Positivity-preserving method for multi-resolution simulations of compressible flows
Abstract
We present a positivity-preserving method for multi-resolution simulations of compressible flows involving extreme conditions such as near vacuum and strong discontinuities. The novelty of this work is due to two aspects. First we extend the positivity-preserving flux limiter of (Hu et al., J Comput Phys 242, 2013) to the multi-resolution framework by modifying the prediction operator, based on the same limiting concept. Second, we develop a positivity-preserving local time stepping scheme for adaptive time marching. Instead of using fixed hierarchical time steps, the local time stepping scheme dynamically adjusts the time steps of all multi-resolution levels to maintain positivity. The method is validated and its capabilities are demonstrated by a range of test cases.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.07053
- arXiv:
- arXiv:1807.07053
- Bibcode:
- 2018arXiv180707053P
- Keywords:
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- Physics - Computational Physics
- E-Print:
- 27 pages and 9 figures