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首页> 外文学位 >Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations.
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Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations.

机译：不连续Galerkin的微分公式和可压缩的Euler和Navier-Stokes方程的相关方法。

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摘要

A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin (DG), staggered grid, spectral volume (SV), and spectral difference (SD).;The approach is then extended to diffusion equation and Navier-Stokes equations. In the discretization of the diffusion terms, the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches are used. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh.;The current work also includes a study of high-order curve boundaries representations. A new boundary representation based on the Bezier curve is then developed and analyzed, which is shown to have several advantages for complicated geometries.;To further enhance the efficiency, the capability of h/p mesh adaptation is developed for the CPR solver. The adaptation is driven by an efficient multi-p a posteriori error estimator. P-adaptation is applied to smooth regions of the flow field while h-adaptation targets the non-smooth regions, identified by accuracy-preserving TVD marker. Several numerical tests are presented to demonstrate the capability of the technique.
机译：由Huynh提出并通过当前工作扩展到单纯形的一种新的高阶精度的守恒律数值解方法，被重命名为CPR（校正程序或通过重建的搭配罚分）。 CPR方法采用方程的微分形式，并通过校正程序解决了单元边界处通量值的跳跃问题。除了简单和经济之外，它还统一了几种现有方法，包括不连续Galerkin（DG），交错网格，光谱量（SV）和光谱差（SD）;然后将该方法扩展到扩散方程和Navier-Stokes方程。在离散化扩散项时，使用了BR2（Bassi和Rebay），内部罚分，紧凑型DG（CDG）和I连续方法。这些方法中的前三种方法最初是使用积分公式推导的，现在已在CPR框架中进行了重铸，而最初从四边形网格推导出的I连续方案已扩展到了三角形网格;当前的工作还包括研究高阶曲线边界表示。然后开发并分析了基于Bezier曲线的新边界表示法，该方法对于复杂的几何图形具有多个优势。为了进一步提高效率，开发了用于CPR求解器的h / p网格自适应功能。自适应由高效的多重后验误差估计器驱动。 P适应应用于流场的平滑区域，而h适应则针对由保持精度的TVD标记识别的非平滑区域。提出了几个数值测试，以证明该技术的能力。

著录项

  • 作者

    Gao, Haiyang.;

  • 作者单位

    Iowa State University.;

  • 授予单位 Iowa State University.;
  • 学科 Engineering Aerospace.
  • 学位 Ph.D.
  • 年度 2011
  • 页码 146 p.
  • 总页数 146
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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