本文選題：Euler　切入點(diǎn)：方程　出處：《長(zhǎng)安大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：雙曲守恒律方程組是計(jì)算流體力學(xué)中的重要研究?jī)?nèi)容之一。求解雙曲守恒律方程組的熵相容格式從熱力學(xué)第二定律出發(fā),是一種滿足熵穩(wěn)定條件的數(shù)值格式,也是目前對(duì)熵的變化估計(jì)得最準(zhǔn)確的一種熵穩(wěn)定格式。該格式有較強(qiáng)的物理背景,能有效避免一些非物理現(xiàn)象的產(chǎn)生。本文在Euler方程的熵相容格式的基礎(chǔ)上,研究了一類高分辨率、高精度的熵相容格式。主要研究?jī)?nèi)容包括:(1)介紹熵相容格式。論述了熵守恒/熵穩(wěn)定格式的基本理論、一般熵守恒格式的構(gòu)造過程,并介紹了兩種簡(jiǎn)單且便于實(shí)現(xiàn)的熵守恒格式;然后給出了熵相容格式的具體形式,并引入限制器使數(shù)值格式具有高分辨率的性質(zhì);最后針對(duì)一維Euler方程,將上述格式應(yīng)用于幾個(gè)數(shù)值算例,驗(yàn)證各種格式的特性。(2)詳細(xì)論述WENO重構(gòu)的過程。首先在一維標(biāo)量方程的情形下給出了WENO重構(gòu)的過程;然后針對(duì)一維Euler方程,給出了通過對(duì)守恒型變量進(jìn)行局部特征變量分解來保證格式的基本無震蕩特性的方法,并論述了進(jìn)行局部特征分解的必要性;最后針對(duì)特征分解過程中向量?jī)?nèi)積運(yùn)算量較大的問題,引入了一類用壓強(qiáng)和熵來代替重構(gòu)權(quán)重計(jì)算中的特征變量的方法,以降低計(jì)算量。(3)構(gòu)造高精度的熵相容格式。首先通過不同模板上的熵守恒格式的線性組合得到高階熵守恒格式;然后將上述WENO重構(gòu)過程應(yīng)用于熵相容格式的數(shù)值粘性項(xiàng),與高階熵守恒格式結(jié)合得到高精度的熵相容格式;最后在幾個(gè)數(shù)值算例上驗(yàn)證了格式的高精度特性,且通過壓強(qiáng)和熵來構(gòu)造權(quán)重的方法比直接用特征變量構(gòu)造權(quán)重更省時(shí)。(4)將熵相容格式、高分辨率熵相容格式推廣至二維情形,通過二維Euler方程的幾個(gè)數(shù)值算例驗(yàn)證格式在二維情況下的特性。其中重點(diǎn)研究了圓柱繞流問題。數(shù)值算例表明熵相容格式比Roe格式能更好地避免高馬赫?qǐng)A柱繞流問題中的紅斑現(xiàn)象。
[Abstract]:Hyperbolic conservation law equations are one of the important research contents in computational fluid mechanics. The entropy compatible scheme for solving hyperbolic conservation law equations is a numerical scheme which satisfies the condition of entropy stability based on the second law of thermodynamics. This scheme has strong physical background and can effectively avoid some non-physical phenomena. This paper is based on the entropy compatible scheme of Euler equation. In this paper, a class of entropy compatible schemes with high resolution and high precision are studied. The main contents of this paper include the introduction of entropy compatible schemes. The basic theory of entropy conservation / entropy stability schemes and the construction process of general entropy conservation schemes are discussed. Two simple and easy to implement entropy conservation schemes are introduced, and then the specific form of entropy compatible scheme is given, and a limiter is introduced to make the numerical scheme have high resolution. Finally, for the one-dimensional Euler equation, The process of WENO reconstruction is discussed in detail by applying the above scheme to several numerical examples to verify the characteristics of various schemes. Firstly, the process of WENO reconstruction is given in the case of one-dimensional scalar equation, and then the one-dimensional Euler equation is discussed. This paper gives a method to guarantee the basic non-oscillatory characteristic of the scheme by decomposing the local characteristic variable of the conserved variable, and discusses the necessity of the local characteristic decomposition. Finally, in order to solve the problem of large computation of vector inner product in the process of feature decomposition, a new method is introduced, which uses pressure and entropy instead of reconstructing the feature variables in weight calculation. The high order entropy conserved scheme is obtained by linear combination of entropy conservation schemes on different templates, and then the above WENO reconstruction process is applied to the numerical viscosity term of entropy compatible schemes. The high precision entropy compatible scheme is obtained by combining with the high order entropy conserved scheme, and the high precision characteristic of the scheme is verified by several numerical examples. Moreover, the method of constructing weights by pressure and entropy is more time-saving than that by using characteristic variables directly.) the entropy compatible scheme and the high-resolution entropy compatible scheme are extended to two-dimensional cases. Several numerical examples of two-dimensional Euler equation are used to verify the characteristics of the scheme in two-dimensional case. The flow around a cylinder is mainly studied. The numerical examples show that the entropy compatible scheme can avoid the flow around a high Mach cylinder better than the Roe scheme. The erythema phenomenon in the problem.
【學(xué)位授予單位】：長(zhǎng)安大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 劉友瓊;封建湖;任炯;龔承啟;;求解多維Euler方程的二階旋轉(zhuǎn)混合型格式[J];應(yīng)用數(shù)學(xué)和力學(xué);2014年05期

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本文編號(hào)：1624678