High-order staggered Lagrangian hydrodynamics (II) : the artificial viscosity and hourglass control algorithm
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866916942679375872 |
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| author | Sun, Zhiyuan Liu, Jun Wang, Pei |
| author_facet | Sun, Zhiyuan Liu, Jun Wang, Pei |
| contents | In this article, we investigate the artificial viscosity and hourglass control algorithms for high-order staggered Lagrangian hydrodynamics(SGH), as proposed in~\cite[Sun et al., 2025]{Sun2025High}. Inspired by the subzonal pressure method in classical staggered Lagrangian hydrodynamics, we extend the stiffness-based hourglass control algorithm to the high-order setting, enriching the pressure field from the $Q^{m-1}$ to the $Q^{m}$ polynomial space. A unified framework for this hourglass control approach is established, from which the classical subzonal pressure method naturally emerges as the special case of the $Q^1-P^0$ space. The artificial viscosity follows the formulation in~\cite[Dobrev et al., 2012]{Dobrev2012High}. We show that the viscosity admits a concise form, with intermediate variables explicitly computable, leading to improved computational efficiency and easier implementation. Moreover, the tensor viscosity in classical staggered Lagrangian hydrodynamics can be derived in a similarly compact and explicit form. Numerical experiments on two-dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order staggered Lagrangian hydrodynamics (II) : the artificial viscosity and hourglass control algorithm Sun, Zhiyuan Liu, Jun Wang, Pei Numerical Analysis 49N45, 65N21 In this article, we investigate the artificial viscosity and hourglass control algorithms for high-order staggered Lagrangian hydrodynamics(SGH), as proposed in~\cite[Sun et al., 2025]{Sun2025High}. Inspired by the subzonal pressure method in classical staggered Lagrangian hydrodynamics, we extend the stiffness-based hourglass control algorithm to the high-order setting, enriching the pressure field from the $Q^{m-1}$ to the $Q^{m}$ polynomial space. A unified framework for this hourglass control approach is established, from which the classical subzonal pressure method naturally emerges as the special case of the $Q^1-P^0$ space. The artificial viscosity follows the formulation in~\cite[Dobrev et al., 2012]{Dobrev2012High}. We show that the viscosity admits a concise form, with intermediate variables explicitly computable, leading to improved computational efficiency and easier implementation. Moreover, the tensor viscosity in classical staggered Lagrangian hydrodynamics can be derived in a similarly compact and explicit form. Numerical experiments on two-dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed algorithms. |
| title | High-order staggered Lagrangian hydrodynamics (II) : the artificial viscosity and hourglass control algorithm |
| topic | Numerical Analysis 49N45, 65N21 |
| url | https://arxiv.org/abs/2509.07636 |