An interior penalty discontinuous Galerkin approach for 3D incompressible Navier-Stokes equation for permeability estimation of porous media. - Chen Liu 015; Florian Frank 001; Faruk O. Alpak; Beatrice Riviere (J. Comput. Phys., 2019)

A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant. - Deep Ray; Chen Liu 015; Beatrice Riviere (CoRR, 2020)

An efficient numerical algorithm for solving viscosity contrast Cahn-Hilliard-Navier-Stokes system in porous media. - Chen Liu 015; Florian Frank 001; Christopher Thiele; Faruk O. Alpak; Steffen Berg; Walter Chapman; Beatrice Riviere (J. Comput. Phys., 2020)

Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations. - Rami Masri; Chen Liu 015; Beatrice Riviere (CoRR, 2021)

A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows. - Chen Liu 015; Deep Ray; Christopher Thiele; Lu Lin; Beatrice Riviere (J. Comput. Phys., 2022)

A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: Stability and convergence. - Rami Masri; Chen Liu 015; Beatrice Riviere (Math. Comput., 2022)

A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier-Stokes equations. - Chen Liu 015; Xiangxiong Zhang (J. Comput. Phys., 2023)

Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System. - Chen Liu 015; Rami Masri; Beatrice Riviere (SIAM J. Numer. Anal., 2023)

An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier-Stokes equations. - Chen Liu 015; Xiangxiong Zhang (CoRR, 2024)

An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier-Stokes equations. - Chen Liu 015; Gregery T. Buzzard; Xiangxiong Zhang (J. Comput. Phys., 2024)

A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn-Hilliard-Navier-Stokes System. - Chen Liu 015; Beatrice Riviere; Jie Shen 001; Xiangxiong Zhang (SIAM J. Sci. Comput., 2024)

Structure Preserving Schemes for Fokker-Planck Equations of Irreversible Processes. - Chen Liu 015; Yuan Gao 004; Xiangxiong Zhang (J. Sci. Comput., 2024)

An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker-Planck equations. - Chen Liu 015; Jingwei Hu; William T. Taitano; Xiangxiong Zhang (Comput. Math. Appl., 2025)

A bound-preserving Runge-Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws. - Chen Liu 015; Zheng Sun 004; Xiangxiong Zhang (J. Comput. Phys., 2025)