CAJ | 학술논문

以三次样条重构有限体积方法为例，研究非均匀网格上截断误差的分析方法。通过推导得到了分析非均匀网格上截断误差的基本准则，即在非均匀网格的截断误差分析中，要保证不显式或者隐含地改变数值方法对应的模板点———当不满足这一准则时，误差分析会得到不自洽的结果；而满足这一准则时，可保证分析结果的正确性。利用正确的误差分析结果，可发展进一步提高计算精度的措施。据此发展了扩散项在非均匀网格上达到三阶精度计算方法，从而可以使对流项和扩散项的计算达到一致三阶精度。
이삼차양조중구유한체적방법위례，연구비균균망격상절단오차적분석방법。통과추도득도료분석비균균망격상절단오차적기본준칙，즉재비균균망격적절단오차분석중，요보증불현식혹자은함지개변수치방법대응적모판점———당불만족저일준칙시，오차분석회득도불자흡적결과；이만족저일준칙시，가보증분석결과적정학성。이용정학적오차분석결과，가발전진일보제고계산정도적조시。거차발전료확산항재비균균망격상체도삼계정도계산방법，종이가이사대류항화확산항적계산체도일치삼계정도。
The derivation of truncation error on non-uniform grid for cubic spline reconstruction in finite volume framework is analyzed in this paper.The basic rule for the derivation of truncation error on non-uni-form grid is proposed which is that all derivations in the truncation error analysis should base on the same stencil.If this rule is not satisfied,the truncation error will not be self-consistent.Furthermore,the third-order discretization of the diffusion terms is obtained based on the correct truncation error analysis which makes both the convection and diffusion terms to achieve consistent third-order accuracy.