High-order staggered Lagrangian hydrodynamics (II) : the artificial viscosity and hourglass control algorithm

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Autori principali: Sun, Zhiyuan, Liu, Jun, Wang, Pei
Natura: Preprint
Pubblicazione: 2025
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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