本文選題：陰陽(yáng)網(wǎng)格 + 守恒強(qiáng)迫��； 參考：《中國(guó)氣象科學(xué)研究院》2017年碩士論文

【摘要】：陰陽(yáng)網(wǎng)格是一種準(zhǔn)均勻重疊網(wǎng)格,能夠有效避免傳統(tǒng)經(jīng)緯度網(wǎng)格的極點(diǎn)奇異性和經(jīng)線在極區(qū)輻合的問(wèn)題,但是由于陰陽(yáng)網(wǎng)格不能自然保證物理量的守恒性,因此,陰陽(yáng)網(wǎng)格上的質(zhì)量守恒算法對(duì)于陰陽(yáng)網(wǎng)格在全球模式構(gòu)建和應(yīng)用具有重要意義,是模式長(zhǎng)期穩(wěn)定積分和保證計(jì)算效果的重要性能指標(biāo)。本文提出了一種改進(jìn)陰陽(yáng)網(wǎng)格守恒算法的方案,就是在已有的質(zhì)量均勻分布假定下陰陽(yáng)網(wǎng)格守恒強(qiáng)迫算法的基礎(chǔ)上,構(gòu)建網(wǎng)格內(nèi)質(zhì)量的雙線性分布和邊界通量線性分布的質(zhì)量守恒強(qiáng)迫算法,以提高陰陽(yáng)網(wǎng)格平流計(jì)算的精度和模式積分的穩(wěn)定性。運(yùn)用CIP-CSLR平流方案對(duì)通量形式平流方程數(shù)值求解,分別通過(guò)“余弦鐘”平流試驗(yàn)、正弦波試驗(yàn)、變形流試驗(yàn)、平衡流試驗(yàn)、全球過(guò)山氣流試驗(yàn),二維Rossby-Haurwitz波試驗(yàn)對(duì)質(zhì)量雙線性分布、邊界通量線性分布的新方案與質(zhì)量和通量均勻分布的原方案進(jìn)行了對(duì)比,標(biāo)準(zhǔn)化誤差和標(biāo)量場(chǎng)分布均表明新方案可有效提高陰陽(yáng)網(wǎng)格守恒算法的計(jì)算效果,且計(jì)算負(fù)擔(dān)沒(méi)有明顯增加,具有較好的實(shí)用價(jià)值。本研究還進(jìn)一步嘗試將三階Runge-Kutta方法應(yīng)用在已有的CIP-CSLR平流方案上,利用同樣的理想試驗(yàn)對(duì)新方案的性能進(jìn)行檢驗(yàn),表明新方案能夠在保證守恒性的前提下有效提高收斂階數(shù)。
[Abstract]:Yin-yang mesh is a kind of quasi-uniform overlapping grid, which can effectively avoid the singularity of the poles of the traditional longitude and latitude grid and the convergence of longitude in the polar region. However, the Yin-yang grid can not guarantee the conservation of physical quantities naturally.The quality conservation algorithm on Yin-Yang mesh is of great significance for the construction and application of Yin-Yang mesh in the global pattern, and is an important performance index for the long-term stable integration of the model and the guarantee of computing effect.In this paper, a scheme for improving the conservation algorithm of Yin and Yang grids is proposed, which is based on the existing forced algorithm of yin and yang grid conservation under the assumption of uniform mass distribution.A mass conservation forcing algorithm for bilinear mass distribution and boundary flux linear distribution is constructed to improve the accuracy of advection calculation and the stability of model integrals.The advection equation of flux form is solved numerically by CIP-CSLR advection scheme. The mass bilinear distribution is obtained by "cosine clock" advection test, sinusoidal wave test, deformation flow test, equilibrium flow test, global mountain flow test and two-dimensional Rossby-Haurwitz wave test.The new scheme for linear distribution of boundary flux is compared with the original scheme for uniform distribution of mass and flux. The standardization error and scalar field distribution show that the new scheme can effectively improve the computational effect of the conservation algorithm of Yin and Yang grids.And the calculation burden does not increase obviously, which has good practical value.Furthermore, the third order Runge-Kutta method is applied to the existing CIP-CSLR advection scheme, and the performance of the new scheme is tested by the same ideal experiment. It is shown that the new scheme can effectively improve the convergence order under the premise of ensuring conservation.
【學(xué)位授予單位】：中國(guó)氣象科學(xué)研究院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：P456.7

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