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 …
Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element
numerical schemes for the Abels-Garcke-Grün (AGG) model, which is a thermodynamically …
numerical schemes for the Abels-Garcke-Grün (AGG) model, which is a thermodynamically …
A structure-preserving, upwind-SAV scheme for the degenerate Cahn–Hilliard equation with applications to simulating surface diffusion
This paper establishes a structure-preserving numerical scheme for the Cahn–Hilliard
equation with degenerate mobility. First, by applying a finite volume method with upwind …
equation with degenerate mobility. First, by applying a finite volume method with upwind …
Some Traveling Wave Solutions to the Fifth‐Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub‐ODE, Modified Auxiliary Equation, and (G′/G) …
The fifth‐order nonlinear wave equation contains terms involving higher‐order spatial
derivatives, such as uxxx and uxxxxx. These terms are responsible for dispersion, which …
derivatives, such as uxxx and uxxxxx. These terms are responsible for dispersion, which …
Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances
We develop structure preserving schemes for a class of nonlinear mobility continuity
equation. When the mobility is a concave function, this equation admits a form of gradient …
equation. When the mobility is a concave function, this equation admits a form of gradient …
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 …
[HTML][HTML] A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber
When a thin liquid film flows down on a vertical fiber, one can observe the complex and
captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in …
captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in …
High order implicit finite difference schemes with a semi-implicit WENO reconstruction for nonlinear degenerate parabolic equations
P Zhang, T Xiong - Journal of Computational Physics, 2022 - Elsevier
In this paper, we develop implicit finite difference schemes with a semi-implicit weighted
essentially non-oscillatory (WENO) reconstruction for nonlinear degenerate parabolic …
essentially non-oscillatory (WENO) reconstruction for nonlinear degenerate parabolic …
Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects
We propose a new generalized compressible diphasic Navier–Stokes Cahn–Hilliard model
that we name G-NSCH. This new G-NSCH model takes into account important properties of …
that we name G-NSCH. This new G-NSCH model takes into account important properties of …
Efficiently high-order time-stepping R-GSAV schemes for the Navier–Stokes-Poisson-Nernst–Planck equations
Y He, H Chen - Physica D: Nonlinear Phenomena, 2024 - Elsevier
We propose in this paper two kinds of generalized scalar auxiliary variable (GSAV)
approach with relaxation (R-GSAV) for the Navier–Stokes-Poisson-Nernst–Planck …
approach with relaxation (R-GSAV) for the Navier–Stokes-Poisson-Nernst–Planck …