Recently, Eulerian methods for capturing interfaces in multi-fluid problems become increasingly popular. While these methods can effectively handle significant deformations of interface, they have been known to produce nonphysical oscillations near material interfaces due to the smeared out density profile and radical change in equation of state across a material interface. One promising recent development to overcome these problems is the ‘Ghost Fluid Method’ (GFM). While being able to produce excellent results for simulation of gas-gas flows, the GFM boundary treatment is unsatisfactory for the case of liquid-liquid or liquid-gas compressible flows. The present study devotes to a new methodology for boundary condition capturing in multi-fluid compressible flows. The method, named ‘Characteristics-Based Matching (CBM)’, capitalizes on the recent development of the level set method and related techniques, i.e., PDE-based re-initialization and extrapolation, and the ‘Ghost Fluid Method’ (GFM). Specifically, the CBM utilizes the level set function to ‘capture’ interface position and a GFM-like strategy to tag computational nodes. In difference to the GFM method, which employs a boundary condition capturing in primitive variables, the CBM method implements boundary conditions based on a characteristic decomposition in the direction normal to the boundary. Since the method allows to avoid over-specification of boundary conditions by respecting the information flow, we believe that the CBM is able to ‘cure’ above-mentioned problems of the GFM boundary condition capturing technique. In this paper, the method’s performance is examined on fluid dynamics problems with stationary and moving boundaries. Numerical results agree well with known analytical or computational solutions and experimental data. Robust and accurate solutions were obtained. In particular, spurious over/under-heating errors, typical for moving boundary treatment by other methods, are essentially eliminated in the CBM solutions.
The ‘Characteristics-Based Matching’ (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces
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Nourgaliev, R, Dinh, N, & Theofanous, T. "The ‘Characteristics-Based Matching’ (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces." Proceedings of the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. Volume 1: Fora, Parts A, B, C, and D. Honolulu, Hawaii, USA. July 6–10, 2003. pp. 1705-1727. ASME. https://doi.org/10.1115/FEDSM2003-45550
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