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首页> 外文期刊>Journal of Computational Physics >A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows
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A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows

机译：无粘性可压缩流的高阶精确非结构有限体积牛顿-克里洛夫算法

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摘要

A fast implicit Newton-Krylov finite volume algorithm has been developed for high-order unstructured steady-state computation of inviscid compressible flows. The matrix-free generalized minimal residual (GMRES) algorithm is used for solving the linear system arising from implicit discretization of the governing equations, avoiding expensive and complex explicit computation of the high-order Jacobian matrix. The solution process has been divided into two phases: startup and Newton iterations. In the start-up phase an approximate solution with the general characteristics of the steady-state flow is computed by using a defect correction procedure. At the end of the start-up phase, the linearization of the flow field is accurate enough for steady-state solution, and a quasi-Newton method is used, with an infinite time step and very rapid convergence. A proper limiter implementation for efficient convergence of the high-order discretization is discussed and a new formula for limiting the high-order terms of the reconstruction polynomial is introduced. The accuracy, fast convergence and robustness of the proposed high-order unstructured Newton-Krylov solver for different speed regimes is demonstrated for the second, third and fourth-order discretization. The possibility of reducing computational cost required for a given level of accuracy by using high-order discretization is examined. (c) 2007 Elsevier Inc. All rights reserved.
机译：快速的隐式牛顿-克雷洛夫有限体积算法已被开发用于无粘性可压缩流的高阶非结构化稳态计算。使用无矩阵的广义最小残差（GMRES）算法来求解由控制方程的隐式离散化引起的线性系统，从而避免了高阶Jacobian矩阵的昂贵且复杂的显式计算。解决过程已分为两个阶段：启动和牛顿迭代。在启动阶段，使用缺陷校正程序计算出具有稳态流量一般特征的近似解。在启动阶段结束时，流场的线性化对于稳态解来说足够精确，并且使用了拟牛顿法，具有无限的时间步长和非常快的收敛性。讨论了有效收敛高阶离散化的适当限幅器实现，并介绍了一种用于限制重构多项式高阶项的新公式。针对二阶，三阶和四阶离散化，证明了所提出的高阶非结构化牛顿－克里洛夫求解器在不同速度范围下的精度，快速收敛性和鲁棒性。研究了通过使用高阶离散化来降低给定精度水平所需的计算成本的可能性。 （c）2007 Elsevier Inc.保留所有权利。

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