, R.
Challenges in developing a multidimensional feature Selective Validation implementation.
Challenges in developing a multidimensional feature Selective Validation implementation. Archambeault, B.; Duffy, A. P.; Sasse, Hugh G.; Li, X. K.; Scase, M. O.; Shafiullah, M.; Orlandi, A.; Di Febo, D.
Smooth interfaces for spectral element method for the solution of incompressible Newtonian fluid flow.
Smooth interfaces for spectral element method for the solution of incompressible Newtonian fluid flow. Meng, S.; Li, X. K.; Mercado, Ronaldo

Click here to view the full listing of Xin Kai Li's publications and outputs.

Key research outputs

Journal Papers:

X.K Li, Y. Luo, Y. Qi and R. Zhang, (2011) On non-Newtonian lubrication with the upper convected Maxwell model. Appl. Math. Modell. Vol. 35, pp2309-2323. DOI:10.1016/j.apm.2010.11.003

S. Meng, X.K. Li and R. Mercado. (2009) Smooth interfaces for spectral element method for the solution of incompressible Newtonian fluid flow. Journal of Supercomputing, Vol. 48, Number 3, pp319-331. DOI 10.1007/s1 1227-008-0230-0.

Research interests/expertise

Mathematical modelling and numerical algorithms for industrial and engineering problems.
Computational rheology and fluid mechanics of viscoelastic complex fluids.
Study of lubricant rheological behaviour in dynamically loaded journal bearing systems.
Numerical methods, in particular, spectral element and finite volume methods for partial differential equations.

Areas of teaching

Engineering mathematics, Computer languages C and Fortran, Java and Matlab. Numerical method for engineers. Currently, He is teaching the following modules:

Engineering Mathematics Module ENGD1001 (UG)
Advanced Engineering Mathematics Module ENGD2014 (UG)
Critical Games Technology Module ENGD1023 (UG)
Numerical Methods for Engineers Module ENGT5140 (MSc)
Digital Signal Processing (DSP) Module ENGT5203 (MSc)

Course leader of Electronics Games Technology.

Module leader of ENGD1001, ENGD2014 and ENGT5140.

Courses taught

Engineering Mathematics Module ENGD1001 (UG)
Advanced Engineering Mathematics Module ENGD2014 (UG)
Numerical Methods for Engineers Module ENGT5140 (MSc)
Digital Signal Processing (DSP) Module ENGT5203 (MSc)