【摘要】：多維雙曲守恒律問題是目前計算流體力學(xué)領(lǐng)域的重要研究內(nèi)容之一。求解雙曲守恒律方程的熵穩(wěn)定數(shù)值格式具有較強的物理背景,能夠有效地避免一些非物理現(xiàn)象的產(chǎn)生。本文詳細(xì)研究了熵穩(wěn)定格式的構(gòu)造方法和主要思想,并根據(jù)熵穩(wěn)定格式的構(gòu)造方法構(gòu)造三角形網(wǎng)格下二維雙曲守恒律的熵穩(wěn)定格式,并通過二維Euler方程圓柱繞流問題的數(shù)值模擬,說明了格式不會產(chǎn)生紅斑現(xiàn)象。主要工作有:(1)通過對熵守恒、熵穩(wěn)定、熵相容格式理論研究的基礎(chǔ)上,直接將幾種格式推廣到二維問題,并對幾個典型算例進(jìn)行了計算,得到了較好的結(jié)果,表明這種推廣是可行的。(2)直接在非結(jié)構(gòu)網(wǎng)格下構(gòu)造熵穩(wěn)定格式。首先通過離散得到非結(jié)構(gòu)網(wǎng)格下二維雙曲守恒律方程的半離散數(shù)值格式,接著以二維Euler方程為例講述在這個半離散格式的基礎(chǔ)之上構(gòu)造熵穩(wěn)定格式的具體過程。先構(gòu)造熵守恒通量函數(shù),然后在此基礎(chǔ)之上添加一個Roe型的耗散項,得到了熵穩(wěn)定格式。由于它只具有一階精度,為了改進(jìn)格式的精度,本文采用在計算區(qū)域相鄰單元的交界面上重構(gòu)熵變量的方法構(gòu)造出了一種新的高精度熵穩(wěn)定格式,并對二維Euler方程圓柱繞流問題進(jìn)行了數(shù)值模擬。(3)通過數(shù)值算例驗證構(gòu)造的三角形網(wǎng)格下熵穩(wěn)定格式的有效性,體現(xiàn)其高精度、高分辨率等特點。
[Abstract]:Multidimensional hyperbolic conservation law problem is one of the important research contents in computational fluid dynamics. The entropy stable numerical scheme for solving hyperbolic conservation law equations has a strong physical background and can effectively avoid some non-physical phenomena. In this paper, the construction method and main idea of entropy stable scheme are studied in detail, and the entropy stable scheme of two dimensional hyperbolic conservation law under triangular mesh is constructed according to the construction method of entropy stable scheme. The numerical simulation of the flow around a cylinder of two dimensional Euler equation shows that the scheme will not produce erythema phenomenon. The main works are as follows: (1) based on the research of entropy conservation, entropy stability and entropy compatible scheme, several schemes are directly extended to two-dimensional problems, and some typical examples are calculated, and good results are obtained. It is shown that this generalization is feasible. (2) Entropy stable schemes are constructed directly under unstructured meshes. First, the semi-discrete numerical scheme of two-dimensional hyperbolic conservation law equation under unstructured grid is obtained by discretization. Then, taking the two-dimensional Euler equation as an example, the concrete process of constructing entropy stable scheme based on this semi-discrete scheme is described. First, the entropy conservation flux function is constructed, and then a dissipative term of Roe type is added on this basis, and the entropy stable scheme is obtained. Because it has only the first order precision, in order to improve the accuracy of the scheme, a new high precision entropy stable scheme is constructed by using the method of reconstructing entropy variables at the interface of the adjacent units in the calculation area. Numerical simulation of the flow around a cylinder of two-dimensional Euler equation is carried out. (3) A numerical example is given to verify the effectiveness of the entropy stability scheme constructed under triangular meshes, which embodies the characteristics of high precision and high resolution.
【學(xué)位授予單位】：長安大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.82

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本文編號：2400090