粘性不可压流的变分多尺度数值模拟

计算物理 ›› 2011, Vol. 28 ›› Issue (3): 347-354.

粘性不可压流的变分多尺度数值模拟

朱海涛, 欧阳洁, 王晓东

西北工业大学应用数学系, 陕西西安 710129

收稿日期:2010-01-29 修回日期:2010-09-19 出版日期:2011-05-25 发布日期:2011-05-25
作者简介:朱海涛(1982-),男,山西,硕士生,从事工程和科学领域的数值仿真研究
基金资助:
国家自然科学基金(10590353,10871159);国家重点基础研究发展计划(2005CB321704)资助项目

Numerical Simulation of Viscous Incompressible Flow with Variational Multiscale Method

ZHU Haitao, OUYANG Jie, WANG Xiaodong

School of Natural and Applied Science, Northwestern Polytechnical University, Xi'an 710072, China

Received:2010-01-29 Revised:2010-09-19 Online:2011-05-25 Published:2011-05-25

摘要/Abstract

摘要： 在变分多尺度的理论框架内,将待求解的各个物理量分解到"粗"、"细"两种尺度上.在"细"尺度上采用"泡"函数作为近似函数,通过Petrov-Galerkin方法得到"细"尺度上的近似解;然后引入求解"粗"尺度方程所需的稳定项及与其相适应的稳定化因子;最后运用有限元方法求解"粗"、"细"两种尺度耦合的整体变分多尺度方程,得到有限元近似解.数值算例表明,该处理方法成功地消除了数值求解粘性不可压Navier-Stokes方程过程中,由对流占优和速度-压力失耦引起的数值伪振荡;所引入的稳定化因子适用于结构网格及非结构网格上的数值计算.

关键词: 不可压N-S方程, 变分多尺度, 稳定化方法, 稳定化因子

Abstract: Velocity filed is decomposed into "coarse" and "fine" scales with a variational mulitiscale method.The "fine" scale is modeled by bubble functions,and solved with Petrov-Galerkin method.A stabilized term and stabilization parameter are introduced by coupling the "fine" and "coarse" scales.A variational multiscale equation which preserves properties of both "fine" and "coarse" scales is solved with a finite element method.It shows that the method is stable and accurate.It eliminates spurious oscillations caused by dominated advection term and uncoupling between velocity and pressure in numerical simulation of incompressible flows.The stabilization parameter can be applied to structure and unstructure meshes as well.

Key words: viscous incompressible, variational multiscale, stabilized method, stabilization parameter

中图分类号:

O24l

朱海涛, 欧阳洁, 王晓东. 粘性不可压流的变分多尺度数值模拟[J]. 计算物理, 2011, 28(3): 347-354.

ZHU Haitao, OUYANG Jie, WANG Xiaodong. Numerical Simulation of Viscous Incompressible Flow with Variational Multiscale Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(3): 347-354.