High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI
High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI
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DOI：
10.21236/ada364301
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发表时间：
1998-08
期刊：
影响因子：
--
通讯作者：
D. Gaitonde;M. Visbal
中科院分区：
文献类型：
--
作者：
D. Gaitonde;M. Visbal
翻译后摘要：频谱的高阶计划的开发，以解决有限差分公式的Navier-Stokes方程。Pade型公式的第六阶与五点模板开发的差分格式。粘性项是由一阶导数算子的连续应用来处理的。然而，公式也推导出用于中点插值微分策略。为了数值稳定性，高达十阶滤波方案的开发。的微分和滤波方案的频谱特性进行检查和指导方针，以选择适当的滤波器系数。在边界附近的微分和滤波得到了特殊的高阶公式。系统实施Neumann型边界条件所需的系数也被提出。简要描述的方式，其中FDL 3DI代码是通过耦合的近似因子的程序与这些基于紧致差分的算法，并通过将一个显式的四阶龙格-库塔法增强。
Abstract : A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme.