Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system

JOURNAL OF COMPUTATIONAL PHYSICS

卷:408

Article

Manzanero, Juan^1,2  Rubio, Gonzalo^1,2  Kopriva, David A.^3,4  Ferrer, Esteban^1,2  Valero, Eusebio^1,2 

[1] UPM, Sch Aeronaut, ETSIAE, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain

[2] Univ Politecn Madrid, Ctr Computat Simulat, Campus Montegancedo, Madrid 28660, Spain

[3] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[4] San Diego State Univ, Computat Sci Res Ctr, San Diego, CA 92182 USA

关键词: Navier-Stokes;    Cahn-Hilliard;    Computational fluid dynamics;    High-order methods;    Discontinuous Galerkin;    SBP-SAT;   

DOI  :  10.1016/j.jcp.2020.109363

来源: Elsevier

【 摘 要 】

We develop an entropy-stable two-phase incompressible Navier-Stokes/Cahn-Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum equation, and an artificial compressibility method to compute the pressure. We design the model so that it satisfies an entropy law, including free- and no-slip wall boundary conditions with non-zero wall contact angle. We then construct a high-order DG approximation of the model that satisfies the summation-by-parts simultaneous-approximation-term property. With the help of a discrete stability analysis, the scheme has two modes: an entropy-conserving approximation with central advective fluxes and the Bassi-Rebay 1 (BR1) method for diffusion, and an entropy-stable approximation with an exact Riemann solver for advection and interface stabilization added to the BR1 method. The scheme is applicable to, and the stability proofs hold for, three-dimensional unstructured meshes with curvilinear hexahedral elements. We test the convergence of the schemes on a manufactured solution, and their robustness by solving a flow initialized from random numbers. In the latter, we find that a similar scheme that does not satisfy an entropy inequality had 30% probability to fail, while the entropy-stable scheme never does. We also solve the static and rising bubble test problems, and to challenge the solver capabilities we compute a three-dimensional pipe flow in the annular regime. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free