Revisting High-Resolution Schemes with van Albada Slope Limiter

doi:10.1007/s42967-023-00348-9

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (3): 1924-1953.doi: 10.1007/s42967-023-00348-9

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Revisting High-Resolution Schemes with van Albada Slope Limiter

Jingcheng Lu^1,2, Eitan Tadmor³

1 Department of Mathematics, University of Maryland, College Park, MD, USA;
2 School of Mathematics, University of Minnesota, Minneapolis, MN, USA;
3 Department of Mathematics and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD, USA

收稿日期:2023-04-06 修回日期:2023-08-07 接受日期:2023-10-29 发布日期:2024-12-20
通讯作者: Eitan Tadmor,tadmor@umd.edu;Jingcheng Lu,lu000688@umn.edu E-mail:tadmor@umd.edu;lu000688@umn.edu
基金资助:
Research was supported in part by the ONR Grant N00014-2112773.

Revisting High-Resolution Schemes with van Albada Slope Limiter

Jingcheng Lu^1,2, Eitan Tadmor³

1 Department of Mathematics, University of Maryland, College Park, MD, USA;
2 School of Mathematics, University of Minnesota, Minneapolis, MN, USA;
3 Department of Mathematics and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD, USA

Received:2023-04-06 Revised:2023-08-07 Accepted:2023-10-29 Published:2024-12-20
Contact: Eitan Tadmor,tadmor@umd.edu;Jingcheng Lu,lu000688@umn.edu E-mail:tadmor@umd.edu;lu000688@umn.edu
Supported by:
Research was supported in part by the ONR Grant N00014-2112773.

摘要/Abstract

摘要： Slope limiters play an essential role in maintaining the non-oscillatory behavior of highresolution methods for nonlinear conservation laws. The family of minmod limiters serves as the prototype example. Here, we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al. (Astron Astrophys 108: 76–84, 1982). The van Albada (vA) limiter is smoother near extrema, and consequently, in many cases, it outperforms the results obtained using the standard minmod limiter. In particular, we prove that the vA limiter ensures the onedimensional Total-Variation Diminishing (TVD) stability and demonstrate that it yields noticeable improvement in computation of one- and two-dimensional systems.

关键词: High resolution, Limiters, Total-Variation Diminishing (TVD) stability, Central schemes

Abstract: Slope limiters play an essential role in maintaining the non-oscillatory behavior of highresolution methods for nonlinear conservation laws. The family of minmod limiters serves as the prototype example. Here, we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al. (Astron Astrophys 108: 76–84, 1982). The van Albada (vA) limiter is smoother near extrema, and consequently, in many cases, it outperforms the results obtained using the standard minmod limiter. In particular, we prove that the vA limiter ensures the onedimensional Total-Variation Diminishing (TVD) stability and demonstrate that it yields noticeable improvement in computation of one- and two-dimensional systems.

Key words: High resolution, Limiters, Total-Variation Diminishing (TVD) stability, Central schemes

中图分类号:

35L65
65M10

Jingcheng Lu, Eitan Tadmor. Revisting High-Resolution Schemes with van Albada Slope Limiter[J]. Communications on Applied Mathematics and Computation, 2024, 6(3): 1924-1953.

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Revisting High-Resolution Schemes with van Albada Slope Limiter

Revisting High-Resolution Schemes with van Albada Slope Limiter

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