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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem
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A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem

机译：一维对流扩散反应的高分辨率Petrov-Galerkin方法

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摘要

We present the design of a high-resolution Petrov-Galerkin (HRPG) method using linear finite elements for the problem defined by the residualrnR(Φ):=partial derivΦ/partial derivt+upartial derivΦ/partial derivx-kpartial deriv~2Φ/partial derivx~2+sΦ-frnwhere k,s ≥ 0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov-Galerkin (CAU/PG) method [A.C. Galeao, E.G. Dutra do Carmo, A consistent approximate upwind Petrov-Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83-95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Onate, Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233-265; E. Onate, J. Miquel, G. Hauke, Stabilized formulation for the advection-diffusion-absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926-3946] by an appropriate definition of the characteristic length. The prefix 'high-resolution' is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L_2-Projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u, k, s and f. Finally, some remarks are made on the extension of the HRPG method to multidimensions.
机译：我们针对残差R（Φ）定义的问题，提出了一种使用线性有限元的高分辨率Petrov-Galerkin（HRPG）方法的设计：=偏导数Φ/偏导数+偏导数Φ/偏导数-k偏导数〜2Φ/偏导数derivx〜2 +sΦ-frn其中k，s≥0。一维方法的结构与一致的近似迎风彼得罗夫-加勒金（CAU / PG）方法[AC加莱奥（Galeao） Dutra do Carmo，对流占主导地位的问题的一致近似上风Petrov-Galerkin方法，Comput。方法应用。机甲gr 68（1988）83-95]。也可以通过有限演算（FIC）程序[E. Onate，对流扩散运输和流体流动问题数值解的稳定方程的推导，计算机。方法应用。机甲gr 151（1998）233-265; E. Onate，J。Miquel，G。Hauke，使用有限积分和线性有限元计算对流-扩散-吸收方程的稳定公式，计算。方法应用。机甲gr 195（2006）3926-3946]通过适当定义特征长度。此处使用的前缀“高分辨率”是Harten所推广的含义，即平滑/常规状态下的二阶精度和非常规状态下的良好震荡捕获。设计程序着手解决在L_2投影中观察到的吉布斯现象的问题。接下来，我们研究稳定参数的条件，以避免由于对流项而引起的整体振荡。将这两个结果结合起来可以解决通常由吉布斯所困扰的问题，即数值解中的整体振动和色散振动。结果表明，该方法的确可以为宽范围的u，k，s和f值重现稳定的高分辨率数值解。最后，对HRPG方法扩展到多维提出了一些意见。

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  • 作者

    Prashanth Nadukandi; Eugenio Onate; Julio Garcia;

  • 作者单位

    International Center for Numerical Methods in Engineering (CIMNE), Universitat Politecnica de Catalunya (UPC), Campus Nord, Edifici C1, Gran Capitan s, 08034 Barcelona, Spain;

    International Center for Numerical Methods in Engineering (CIMNE), Universitat Politecnica de Catalunya (UPC), Campus Nord, Edifici C1, Gran Capitan s, 08034 Barcelona, Spain;

    International Center for Numerical Methods in Engineering (CIMNE), Universitat Politecnica de Catalunya (UPC), Campus Nord, Edifici C1, Gran Capitan s, 08034 Barcelona, Spain;

  • 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

    convection-diffusion-reaction; finite element; petrov-galerkin; stabilized high-resolution methods;

    机译：对流扩散反应;有限元;彼得罗夫-加勒金稳定的高分辨率方法;

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