Publications of Jie Liu

Here is the fish swimming movie from my 2015 CAF paper. The fish has elastic body and rigid bones.
  • J. Liu, A second-order changing-connectivity ALE scheme and its application to FSI with large convection of fluids and near contact of structures, Journal of Computational Physics, 304 (2016) 380--423.
  • J. Liu, A second-order stable explicit interface advancing scheme for FSI with both rigid and elastic structures and its application to fish swimming simulations, Computers and Fluids, 118 (2015) 274--292.
  • J. Liu, R. K. Jaiman, P. S. Gurugubelli, A stable second-order scheme for fluid-structure interaction with strong added-mass effects, Journal of Computational Physics, 270 (2014) 687--710.
  • J. Liu, Order of convergence of splitting schemes for both deterministic and stochastic nonlinear Schrodinger equations, SIAM Journal on Numerical Analysis, 51 (2013) 1911--1932.
  • J. Liu, A mass preserving splitting scheme for the stochastic Schrodinger equation with multiplicative noise, IMA Journal of Numerical Analysis, 33 (2013) 1469--1479.
  • J. Liu, Combined field formulation and a simple stable explicit interface advancing scheme for fluid structure interaction, Manuscript, 2013, (It is called one field formulation in my 2013 SINUM paper on ALE.) Posted at http://arxiv.org/abs/1401.0082
  • J. Liu, Simple and efficient ALE methods with provable temporal accuracy up to fifth order for the Stokes equations on time varying domains, SIAM Journal on Numerical Analysis, 51 (2013) 743-772.
  • J. Jia and J. Liu, Stable and spectrally accurate schemes for Navier-Stokes equations, SIAM Journal on Scientific Computing, 33 (2011) 2421--2439.
  • J.-G. Liu, J. Liu and R. L. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, 229 (2010) 3428-3453
  • J. Liu, J. Xin and Y. Qi, A time domain blind decorrelation method of convolutive mixtures based on an IIR model, Journal of Computational Mathematics, 28 (2010) 371--385
  • J. Liu, Open and traction boundary conditions for the incompressible Navier-Stokes equations, Journal of Computational Physics, 228 (2009) 7250--7267
  • J. Liu, J. Xin and Y. Qi, A soft-constrained dynamic iterative method of blind source separation, SIAM: Multiscale Modeling and Simulation, 7 (2009) 1795--1810
  • J.-G. Liu, J. Liu and R. L. Pego, Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions, Chinese Annals of Mathematics, Series B, 30 (2009) 743--768.
  • J. Liu, J. Xin, Y. Qi and F.-G. Zeng, A time domain algorithm for blind separation of convolutive sound mixtures and $l_{1}$ constrained minimization of cross correlations with time lags, Communications in Mathematical Sciences, 7 (2009) 109--128
  • J. Liu, J. Xin and Y. Qi, A dynamic algorithm for blind separation of convolutive sound mixtures, Neurocomputing, 72 (2008) 521--532.
  • J.-G. Liu, J. Liu and R. L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Communications on Pure and Applied Mathematics, 60 (2007) 1443--1487
  • J.-G. Liu, J. Liu and R. L. Pego, Estimates on the Stokes pressure by partitioning the energy of harmonic functions, Proceedings of the Kyoto conference on the Navier-Stokes equations, edited by H. Okamoto, RIMS. Kokyuroku Bessatsu Kyoto Univ. (2006) 227--246.
  • J.-G. Liu, J. Liu and R. L. Pego, On incompressible Navier-Stokes dynamics: a new approach for analysis and computation, Proceedings of the Tenth International Conference on Hyperbolic Problems, edited by F. Asakura, etc., Yokohama Publishers, Inc. (2006) 29--44.