重庆理工大学学报：自然科学
重慶理工大學學報：自然科學
중경리공대학학보：자연과학
Journal of Chongqing Institute of Technology
2012年
2期
112-117
,共6页
对流扩散方程%紧致格式%高精度%隐式差分%Richardson外推法%有限差分法
對流擴散方程%緊緻格式%高精度%隱式差分%Richardson外推法%有限差分法
대류확산방정%긴치격식%고정도%은식차분%Richardson외추법%유한차분법
convection diffusion equation%compact scheme%high order accuracy%implicit differ- ence%Richardson extrapolation%finite difference scheme
对于二维对流扩散方程,利用一阶和二阶导数的四阶Padé型紧致差分逼近式,结合原方程,得到了求解该方程的一种四阶精度的隐式紧致差分格式。该格式在每个空间方向上只涉及到3个点处的未知量及导数值,对导数利用四阶显式偏心格式,然后利用Richardson外推法、算子插值法及导数在边界点处的六阶显式偏心格式,将构造的四阶紧致差分格式的精度提高到六阶。最后通过数值实验验证了该方法的精确性和有效性。
對于二維對流擴散方程,利用一階和二階導數的四階Padé型緊緻差分逼近式,結閤原方程,得到瞭求解該方程的一種四階精度的隱式緊緻差分格式。該格式在每箇空間方嚮上隻涉及到3箇點處的未知量及導數值,對導數利用四階顯式偏心格式,然後利用Richardson外推法、算子插值法及導數在邊界點處的六階顯式偏心格式,將構造的四階緊緻差分格式的精度提高到六階。最後通過數值實驗驗證瞭該方法的精確性和有效性。
대우이유대류확산방정,이용일계화이계도수적사계Padé형긴치차분핍근식,결합원방정,득도료구해해방정적일충사계정도적은식긴치차분격식。해격식재매개공간방향상지섭급도3개점처적미지량급도수치,대도수이용사계현식편심격식,연후이용Richardson외추법、산자삽치법급도수재변계점처적륙계현식편심격식,장구조적사계긴치차분격식적정도제고도륙계。최후통과수치실험험증료해방법적정학성화유효성。
Based on the fourth-order Pade formula of the first and second-order derivatives, a fourth- order compact difference scheme is proposed for solving two-dimensional convection diffusion equa- tion. Fourth order explicit difference schemes are used to construct the same order discretization of boundary points. Then, the accuracy of the fourth-order compact difference schemes is upgraded to sixth-order by using Richardson extrapolation technique and operator interpolation scheme. Sixth-order explicit difference schemes of first and second-order derivatives on the boundaries are used. Finally, numerical experiments are given to prove the accuracy and efficiency of the present method.
