Energy stable discontinuous Galerkin method for compressible Navier-Stokes-Allen-Cahn system

DOI10.1016/j.cnsns.2021.105771zbMath1471.65141OpenAlexW3131251937MaRDI QIDQ2025492

Xiao-ding Shi, Qiao-lin He

Publication date: 14 May 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.105771

zbMATH Keywords

Navier-Stokesdiscontinuous Galerkintwo-phaseAllen-Cahncompressible

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Liquid-liquid two component flows (76T06)

Related Items

Optimal convergence of the scalar auxiliary variable finite element method for the natural convection equations ⋮ Global solutions to 1D compressible Navier-Stokes/Allen-Cahn system with density-dependent viscosity and free-boundary ⋮ Three linear, unconditionally stable, second order decoupling methods for the Allen-Cahn-Navier-Stokes phase field model

Cites Work

• An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system
• A gradient stable scheme for a phase field model for the moving contact line problem
• On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework
• Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations
• A least-squares/finite element method for the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line
• Spectral deferred correction methods for ordinary differential equations
• Asymptotic stability of solutions for 1-D compressible Navier-Stokes-Cahn-Hilliard system
• The scalar auxiliary variable (SAV) approach for gradient flows
• Numerical study of phase transition in van der Waals fluid
• Strong solutions of the Navier-Stokes equations for a compressible fluid of Allen-Cahn type
• 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
• Global solutions for a coupled compressible Navier-Stokes/Allen-Cahn system in 1D
• An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems
• Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations
• Numerical study of compressible Navier-Stokes-Cahn-Hilliard system
• An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation
• ANALYSIS OF A PHASE-FIELD MODEL FOR TWO-PHASE COMPRESSIBLE FLUIDS
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Phase Transition in Van der Waals Fluid
• A Model Numerical Scheme for the Propagation of phase Transitions in Solids
• Efficient, Accurate and Energy Stable Discontinuous Galerkin Methods for Phase Field Models of Two-Phase Incompressible Flows
• A Numerical Study of Riemann Problem Solutions and Stability for a System of Viscous Conservation Laws of Mixed Type
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation