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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Development of a locally analytic prolongation operator in the two-grid, three-level method for the Navier-Stokes equations
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Development of a locally analytic prolongation operator in the two-grid, three-level method for the Navier-Stokes equations

机译：用两网格，三层方法为Navier-Stokes方程开发局部解析延长算子

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摘要

In this article, two three-level methods employing the same prolongation operator are proposed for efficiently solving the incompressible Navier-Stokes equations in a two-grid system. Each method involves solving one smaller system of nonlinear equations in the coarse mesh. The chosen Newton- or Oseen-type linearized momentum equations along with a correction step are solved only once on the fine mesh. Within the three-level framework, the locally analytic prolongation operator needed to bridge the convergent Navier-Stokes solutions obtained at the coarse mesh and the interpolated velocities at the fine mesh is developed to improve the prediction quality. To increase prediction accuracy, the linearized momentum equations are discretized within the alternating direction implicit context using our previously developed nodally exact convection-diffusion-reaction finite-difference scheme. Two proposed three-level methods are rigorously assessed in terms of simulated accuracy, nonlinear convergence rate, and elapsed CPU time.
机译：在本文中，为有效地解决两网格系统中不可压缩的Navier-Stokes方程，提出了两种使用同一延长算子的三级方法。每种方法都涉及在粗网格中求解一个较小的非线性方程组。所选的牛顿型或Oseen型线性动量方程式以及校正步骤在精细网格上仅求解一次。在三级框架内，开发了桥接粗糙网格处的收敛Navier-Stokes解和精细网格处的插值速度所需的局部分析延长算子，以提高预测质量。为了提高预测精度，使用我们以前开发的节点精确对流扩散反应有限差分方案在交替方向隐式上下文内离散化线性动量方程。在模拟精度，非线性收敛速度和经过的CPU时间方面严格评估了两种建议的三级方法。

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