对流扩散方程数值耗散的定量研究方法

Quantitative research method of numerical dissipation levels of convective-diffusive equation

针对对流扩散方程数值耗散问题普遍缺乏明确定量指标的现状,提出了度量数值耗散程度的定量指标及其研究方法,即借助广义"假扩散"系数这一定量指标来度量某一离散格式的数值耗散程度,其数值上近似等于具有相同扩散效应的真扩散所对应的扩散系数,其中真扩散效应可通过求解纯扩散问题的高精度数值解近似得到。采用该方法研究了三阶QUICKEST离散格式的数值耗散规律,分析了时间步长、流速大小及空间步长对"假扩散"系数的敏感性以及相关性,得到了"假扩散"系数的具体表达式,进而验证了该定量研究方法的可行性。

Considering the fact that quantitative indicator on numerical dissipation is lacking, in this paper the quantitative indicator and research method were given. The method is, namely, using generalized ＂false diffusive＂ coefficient of the certain indicators to measure the degree of numerical dissipation of a discrete tonnat. The numerical value of the above method approximately equals to the same effect on the true diffusion of the diffusion coefficient. As to the true diffusion effect, the highly precise numerical value can be approximately obtained by the solution of the pure diffusion tonnulas. This method was successfully applied to third-order QUICKEST discrete scheme. The overall results show that false diffusion coefficient could he introduced to characterize the numerical dissipation level, whose value can be obtained by comparing the true diffusion effect.