High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics
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| Format: | Preprint |
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2025
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| author | Chu, Shaoshuai Herty, Michael Toro, Eleuterio F. |
| author_facet | Chu, Shaoshuai Herty, Michael Toro, Eleuterio F. |
| contents | We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in [ E. F. Toro, M. E. Vázquez-Cendón, Comput. \& Fluids, 70 (2012), pp. 1--12], where the Euler equations of gas dynamics are split into two subsystems: the advection and pressure systems. In this paper, we formulate the TV splitting within the semi-discrete framework to extend it to higher orders of accuracy for the first time. The second-order extension is obtained by using piecewise linear interpolant to reconstruct the one-sided point values of the unknowns. The third- and fifth-order schemes are developed using the finite-difference alternative weighted essentially non-oscillatory (A-WENO) framework, which is particularly effective in handling multidimensional problems and provides a more straightforward approach to constructing higher-order WENO schemes. These extensions significantly improve the resolution of discontinuities and the accuracy of numerical solutions, as demonstrated by a series of numerical experiments of both the one- and two-dimensional Euler equations of gas dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics Chu, Shaoshuai Herty, Michael Toro, Eleuterio F. Numerical Analysis We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in [ E. F. Toro, M. E. Vázquez-Cendón, Comput. \& Fluids, 70 (2012), pp. 1--12], where the Euler equations of gas dynamics are split into two subsystems: the advection and pressure systems. In this paper, we formulate the TV splitting within the semi-discrete framework to extend it to higher orders of accuracy for the first time. The second-order extension is obtained by using piecewise linear interpolant to reconstruct the one-sided point values of the unknowns. The third- and fifth-order schemes are developed using the finite-difference alternative weighted essentially non-oscillatory (A-WENO) framework, which is particularly effective in handling multidimensional problems and provides a more straightforward approach to constructing higher-order WENO schemes. These extensions significantly improve the resolution of discontinuities and the accuracy of numerical solutions, as demonstrated by a series of numerical experiments of both the one- and two-dimensional Euler equations of gas dynamics. |
| title | High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.01699 |