Semi-implicit method to solve compressible multiphase fluid flows without acoustic time step restrictions

Journal Article · Thu Jul 02 00:00:00 EDT 2020 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2020.104651· OSTI ID:1765291

Kanarska, Yuliya ^[1]; Dunn, Timothy ^[1]; Glascoe, Lee ^[1]; Lundquist, Katherine ^[1]; Noble, Charles ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Furthermore, since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1765291
• Alternate ID(s): OSTI ID: 1682507
• Report Number(s): LLNL-JRNL--797139; 998624
• Journal Information: Computers and Fluids, Journal Name: Computers and Fluids Journal Issue: no. 15 Vol. 210; ISSN 0045-7930
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Compressible flow
implicit pressure correction
multiphase flow