Published October 1, 2025 | Published
Journal Article

Wave-appropriate multidimensional upwinding approach for compressible multiphase flows

  • 1. ROR icon California Institute of Technology

Abstract

This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In characteristic space, upwind schemes are used for acoustic waves, central schemes for vorticity and entropy waves, and Tangent of Hyper-bola for INterface Capturing (THINC) reconstruction for material interfaces and contact discontinuities (a subset of entropy waves). This approach prevents spurious vortices in periodic shear layers, accurately captures vortical structures in gas-gas and gas-liquid interactions, and improves the accuracy of shock-entropy wave interactions. In physical space, phasic densities are computed using THINC in regions of contact discontinuities and material interfaces, while tangential velocities are calculated with central schemes to improve vortical structures. An adaptive reconstruction technique is also introduced to mitigate oscillations near shocks, which arise from primitive variable reconstruction, by combining primitive and characteristic variable reconstructions with the liquid phase being identified using the stiffened gas parameter. The proposed multidimensional upwinding approach outperforms traditional schemes, demonstrating superior accuracy in capturing physical phenomena, reducing numerical artifacts, and better matching experimental results across complex test cases.

Copyright and License

© 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Acknowledgement

The author acknowledges discussions with Prof. Tim Colonius and Dr. Josette Bellan during this work. Additionally, the author had a productive discussion with Prof. Nikolaus Adams (TU Munich) at a conference regarding the periodic shear layer test case and the associated spurious vortices, which served as the motivation for the current paper. Lastly, the author thanks Jyothi and Arya for checking the manuscript and results.

Additional details

Created:
June 16, 2025
Modified:
June 16, 2025