A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn–Hilliard–Navier–Stokes system

C Liu, B Riviere, J Shen, X Zhang - SIAM Journal on Scientific Computing, 2024 - SIAM
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving
without losing conservation and accuracy by a postprocessing procedure of solving a …

Convergence of a decoupled splitting scheme for the Cahn–Hilliard–Navier–Stokes system

C Liu, R Masri, B Riviere - SIAM Journal on Numerical Analysis, 2023 - SIAM
This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm
for solving the Cahn–Hilliard–Navier–Stokes equations within a decoupled splitting …

An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker-Planck equations

C Liu, J Hu, WT Taitano, X Zhang - arxiv preprint arxiv:2410.19143, 2024 - arxiv.org
For high-order accurate schemes such as discontinuous Galerkin (DG) methods solving
Fokker-Planck equations, it is desired to efficiently enforce positivity without losing …

A second-order, mass-conservative, unconditionally stable and bound-preserving finite element method for the quasi-incompressible Cahn-Hilliard-Darcy system

Y Gao, D Han, X Wang - Journal of Computational Physics, 2024 - Elsevier
A second-order numerical method is developed for solving the quasi-incompressible Cahn-
Hilliard-Darcy system with the Flory-Huggins potential for two immiscible fluids of variable …

Dynamically regularized Lagrange multiplier schemes with energy dissipation for the incompressible Navier-Stokes equations

CK Doan, L Ju, R Lan - Journal of Computational Physics, 2025 - Elsevier
In this paper, we present efficient numerical schemes based on the Lagrange multiplier
approach for the Navier-Stokes equations. By introducing a dynamic equation (involving the …

A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches

F Li, J Yang - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
In this work, we study shape optimization problems in the Stokes flows. By phase-field
approaches, the resulted total objective function consists of the dissipation energy of the …

[HTML][HTML] An enhanced momentum conservation treatment for FDM simulation of two-phase flows with large density ratio

X Wang, M Luo, H Karunarathna, DE Reeve - Journal of Computational …, 2023 - Elsevier
The differences of the fluid properties across a fluid interface in two-phase flow often bring
difficulties into computational simulations, as the conservation of mass, momentum and …

Conservative, bounded, and nonlinear discretization of the Cahn-Hilliard-Navier-Stokes equations

J Goulding, T Shinar, C Schroeder - Journal of Computational Physics, 2025 - Elsevier
Abstract The Cahn-Hilliard equation describes phase separation in a binary mixture,
typically modeled with a phase variable that represents the concentration of one phase or …

Second-Order Decoupled Linear Energy-Law Preserving gPAV Numerical Schemes for Two-Phase Flows in Superposed Free Flow and Porous Media

Y Gao, D Han - Journal of Scientific Computing, 2024 - Springer
We propose second-order numerical methods based on the generalized positive auxiliary
variable (gPAV) framework for solving the Cahn–Hilliard–Navier–Stokes–Darcy model in …

A fully discretization, unconditionally energy stable finite element method solving the thermodynamically consistent diffuse interface model for incompressible two …

K Zhang - arxiv preprint arxiv:2403.05200, 2024 - arxiv.org
A diffusion interface two-phase magnetohydrodynamic model has been used for matched
densities in our previous work [1, 2], which may limit the applications of the model. In this …