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Multi-dimensional limiting process for three-dimensional flow physics analyses. (English) Zbl 1388.76218
Summary: The present paper deals with an efficient and accurate limiting strategy for multi-dimensional compressible flows. The multi-dimensional limiting process (MLP) which was successfully proposed in two-dimensional case [the last two authors, ibid. 208, No. 2, 570–615 (2005; Zbl 1329.76265)] is modified and refined for three-dimensional application. For computational efficiency and easy implementation, the formulation of MLP is newly derived and extended to three-dimensional case without assuming local gradient.
Through various test cases and comparisons, it is observed that the newly developed MLP is quite effective in controlling numerical oscillation in multi-dimensional flows including both continuous and discontinuous regions. In addition, compared to conventional TVD approach, MLP combined with improved flux functions does provide remarkable increase in accuracy, convergence and robustness in steady and unsteady three-dimensional compressible flows.

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
Full Text: DOI
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