A discontinuous Galerkin-based sharp-interface method to simulate three-dimensional compressible two-phase flow

• Published in: International journal for numerical methods in fluids 2015-07, Vol.78 (7), p.413-435
• Main Authors: Fechter, S., Munz, C.-D.
• Format: Article
• Language: English
• Subjects: Compressibility; compressible multiphase flow; Computer simulation; discontinuous Galerkin; DNS; Droplets; Galerkin methods; ghost-fluid method; Mathematical analysis; Mathematical models; Numerical analysis; Oscillating; sharp-interface resolution
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4022

SummaryA numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional PNPM‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd. We present a numerical method for the simulation of compressible two‐phase flows. The capabilities of the numerical method are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3.