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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.