• A tutorial of the immersed interface method (IIM) for fluid-solid interactions, in preparation. (This book will use the codes in a CFD package that I have been developing to cover the theory and practice of the IIM.)
  • An introduction to scientific computing with Matlab and Python Tutorial, Taylor & Francis, 2022. It is available on Amazon (Link) and the web site of the publisher (Link). (This book is intended to serve as a textbook for MATH3315 and MATH4315 – Introductory Scientific Computing at SMU.)


To request a package, please email me.

  • Fluid-solid interactions with deformable objects: IIM2dFSI (2D), IIM3dFSI (3D)
  • Flow around rigid objects: IIM2dSR (serial, 2D, smooth rigid  objects), IIM2dR (serial, 2D), IIM2dMPI (parallel, 2D), IIM3dSR (serial, 3D, smooth rigid objects), IIM3dR (serial, 3D),  IIM3dMPI (parallel, 3D)
  • Two-fluid flows: IIM2d2F (serial, 2D)
  • Newtonian dynamics of a wing-body insect model: FlappingFree


  • [2017PoF.pdf] Acmae El Yacoubi, Sheng Xu and Z. Jane Wang, The effect of gravity and dimensionality on the impact of cylinders and spheres onto a wall in a viscous fluid, Phys. Fluids, 29, 020717, 2017
  • [2015JCP.pdfSheng Xu and Glen D. Pearson, Computing jump conditions for the immersed interface method using triangular mesh representation of an interface, J. Comput. Phys., vol. 302, pp.59-67, 2015
  • [2014NM-TMA.pdf] Miguel Uh and Sheng Xu, The immersed interface method for simulating two-fluid flows, Numer. Math. Theor. Meth. Appl., Vol. 7, No. 4, 447-472, 2014
  • [2012CiCP.pdfSheng Xu, An iterative two-fluid pressure solver based on the immersed interface method, Commun. Comput. Phys., 12 (2), 528-543, 2012
  • [2012JFM.pdf] Acmae El Yacoubi, Sheng Xu and Z. Jane Wang, Computational study of the interaction of free moving particles at intermediate Reynolds numbers, J. Fluid Mech., 705, 135-148, 2012
  • [2012IMA.pdfSheng Xu, A user-friendly formulation of the Newtonian dynamics for the coupled wing-body system in insect flight, In Natural Locomotion in Fluids and on Surfaces, S. Childress et al (ed), 225-234, 2012
  • [2011JCP.pdfSheng Xu, A boundary condition capturing immersed interface method for 3D rigid objects in a flow, J. Comput. Phys., 230, pp.7176-7190, 2011
  • [2009DCDS.pdfSheng Xu, Derivation of principal jump conditions for the immersed interface method in two-fluid flow simulation, Discrete and Continuous Dynamical Systems, Supplement 2009, pp.838-845, 2009
  • [2009AML.pdfSheng Xu, Singular forces in the immersed interface method for 3D rigid objects, Appl. Math. Lett., 22, pp.827-833, 2009
  • [2008JCP.pdfSheng Xu, The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow, J. Comput. Phys., 227, pp.5045-5071, 2008
  • [2008CMAME.pdfSheng Xu and Z. Jane Wang, A 3D immersed interface method for fluid-solid interaction, Comput. Methods Appl. Mech. Engrg., 197, pp. 2068-2086, 2008
  • [2007JFM.pdf] Attila J. Bergou, Sheng Xu and Z. Jane Wang, Passive wing pitch reversal in insect flight, J. Fluid Mech., vol 591, pp.321-337, 2007
  • [2006JCP.pdfSheng Xu and Z. Jane Wang, An immersed interface method for simulating the interaction of a fluid and moving boundaries, J. Comput. Phys., vol 216, no 2, pp.454-493, 2006
  • [2006SISC.pdfSheng Xu and Z. Jane Wang, Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation, SIAM J. Sci. Comput., Vol. 27, No. 6, pp.1948-1980, 2006
  • [2004PoF.pdfSheng Xu and M. Pino Martin, Assessment of inflow boundary conditions for compressible turbulent boundary layers, Physics of Fluids, vol 16, no 7, pp.2623-2639, 2004
  • [2003JFM.pdfS. Xu, D. Rempfer and J. Lumley, Turbulence over a compliant surface: numerical simulation and analysis, J. Fluid Mech., vol 478, pp.11-34, 2003