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A thermodynamic and dynamic subgrid closure model for two-material cells


Correspondence to: Mingyu Sun, Institute of Fluid Science, Tohoku University, Sendai 980-8578, Japan.



A general and robust subgrid closure model for two-material cells is proposed. The conservative quantities of the entire cell are apportioned between two materials, and then, pressure and velocity are fully or partially equilibrated by modeling subgrid wave interactions. An unconditionally stable and entropy-satisfying solution of the processes has been successfully found. The solution is valid for arbitrary level of relaxation. The model is numerically designed with care for general materials and is computationally efficient without recourse to subgrid iterations or subcycling in time. The model is implemented and tested in the Lagrange-remap framework. Two interesting results are observed in 1D tests. First, on the basis of the closure model without any pressure and velocity relaxation, a material interface can be resolved without creating numerical oscillations and/or large nonphysical jumps in the problem of the modified Sod shock tube. Second, the overheating problem seen near the wall surface can be solved by the present entropy-satisfying closure model. The generality, robustness, and efficiency of the model make it useful in principle in algorithms, such as ALE methods, volume of fluid methods, and even some mixture models, for compressible two-phase flow computations. Copyright © 2013 John Wiley & Sons, Ltd.

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