High Order Numerical Simulations for the Binary Fluid--Surfactant System Using the Discontinuous Galerkin and Spectral Deferred Correction Methods

DOI10.1137/18M1235405zbMath1435.65158OpenAlexW3011630162MaRDI QIDQ5220406

Yan Xu, Ruihan Guo

Publication date: 20 March 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1235405

zbMATH Keywords

discontinuous Galerkin methodconvex splittingspectral deferred correction methodinvariant energy quadratizationbinary fluid-surfactant systemlinear and decoupled scheme

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Capillarity (surface tension) for incompressible viscous fluids (76D45) Initial value problems for nonlinear higher-order PDEs (35G25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (2)

A two-grid spectral deferred correction method for the multi-order fractional differential equations ⋮ A second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model

Cites Work

• Unnamed Item
• On the maximum principle preserving schemes for the generalized Allen-Cahn equation
• An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system
• An energy-stable finite-difference scheme for the binary fluid-surfactant system
• A fully discrete stable discontinuous Galerkin method for the thin film epitaxy problem without slope selection
• Simulating binary fluid-surfactant dynamics by a phase field model
• Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations
• Surfactants in foam stability: a phase-field model
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
• Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
• Numerical approximations for the Cahn-Hilliard phase field model of the binary fluid-surfactant system
• Linear and unconditionally energy stable schemes for the binary fluid-surfactant phase field model
• Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation
• An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system
• Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations
• Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals
• Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
• Long Time Numerical Simulations for Phase-Field Problems Using $p$-Adaptive Spectral Deferred Correction Methods
• Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach

This page was built for publication: High Order Numerical Simulations for the Binary Fluid--Surfactant System Using the Discontinuous Galerkin and Spectral Deferred Correction Methods