A study of troubled-cell indicators applied to finite volume methods using a novel monotonicity parameter
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913795187671040 |
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| author | Rao, R. Shivananda Ramakrishna, M. |
| author_facet | Rao, R. Shivananda Ramakrishna, M. |
| contents | We adapt a troubled-cell indicator developed for discontinuous Galerkin (DG) methods to the finite volume method (FVM) framework for solving hyperbolic conservation laws. This indicator depends solely on the cell-average data of the target cell and its immediate neighbours. Once the troubled-cells are identified, we apply the limiter only in these cells instead of applying in all computational cells. We introduce a novel technique to quantify the quality of the solution in the neighbourhood of the shock by defining a monotonicity parameter $μ$. Numerical results from various two-dimensional simulations on the hyperbolic systems of Euler equations using a finite volume solver employing MUSCL reconstruction validate the performance of the troubled-cell indicator and the approach of limiting only in the troubled-cells. These results show that limiting only in the troubled-cells is preferable to limiting everywhere as it improves convergence without compromising on the solution accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study of troubled-cell indicators applied to finite volume methods using a novel monotonicity parameter Rao, R. Shivananda Ramakrishna, M. Numerical Analysis Computational Engineering, Finance, and Science We adapt a troubled-cell indicator developed for discontinuous Galerkin (DG) methods to the finite volume method (FVM) framework for solving hyperbolic conservation laws. This indicator depends solely on the cell-average data of the target cell and its immediate neighbours. Once the troubled-cells are identified, we apply the limiter only in these cells instead of applying in all computational cells. We introduce a novel technique to quantify the quality of the solution in the neighbourhood of the shock by defining a monotonicity parameter $μ$. Numerical results from various two-dimensional simulations on the hyperbolic systems of Euler equations using a finite volume solver employing MUSCL reconstruction validate the performance of the troubled-cell indicator and the approach of limiting only in the troubled-cells. These results show that limiting only in the troubled-cells is preferable to limiting everywhere as it improves convergence without compromising on the solution accuracy. |
| title | A study of troubled-cell indicators applied to finite volume methods using a novel monotonicity parameter |
| topic | Numerical Analysis Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2504.11056 |