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Adaptive mesh refinement algorithm based on dual trees for cells and faces for multiphase compressible flows. (English) Zbl 1452.76132
Summary: A novel adaptive mesh refinement method is proposed. The novelty of the method lies in using a dual data structure with two trees: A classical one for the computational cells and an extra one dedicated to computational cell faces. This new dual structure simplifies the algorithm, making the method easy to implement. It results in an efficient adaptive mesh refinement method that preserves an acceptable memory cost. This adaptive mesh refinement method is then applied to compressible multiphase flows in the framework of diffuse-interface methods. Efficiency of the method is demonstrated thanks to computational results for different applications: Transport, shock tube, surface-tension flow, cavitation and water-droplet atomization, in one and multi-dimensions. The test cases are performed with the open-source code ECOGEN and with quantitative comparisons regarding non-adaptive mesh refinement methods to analyze benefits. A discussion specific to parallel computing is also presented.
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76T10 Liquid-gas two-phase flows, bubbly flows
65Y05 Parallel numerical computation
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics, general
Full Text: DOI
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