本文選題：波動(dòng)數(shù)值模擬 + 譜元法�。� 參考：《力學(xué)學(xué)報(bào)》2017年02期

【摘要】：多次透射公式(multi-transmitting formula,MTF)是一種具有普適性的局部人工邊界條件,但其在近場(chǎng)波動(dòng)數(shù)值模擬中一般與有限元法結(jié)合.由于波動(dòng)譜元模擬的數(shù)值格式與有限元格式有極大的不同,傳統(tǒng)的MTF在譜元離散格式中無法直接實(shí)現(xiàn).為了使物理概念清楚、精度可控的多次透射人工邊界條件能夠適應(yīng)波動(dòng)譜元模擬的需求,首先指出多次透射邊界與譜元離散格式結(jié)合的基本問題,并分析了空間內(nèi)插和時(shí)間內(nèi)插兩種方案的可行性.然后從空間內(nèi)插角度出發(fā),提出基于拉格朗日多項(xiàng)式插值模式的MTF譜元格式,并采用一種簡(jiǎn)單內(nèi)插方法實(shí)現(xiàn)高階MTF.最后通過一維波動(dòng)數(shù)值試驗(yàn)檢驗(yàn)這些MTF譜元格式的精度,并討論其數(shù)值穩(wěn)定性.結(jié)果表明:對(duì)于一、二階MTF,幾種格式的精度相當(dāng);對(duì)于三、四階MTF,基于譜單元位移模式插值的格式精度最高.相反,隨著插值多項(xiàng)式階次的升高,不同MTF格式的穩(wěn)定臨界值逐步降低,但是所有格式均在人工波速大大超過物理波速時(shí)才可能發(fā)生失穩(wěn).
[Abstract]:Multi-transmissive formative MTF is a universal local artificial boundary condition, but it is generally combined with finite element method in numerical simulation of near-field wave. Because the numerical scheme of wave spectral element simulation is very different from the finite element scheme, the traditional MTF can not be realized directly in the spectral element discrete scheme. In order to make the physical concept clear and the precision controllable multiple transmission artificial boundary conditions can meet the needs of wave spectral element simulation, the basic problem of combining multiple transmission boundary with spectral element discrete scheme is pointed out. The feasibility of space interpolation and time interpolation is analyzed. Then, from the point of view of spatial interpolation, an MTF spectral element scheme based on Lagrange polynomial interpolation mode is proposed, and a simple interpolation method is used to realize higher order MTF. Finally, the accuracy and numerical stability of these MTF spectral element schemes are verified by one-dimensional wave numerical experiments. The results show that for the first and second order MTF, the accuracy of several schemes is the same, and for the third and fourth order MTF, the scheme based on spectral element displacement mode interpolation has the highest accuracy. On the contrary, with the increase of interpolation polynomial order, the stable critical value of different MTF schemes decreases gradually, but the instability of all schemes is likely to occur when the artificial wave velocity exceeds the physical wave velocity.
【作者單位】： 南京工業(yè)大學(xué)土木工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(51278245)
【分類號(hào)】：O241.82

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