A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier-Stokes and Euler Equations on Unstructured Meshes

Costa Ricardo; Clain Stephane; Machado Gaspar J.; Loubere Raphael

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A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier-Stokes and Euler Equations on Unstructured Meshes

机译：非结构网格上静态不可压缩Navier-Stokes和Euler方程的非常高阶精确交错有限体积方案

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摘要

We propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order convergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme.

机译：我们提出基于多项式重构的六阶交错有限体积方案，以实现不可压缩的Navier-Stokes和Euler方程的高精度数值解。该方案配备了具有解松弛功能的定点算法，以加快收敛速度并减少计算时间。提供数值测试以评估该方法达到最高六阶收敛速度的有效性。还提供了基准盖驱动腔问题的仿真，以突出提出的高阶方案的好处。

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来源
《Journal of Scientific Computing》 |2017年第3期|1375-1411|共37页
作者
Costa Ricardo; Clain Stephane; Machado Gaspar J.; Loubere Raphael;
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作者单位

Univ Paul Sabatier, Inst Math Toulouse, F-31062 Toulouse, France|Univ Minho, Ctr Matemat, Campus Azurem, P-4800058 Guimaraes, Portugal;

Univ Minho, Ctr Matemat, Campus Azurem, P-4800058 Guimaraes, Portugal;

Univ Minho, Ctr Matemat, Campus Azurem, P-4800058 Guimaraes, Portugal;

Univ Paul Sabatier, Inst Math Toulouse, F-31062 Toulouse, France;

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正文语种 eng
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关键词
Finite volume method; High-order scheme; Polynomial reconstruction; Navier-Stokes equations; Euler equations; Fixed-point algorithm;

机译：有限体积法;高阶格式;多项式重构;Navier-Stokes方程;Euler方程;定点算法;

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专利

1. A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes [J] . Ricardo Costa, Stéphane Clain, Gaspar J. Machado Journal of Computational Physics . 2017,第期

机译：用于交错非结构化网格上的稳态不可压缩的斯托克斯方程的第六阶有限体积方案
2. HIGH-ORDER ACCURATE AND HIGH-RESOLUTION UPWIND FINITE VOLUME SCHEME FOR SOLVING EULER/REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS [J] . 王保国, 郭延虎, 刘秋生, 力学学报：英文版 . 1998,第001期

机译：用于求解欧拉/雷诺瓦尔平均Navier-Stokes方程的高阶准确和高分辨率锻造有限卷方案
3. A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes [J] . Sylvain Boivin, Florent Cayre, Jean-Marc Harard International Journal of Thermal Sciences . 2000,第8期

机译：求解非结构网格上不可压缩流的Navier-Stokes方程的有限体积方法
4. An accurate finite volume scheme for euler and navier-stokes equations on unstructured adaptive grids [C] . M. Delanaye, J. A. Essers AIAA computational fluid dynamics conference . 1995

机译：非结构化自适应网格上欧拉-纳斯托克斯方程的精确有限体积方案
5. Finite volume, adaptive-multigrid methods for Euler and Navier-Stokes equations on three-dimensional unstructured grids. [D] . Parthasarathy, Vijayan. 1994

机译：三维非结构化网格上Euler和Navier-Stokes方程的有限体积自适应多网格方法。
6. High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling [O] . H T Banks, Malcolm J Birch, Mark P Brewin, -1

机译：具有时间解耦的声波和粘滞波动方程的高阶时空有限元格式
7. A sixth-order finite volume scheme for the steady-state incompressible Stokes equations on staggered unstructured meshes [O] . Costa, Ricardo, Clain, Stéphane, Machado, Gaspar J. 2017

机译：交错非结构网格上稳态不可压缩Stokes方程的六阶有限体积格式

A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier-Stokes and Euler Equations on Unstructured Meshes

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