A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn–Hilliard–Navier–Stokes system
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving
without losing conservation and accuracy by a postprocessing procedure of solving a …
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
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 …
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
For high-order accurate schemes such as discontinuous Galerkin (DG) methods solving
Fokker-Planck equations, it is desired to efficiently enforce positivity without losing …
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
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 …
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
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 …
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 …
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
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 …
difficulties into computational simulations, as the conservation of mass, momentum and …
Conservative, bounded, and nonlinear discretization of the Cahn-Hilliard-Navier-Stokes equations
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 …
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
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 …
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 …
densities in our previous work [1, 2], which may limit the applications of the model. In this …