C. Liu, J. Hu, W. T. Taitano, and X. Zhang (2024). “An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker–Planck equations.” Submitted [link]
Journal publications
C. Liu, G. T. Buzzard, and X. Zhang (2024). “An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier–Stokes equations.” Journal of Computational Physics, 519, p. 113440. [link]
C. Liu, B. Rivière, S. Shen, and X. Zhang (2024). “A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn–Hilliard–Navier–Stokes system.” SIAM Journal on Scientific Computing, 46(3), A1923-A1948. [link]
C. Liu, Y. Gao, and X. Zhang (2024). “Structure preserving schemes for Fokker-Planck equations of irreversible processes.” Journal of Scientific Computing, 98(4). [link]
C. Liu, R. Masri, and B. Rivière (2023). “Convergence of a decoupled splitting scheme for the Cahn–Hilliard–Navier–Stokes system.” SIAM Journal on Numerical Analysis, 61(6), pp. 2651–2694. [link]
C. Liu and X. Zhang (2023). “A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier–Stokes equations.” Journal of Computational Physics, 493, p. 112496. [link]
R. Masri, C. Liu, and B. Rivière (2023). “Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier–Stokes equations.” Numerical Methods for Partial Differential Equations, 39(4), pp. 3108–3144. [link]
R. Masri, C. Liu, and B. Rivière (2022). “A discontinuous Galerkin pressure correction scheme for the incompressible Navier–Stokes equations: Stability and convergence.” Mathematics of Computation, 91(336), pp. 1625–1654. [link]
C. Liu, D. Ray, C. Thiele, L. Lin, and B. Rivière (2022). “A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows.” Journal of Computational Physics, 449, p. 110769. [link]
D. Ray, C. Liu, and B. Rivière (2021). “A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant.” Computational Geosciences, 25(5), pp. 1775–1792 [link]
C. Liu, F. Frank, C. Thiele, F. O. Alpak, S. Berg, W. Chapman, and B. Rivière (2020). “An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media.” Journal of Computational Physics, 400, p. 108948. [link]
C. Liu and B. Rivière (2020). “A priori error analysis of a discontinuous Galerkin method for Cahn–Hilliard–Navier–Stokes equations.” CSIAM Transactions on Applied Mathematics, 1(1), pp. 104–141. [link]
C. Liu, F. Frank, F. O. Alpak, and B. Rivière (2019). “An interior penalty discontinuous Galerkin approach for 3D incompressible Navier–Stokes equation for permeability estimation of porous media.” Journal of Computational Physics, 396, pp. 669–686. [link]
C. Liu, F. Frank, and B. Rivière (2019). “Numerical error analysis for non-symmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation.” Numerical Methods for Partial Differential Equations, 35(4), pp. 1509–1537. [link]
F. Frank, C. Liu, A. Scanziani, F. O. Alpak, and B. Rivière (2018). “An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods.” Journal of Colloid and Interface Science, 523, pp. 282–291. [link]
F. Frank, C. Liu, F. O. Alpak, S. Berg, and B. Rivière (2018). “Direct numerical simulation of flow on pore-scale images using the phase-field method.” SPE Journal, 23(5), pp. 1833–1850. [link]
F. Frank, C. Liu, F. O. Alpak, and B. Rivière (2018). “A finite volume/discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging.” Computational Geosciences, 22(2), pp. 543–563. [link]
Conference proceedings
F. Frank, C. Liu, F. O. Alpak, M. Araya-Polo, and B. Rivière (2017). “A discontinuous Galerkin finite element framework for the direct numerical simulation of flow on high-resolution pore-scale images.” SPE Reservoir Symposium. SPE-182606-MS. Society for Petroleum Engineers. [link]
Doctoral thesis
Discontinuous Galerkin methods for pore-scale multiphase flow: theoretical analysis and simulation, 2019 (Rice University). [link]