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A real ghost fluid method for the simulation of multimedium compressible flow. (English) Zbl 1114.35119
In the second section of the paper, the governing equations, essentially nonoscillatory schemes for gases and water, and the level set equation are provided. To avoid or prevent the appearance of hugely distorted level set contours caused by (potential) large flow velocity gradient, an extended artificial velocity field is constructed, for solving the level set equation. In the third section the detailed implementation of the real ghost fluid method (rGFM) based on the third-order essentially nonoscillatory schemes with Lax-Friedricins flux for one- and two-dimensional problems is presented. Some conclusions based on analysis for the rGFM are also obtained. Tests on the accuracy, convergence, and conservation errors incurred for the rGFM are given in section 4. In section 5 extensive comparisons are made between the simulations and analytical results.

MSC:
35L45 Initial value problems for first-order hyperbolic systems
65C20 Probabilistic models, generic numerical methods in probability and statistics
76T10 Liquid-gas two-phase flows, bubbly flows
35L67 Shocks and singularities for hyperbolic equations
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