基于牛顿插值的高分辨率有限体积格式精选.pdf

Advances in Applied Mathematics 应用数学进展, 2015, 4, 150-161 Published Online May 2015 in Hans. /journal/aam /10.12677/aam.2015.42020 A High-Resolution Finite Volume Scheme Based on Newtonian Interpolation Wei Gao, Qing Zhang, Hong Li, Yang Liu School of Mathematical Sciences, Inner Mongolia University, Hohhot Inner Mongolia Email: gaow@, math_zhangqing@163.com, smslh@, mathliuyang@ th th th Received: Apr. 24 , 2015; accepted: May 10 , 2015; published: May 15 , 2015 Copyright © 2015 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract Finite volume method plays an important role in fluid flow and heat transfer numerical calcula- tion. How to eliminate unphysical oscillations caused by numerical solution of convection diffu- sion equation selecting discontinuity wave as the initial condition is a key task for studying finite volume method. New high-resolution schemes were constructed by Newton interpolation poly- nomial based on convection boundness criterion (CBC). Classic test cases demonstrated that the present numerical scheme possesses high resolution and good stability for high gradient and dis- continuous solution. Keywords Convection Diffusion Equation, Newton Interpolation Polynomial, Convection Boundness Criterion (CBC), Total Variation Diminishing (TVD) 基于牛顿插值的高分辨率有限体积格式 高 巍，张 庆，李 宏，刘 洋 内蒙古大学数学科学学院，内蒙古 呼和浩特 Email: gaow@, math_zhangqing@163.com, smslh@, mathliuyang@ 收稿日期：2015年4月24 日；录用日期：2015年5月10 日；发布日期：2015年5月15 日 150 基于牛顿插值的高分辨率有限体积格式 摘 要 有