For additional information see Zhiliang Xu's Personal Page.

Research Interests

My recent research interests have been on the numerical methods for solving partial differential equations, specially for equations related to convection dominated flow phenomena (e.g. Euler equations, Navier-Stokes equations), scientific computing, and computational math-biology. I am currently working on:

1. Blood flow model.
2. Conservative front tracking.
3. Modeling blood thrombus formation in the blood vessel with a multiscale model which couples stochastic discrete Cellular Potts Model with continuum PDE model such as Navier-Stokes equations for the blood flow and convection-diffusion-reaction equations for coagulation reactions.
4. Modeling P. aeruginosa (a bacterium) swarm pattern formation.  The model couples thin liquid film model with stochastic discrete off-lattice model for individual cells.
5. Discontinuous Galerkin methods for solving conservation laws.

Selected Publications

• Z.L. Xu, J. Lioi, J. Mu, M.M. Kamocka, X. Liu, D.Z. Chen, E.D. Rosen, and M.S. Alber, “A Multiscale Model of Venous Thrombus Formation with Surface-Mediated Constrol of Blood Coagulation Cascade”, Biophysical Journal, 2010  (to appear).
• Z.L. Xu, Y.J. Liu, C.-W. Shu, “Hierarchical Reconstruction for Spectral Volume Methods on Unstructured Grids”, Journal of Computational Physics, Vol 228(16):5787-5802, 2009.
• Z.L. Xu, Y.J. Liu, C.-W. Shu, “Hierarchical Reconstruction for Discontinuous Galerkin Methods on Unstructured Grids with WENO Type Linear Reconstruction”, Journal of Computational Physics, Vol 228:2194-2212, 2009
• Xu, Z.L., Chen, N., , Kamocka, M.M., Rosen, E.D., and M.S. Alber, Multiscale Model of Thrombus Development, Journal of the Royal Society Interface Vol4, No24, 705-723, 2008.
• T. Lu, Z.L. Xu, R. Samulyak, J. Glimm and X. M. Ji, "Dynamic Phase Boundaries for Compressible Fluids", Siam J. on Scientific Computing, Vol 30, Issue 3, 895-915, 2008.