Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (1): 151-178.doi: 10.1007/s42967-024-00414-w

• ORIGINAL PAPERS • 上一篇    下一篇

Semi-implicit-Type Order-Adaptive CAT2 Schemes for Systems of Balance Laws with Relaxed Source Term

Emanuele Macca, Sebastiano Boscarino   

  1. Dipartimento di Matematica ed Informatica, Universitá di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
  • 收稿日期:2023-09-27 修回日期:2024-03-13 接受日期:2024-04-08 出版日期:2025-04-21 发布日期:2025-04-21
  • 通讯作者: Emanuele Macca,emanuele.macca@unict.it;Sebastiano Boscarino,sebastiano.boscarino@unict.it E-mail:emanuele.macca@unict.it;sebastiano.boscarino@unict.it
  • 基金资助:
    Open access funding provided by Università degli Studi di Catania within the CRUI-CARE Agreement.

Semi-implicit-Type Order-Adaptive CAT2 Schemes for Systems of Balance Laws with Relaxed Source Term

Emanuele Macca, Sebastiano Boscarino   

  1. Dipartimento di Matematica ed Informatica, Universitá di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
  • Received:2023-09-27 Revised:2024-03-13 Accepted:2024-04-08 Online:2025-04-21 Published:2025-04-21
  • Supported by:
    Open access funding provided by Università degli Studi di Catania within the CRUI-CARE Agreement.

摘要: In this paper, we present two semi-implicit-type second-order compact approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori multi-dimensional optimal order detection (MOOD) paradigm to solve hyperbolic systems of balance laws with relaxed source terms. The resulting scheme presents the high accuracy when applied to smooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearly fail-safe property in terms of ensuring the positivity. The numerical results obtained from a variety of test cases, including smooth and non-smooth well-prepared and unprepared initial conditions, assessing the appropriate behavior of the semi-implicit-type second order CATMOOD schemes. These results have been compared in the accuracy and the efficiency with a second-order semi-implicit Runge-Kutta (RK) method.

关键词: Semi-implicit, Compact approximate Taylor (CAT), Multi-dimensional optimal order detection (MOOD), Hyperbolic system of balance laws with stiff source term

Abstract: In this paper, we present two semi-implicit-type second-order compact approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori multi-dimensional optimal order detection (MOOD) paradigm to solve hyperbolic systems of balance laws with relaxed source terms. The resulting scheme presents the high accuracy when applied to smooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearly fail-safe property in terms of ensuring the positivity. The numerical results obtained from a variety of test cases, including smooth and non-smooth well-prepared and unprepared initial conditions, assessing the appropriate behavior of the semi-implicit-type second order CATMOOD schemes. These results have been compared in the accuracy and the efficiency with a second-order semi-implicit Runge-Kutta (RK) method.

Key words: Semi-implicit, Compact approximate Taylor (CAT), Multi-dimensional optimal order detection (MOOD), Hyperbolic system of balance laws with stiff source term

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