Title: A higher‐order unsplit 2D direct Eulerian finite volume method for two‐material compressible flows based on the MOOD paradigms

Abstract

SUMMARY A higher‐order unsplit multi‐dimensional discretization of the diffuse interface model for two‐material compressible flows proposed by R. Saurel, F. Petitpas and R. A. Berry in 2009 is developed. The proposed higher‐order method is based on the concepts of the Multidimensional Optimal Order Detection (MOOD) method introduced in three recent papers for single‐material flows. The first‐order unsplit multi‐dimensional Finite Volume discretization presented by SPB serves as foundation for the development of the higher‐order unlimited schemes. Specific detection criteria along with a novel decrementing algorithm for the MOOD method are designed in order to deal with the complexity of multi‐material flows. Numerically, we compare errors and computational times on several 1D problems (stringent shock tube and cavitation problems) computed on 2D meshes with the second‐ and fourth‐order MOOD methods using a classical MUSCL method as reference. Several simulations of a 2D shocked R22 bubble in the air are also presented on Cartesian and unstructured meshes with the second‐ and fourth‐order MOOD methods, and qualitative comparisons confirm the conclusions obtained with 1D problems. These numerical results demonstrate the robustness of the MOOD approach and the interest of using more than second‐order methods even for locally singular solutions of complex physics models. Copyrightmore » © 2014 John Wiley & Sons, Ltd.« less

Authors:

Diot, S. ^[1]; François, M. M. ^[1]; Dendy, E. D. ^[2]

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+ Show Author Affiliations

1. Fluid Dynamics and Solid Mechanics (T‐3) Los Alamos National Laboratory NM 87545 Los Alamos USA
2. Computational Physics and Methods (CCS‐2) Los Alamos National Laboratory NM 87545 Los Alamos USA

Publication Date:

Tue Oct 07 00:00:00 EDT 2014

Sponsoring Org.:

USDOE

OSTI Identifier:

1401588

Grant/Contract Number:  

DE‐AC52‐06NA25396

Resource Type:

Publisher's Accepted Manuscript

Journal Name:

International Journal for Numerical Methods in Fluids

Additional Journal Information:

Journal Name: International Journal for Numerical Methods in Fluids Journal Volume: 76 Journal Issue: 12; Journal ID: ISSN 0271-2091

Publisher:

Wiley Blackwell (John Wiley & Sons)

Country of Publication:

United Kingdom

Language:

English