基于节点的一致不符梯度平滑方案,用于高效伽勒金无网格计算

IF 8.7 2区 工程技术 Q1 Mathematics
Liheng Fan, Like Deng, Dongdong Wang
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引用次数: 0

摘要

稳定保形节点积分(SCNI)目前广泛应用于 Galerkin 无网格计算。SCNI 的一个关键要素是在一组保形节点代表域内定义应变或梯度平滑,这些代表域通常由无网格节点之外的辅助点构成。然而,与直接节点积分相比,这些辅助点可能会大大增加 SCNI 的存储要求和计算成本。为了解决这个问题,本文提出了一种纯节点一致非一致性梯度平滑(CNGS)方案,以加速 Galerkin 无网格计算。在所提出的方法中,只使用无网格节点来构建重叠和不一致的节点代表域,然后采用这些节点进行节点梯度平滑操作。然而,与常见的违反积分一致性的现有不符合梯度平滑算法不同,本文提出的方法通过将节点梯度平滑域与节点积分域按比例分离,保持了理想的积分一致性,从根本上确保了无网格求解的精度。同时,由于梯度平滑评估中没有辅助点,与 SCNI 相比,所提出的 CNGS 方法大大提高了计算效率。数值结果充分证明了所提方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation

A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation

The stabilized conforming nodal integration (SCNI) is currently widely employed in Galerkin meshfree formulation. A key ingredient of SCNI is the strain or gradient smoothing defined within a set of conforming nodal representative domains, which usually are formed by the auxiliary points in addition to the meshfree nodes. Nonetheless, these auxiliary points may significantly increase the storage requirement and computational cost of SCNI, in comparison with the direct nodal integration. In order to address this issue, a purely node-based consistent non-conforming gradient smoothing (CNGS) scheme is proposed herein to accelerate the Galerkin meshfree computation. In the proposed method, only the meshfree nodes are employed to construct overlapping and non-conforming nodal representative domains, which are then adopted for the nodal gradient smoothing operation. However, unlike the existing non-conforming gradient smoothing algorithms that commonly violate the integration consistency, the proposed method maintains the desirable integration consistency through a proportional separation between the nodal gradient smoothing domains and the nodal integration domains, which essentially ensures the meshfree solution accuracy. Meanwhile, due to the absence of auxiliary points in the gradient smoothing evaluation, the computational efficiency is substantially improved by the proposed method of CNGS compared with SCNI. The effectiveness of the proposed methodology is well demonstrated by numerical results.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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