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首页> 外文期刊>Applied Mathematical Modelling >Very high-order accurate finite volume scheme on curved boundaries for the two-dimensional steady-state convection-diffusion equation with Dirichlet condition
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Very high-order accurate finite volume scheme on curved boundaries for the two-dimensional steady-state convection-diffusion equation with Dirichlet condition

机译：具有Dirichlet条件的二维稳态对流扩散方程的曲线边界上的超高阶精确有限体积格式

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摘要

Accuracy may be dramatically reduced when the boundary domain is curved and numerical schemes require a specific treatment of the boundary condition to preserve the optimal order. In the finite volume context, Ollivier-Gooch and Van Altena (2002) has proposed a technique to overcome such limitation and restore the very high-order accuracy which consists in specific restrictions considered in the least-squares minimization associated to the polynomial reconstruction. The method suffers from several drawbacks, particularly, the use of curved elements that requires sophisticated meshing algorithms. We propose a new method where the physical domain and the computational domain are distinct and we introduce the Reconstruction for Off-site Data (ROD) where polynomial reconstructions are carried out on the mesh using data localized outside of the computational domain, namely the Dirichlet condition situated on the physical domain. A series of numerical tests assess the accuracy, convergence rates, robustness, and efficiency of the new method and show that the boundary condition is fully integrated in the scheme with a very high-order accuracy and the optimal convergence rate is achieved.
机译：当边界域是弯曲的并且数值方案需要对边界条件进行特定处理以保持最佳顺序时，准确性可能会大大降低。在有限体积的情况下，Ollivier-Gooch和Van Altena（2002）提出了一种克服这种局限性并恢复非常高阶精度的技术，该技术包括与多项式重构相关的最小二乘最小化中所考虑的特定限制。该方法具有几个缺点，特别是使用需要复杂的网格划分算法的弯曲元件。我们提出了一种物理域和计算域是截然不同的新方法，并介绍了场外数据重建（ROD），其中使用计算域外的数据（即Dirichlet条件）在网格上进行多项式重建位于物理域上。一系列数值测试评估了该新方法的准确性，收敛速度，鲁棒性和效率，并表明边界条件以非常高的精度完全集成到了该方案中，并获得了最佳收敛速度。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第2期|752-767|共16页
  • 作者

    Ricardo Costa; Stephane Clain; Raphaeel Loubere; Gaspar J. Machado;

  • 作者单位

    Institut de Mathematiques de Toulouse. Universite Paul Sabatier, 31062 Toulouse, France,Centra de Matematica, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes, Portugal;

    Centra de Matematica, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes, Portugal;

    CNRS DR researcher, University of Bordeaux Mathematical Institute of Bordeaux (IMB), 33405 Talence, France;

    Centra de Matematica, Universidade do Minho, Campus de Azurem, 4800-058 Guimaraes, Portugal;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Very high-order finite volume method; Curved boundaries; Reconstruction for Off-site Data (ROD);

    机译：超高阶有限体积法;弯曲的边界;异地数据重建（ROD）;

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