CAJ | 학술논문

拟线性频谱特性分析方法，能够更加准确地给出非线性空间离散格式的频谱特性，已成为非线性格式性能评估的重要手段，但时间离散方法和计算点数等因素严重影响了该方法的预估精度和使用的方便性。为了剔除这些因素的影响，首先，通过理论推导获得了与时间离散无关的频谱表达式，解释了该式中各项的物理含义，并给出了推进时间步长对频谱计算结果的影响；其次，基于时间离散无关的拟线性频谱分析方法，分析了格式频谱特性曲线在某些点发生跳跃的主要原因是选取了不恰当的计算点数，并给出了一种计算点数选取方法，当计算点数超过某整数后，该方法可以有效地消除计算点数和初始相位变化对格式频谱特性所带来的影响。在此基础上，基于两个三阶精度 WCNS 格式，开展了它们的频谱特性和典型算例的数值模拟研究，结果表明，所发展的方法得到的拟线性频谱特性在定性上能够正确评价非线性空间离散格式特性，但定量上仍显不足。
의선성빈보특성분석방법，능구경가준학지급출비선성공간리산격식적빈보특성，이성위비선성격식성능평고적중요수단，단시간리산방법화계산점수등인소엄중영향료해방법적예고정도화사용적방편성。위료척제저사인소적영향，수선，통과이론추도획득료여시간리산무관적빈보표체식，해석료해식중각항적물리함의，병급출료추진시간보장대빈보계산결과적영향；기차，기우시간리산무관적의선성빈보분석방법，분석료격식빈보특성곡선재모사점발생도약적주요원인시선취료불흡당적계산점수，병급출료일충계산점수선취방법，당계산점수초과모정수후，해방법가이유효지소제계산점수화초시상위변화대격식빈보특성소대래적영향。재차기출상，기우량개삼계정도 WCNS 격식，개전료타문적빈보특성화전형산례적수치모의연구，결과표명，소발전적방법득도적의선성빈보특성재정성상능구정학평개비선성공간리산격식특성，단정량상잉현불족。
The quasi-linear spectral analysis method based on an approximate dispersion relation (ADR)can give spectral properties of nonlinear space-discrete schemes more accurately. It has become to be a very important tool for the assessment of nonlinear schemes up to date. However,some factors,such as time-discrete schemes and number of computation grid points, may affect the prediction accuracy seriously and make the ADR formula hard to be employed.In some cases,the spectral curve may even jump at some points under some conditions.In order to develop the formula independent of the influences of these factors,time-discrete independent ADR formula is proposed firstly through theoretical analysis.The meanings of each term in the ADR formula are explained,and the influence of time step on the time dependent ADR is investi-gated.Secondly,the reason resulting in the curve jumps at some wave numbers is analyzed using this new time-independent ADR formula.It is shown that the jumps may happen in case the number of grid points is improperly chosen.The proper method to selected grid points number is introduced,the proposed formula may eliminate the influence of number of grid points and initial phase angle effectively when the number of grid points is larger than this supposed number. Based on these works,the spectral properties of two 3rd-order WCNS schemes are investigated, and some typical cases are simulated using these two schemes.The results show that the quasi-linear spectral curve calculated by the ADR formula evaluates the properties of nonlinear schemes qualitatively.However,in respect of quantity,the errors cannot be ignored.