- Finite element methods
- Diffuse-interface modeling for phase transition phenomena
- Biomechanics and modeling in mechanobiology
- High-performance computing

J. Liu, A.L. Marsden, and Z. Tao, "An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics.", International Journal for Numerical Methods in Engineering, in press. [DOI:10.1002/nme.6165][preprint]

J. Liu and A.L. Marsden, "A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning." Journal of Computational Physics, 383:72-93, 2019. [DOI:10.1016/j.jcp.2019.01.019][preprint]

J. Liu and A.L. Marsden, "A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction.", Computer Methods in Applied Mechanics and Engineering, 337:549-597, 2018. [DOI:10.1016/j.cma.2018.03.045][preprint]

J. Liu, C.M. Landis, H. Gomez, and T.J.R. Hughes, "Liquid-Vapor Phase Transition: Thermomechanical Theory, Entropy Stable Numerical Formulation, and Boiling Simulations." Computer Methods in Applied Mechanics and Engineering, 297:476-553, 2015. [DOI:10.1016/j.cma.2015.09.007][preprint][slides]

J. Liu, H. Gomez, J.A. Evans, T.J.R. Hughes, and C.M. Landis, "Functional Entropy Variables: A New Methodology for Deriving Thermodynamically Consistent Algorithms for Complex Fluids, with Particular Reference to the Isothermal Navier-Stokes-Korteweg Equations." Journal of Computational Physics, 248:47-86, 2013. [DOI:10.1016/j.jcp.2013.04.005][preprint]

J. Liu, L. Dede, J.A. Evans, M.J. Borden, and T.J.R. Hughes, "Isogeometric analysis of the advective Cahn-Hilliard equation: Spinodal decomposition under shear flow." Journal of Computational Physics, 242:321-350, 2013. [DOI:10.1016/j.jcp.2013.02.008][preprint]

H. Guan, Y. Jiao, J. Liu and Y. Tang, "Explicit Symplectic Methods for the Nonlinear Schrodinger Equation." Communications in Computational Physics, 6:639-654, 2009. [Link]

J. Liu, "Thermal convection in the van der Waals fluid." in Frontiers in Computational Fluid-Structure Interaction and Flow Simulation, Research from Lead Investigators under Forty - 2018, edited by T.E. Tezduyar, Springer, 2018 [DOI:10.1007/978-3-319-96469-0_9][preprint]

J. Liu and T.J.R. Hughes, "Isogeometric Phase-field Simulation of Boiling", in Advances in Computational Fluid-Structure Interaction and Flow Simulation, A Tribute to Tayfun Tezduyar on the Occasion of his 60th Birthday, edited by K. Takizawa and Y. Bazilevs, Springer, 2015.[DOI:10.1007/978-3-319-40827-9_17]

Thermodynamically consistent modeling and simulation of multiphase flows. [Link]

Boiling is a complex phase transition phenomenon. It involves complex fluid flows, various instability phenomena, and liquid-vapor phase change. We have developed a suite of novel theoretical and numerical methodologies for the study of boiling. The following figure shows a snapshot of the temperature field in a boiling simulation.