Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg system

DOI10.1090/S0025-5718-2014-02792-0zbMath1391.76331arXiv1207.4647MaRDI QIDQ3189414

Tristan Pryer, Jan Giesselmann, Charalambos G. Makridakis

Publication date: 10 September 2014

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4647

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (16)

A parabolic relaxation model for the Navier-Stokes-Korteweg equations ⋮ Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics ⋮ A local discontinuous Galerkin method for the (non)-isothermal Navier-Stokes-Korteweg equations ⋮ The least-squares spectral element method for phase-field models for isothermal fluid mixture ⋮ A phase-field model for liquid-gas mixtures: mathematical modelling and discontinuous Galerkin discretization ⋮ The design of conservative finite element discretisations for the vectorial modified KdV equation ⋮ Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions ⋮ Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics ⋮ Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in \(R^N\) ⋮ A novel diffuse-interface model and a fully-discrete maximum-principle-preserving energy-stable method for two-phase flow with surface tension and non-matching densities ⋮ An \(h\)-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations ⋮ Liquid-vapor transformations with surfactants. Phase-field model and isogeometric analysis ⋮ Conservative Galerkin methods for dispersive Hamiltonian problems ⋮ Binary-fluid–solid interaction based on the Navier–Stokes–Korteweg equations ⋮ Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model ⋮ A new class of entropy stable schemes for hyperbolic systems: Finite element methods

Uses Software

• DOLFIN
• parDG

Cites Work

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• DOLFIN
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• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
• Existence of solutions for compressible fluid models of Korteweg type
• The second gradient method for the direct numerical simulation of liquid-vapor flows with phase change.

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