非結(jié)構(gòu)網(wǎng)格緊致高精度有限體積方法

目錄

第1章引言

1.1研究背景

1.2非結(jié)構(gòu)網(wǎng)格高精度數(shù)值方法的發(fā)展與應(yīng)用

1.2.1有限體積方法

1.2.2間斷有限元方法

1.2.3混合方法

1.3非結(jié)構(gòu)網(wǎng)格高精度數(shù)值方法亟待解決的關(guān)鍵技術(shù)問(wèn)題

1.3.1有限體積方法的大模板

1.3.2間斷有限元方法的限制器

1.3.3間斷有限元方法的隱式時(shí)間推進(jìn)

1.3.4曲面邊界處理

1.4本書的出發(fā)點(diǎn)與目標(biāo)

第2章可壓縮流動(dòng)的高精度有限體積方法

2.1NavierStokes方程的半離散有限體積格式

2.2空間離散

2.2.1重構(gòu)

2.2.2限制器

2.2.3數(shù)值通量

2.3時(shí)間積分

2.3.1顯式時(shí)間積分

2.3.2隱式時(shí)間積分

2.4本章小結(jié)

第3章緊致最小二乘有限體積方法

3.1一維緊致最小二乘重構(gòu)

3.2譜特性和穩(wěn)定性

3.2.1傅里葉分析

3.2.2色散和耗散特性

3.2.3穩(wěn)定性

3.3多維緊致最小二乘重構(gòu)

3.3.1多維緊致最小二乘重構(gòu)線性方程組

3.3.2重構(gòu)線性方程組的解法

3.3.3邊界處理

3.4重構(gòu)和時(shí)間推進(jìn)耦合迭代方案

3.4.1基本原理

3.4.2算法實(shí)現(xiàn)

3.4.3收斂性分析

3.5一維數(shù)值算例

3.5.1線性波動(dòng)方程

3.5.2氣動(dòng)噪聲的傳播

3.5.3激波管問(wèn)題

3.5.4沖擊波問(wèn)題

3.5.5ShuOsher問(wèn)題

3.6二維數(shù)值算例

3.6.1等熵渦

3.6.2亞聲速圓柱繞流

3.6.3亞聲速NACA0012翼型繞流

3.6.4雙馬赫反射

3.6.5正激波繞過(guò)復(fù)雜形狀障礙物

3.7本章小結(jié)

第4章變分有限體積方法

4.1變分重構(gòu)基本原理

4.1.1變分重構(gòu)基本原理

4.1.2重構(gòu)矩陣特性分析

4.1.3重構(gòu)線性方程組解法

4.2譜特性和穩(wěn)定性

4.3邊界條件在重構(gòu)中的實(shí)施

4.4泛函的構(gòu)造

4.5數(shù)值算例

4.5.1NavierStokes方程制造解

4.5.2超聲速等熵渦

4.5.3平板邊界層

4.5.4NACA0012翼型的亞聲速繞流

4.5.5斜激波沖擊混合層

4.5.6黏性激波管

4.5.7等熵渦

4.6本章小結(jié)

第5章三維流動(dòng)模擬

5.1高階網(wǎng)格

5.1.1高階網(wǎng)格及其生成方法

5.1.2高階網(wǎng)格的參數(shù)變換

5.1.3高階網(wǎng)格上的數(shù)值積分

5.2并行計(jì)算

5.2.1網(wǎng)格分塊

5.2.2數(shù)據(jù)傳遞

5.2.3求解器的并行化

5.3到壁面的最小距離

5.4數(shù)值算例

5.4.1精度測(cè)試

5.4.2ONERAM6翼型跨聲速無(wú)黏繞流

5.4.3圓球亞聲速定常層流繞流

5.4.4三角翼大攻角繞流

5.4.5湍流平板邊界層

5.5本章小結(jié)

第6章總結(jié)與展望

參考文獻(xiàn)

在學(xué)期間發(fā)表的學(xué)術(shù)論文

致謝



此部分只要英文目錄部分




Contents
非結(jié)構(gòu)網(wǎng)格緊致高精度有限體積方法


Contents

1Introduction

1.1Research Background

1.2HihgOrder Methods on Unstructured Grids

1.2.1Finite Volume

1.2.2Discontinuous Finite Element

1.2.3Hybrid Method

1.3Bottleneck Problems

1.3.1Large Reconstruction Stencil of Finite Volume

1.3.2Limiter of Discontinuous Finite Element

1.3.3Implicit Time Integration of Discontinuous
Finite Element

1.3.4Curved Boundaries

1.4Motivations and Objectives

2HighOrder Finite Volume Framework of Compressible Flow
Simulation

2.1SemiDiscrete Finite Volume Scheme for NavierStokes
Equations

2.2Spatial Discretization

2.2.1Reconstruction

2.2.2Limiter

2.2.3Numerical Flux

2.3Time Integration

2.3.1Explicit Time Integration

2.3.2Implicit Time Integration

2.4Summary

3Compact LeastSquares Finite Volume Method

3.1OneDimensional Compact LeastSquares Reconstruction

3.2Spectral Property and Stability

3.2.1Fourier Analysis

3.2.2Dispersion and Dissipation

3.2.3Stability

3.3MultiDimensional Compact LeastSquares
Reconstruction

3.3.1Linear Equation System

3.3.2Iterative Solver

3.3.3Boundary Treatment

3.4Reconstruction and Time Integration Coupled Iteration

3.4.1Key Idea

3.4.2Algorithm

3.4.3Convergence

3.5OneDimensional Numerical Results

3.5.1Linear Advection Equation

3.5.2Propagation of Broadband Sound Waves

3.5.3Shock Tube

3.5.4Two Interacting Blast Waves

3.5.5ShuOsher Problem

3.6TwoDimensional Numerical Results

3.6.1Isentropic Vortex

3.6.2Subsonic Flow past a Circular Cylinder

3.6.3Subsonic Flow Around a NACA0012 Airfoil

3.6.4Double Mach Reflection

3.6.5A Mach 2 Shock Wave Past Complex Shape
Obstacles

3.7Conclusions

4Variational Finite Volume Method

4.1Variational Reconstruction

4.1.1Key Idea

4.1.2Analysis of the Reconstruction Matrix

4.1.3Linear Equation System Solver of Variational
Reconstruction

4.2Spectral Property and Stability

4.3Implementation of Boundary Conditions in
Reconstruction

4.4Cost Function Construction

4.5Numerical Results

4.5.1Manufactured Solution of NavierStokes Equations

4.5.2Supersonic Vortex

4.5.3Flat Plate Boundary Layer

4.5.4Subsonic Flow past a NACA0012 Airfoil

4.5.5Shock Wave Impingement on a Spatially Evolving
Mixing Layer

4.5.6Viscous Shock Tube

4.5.7Isentropic Vortex

4.6Conclusions

5ThreeDimensional Simulations

5.1HighOrder Mesh

5.1.1Introduction

5.1.2Isoparametric Transformation

5.1.3Numerical Integration on HighOrder Mesh

5.2Parallel Computing

5.2.1Mesh Partion

5.2.2Data Transfer

5.2.3Solver Parallelization

5.3Minimum Distance to Nearest Wall

5.4Numerical Results

5.4.1Accuracy Test

5.4.2Transonic Inviscid Flow past an ONERAM6
Airfoil

5.4.3SteayState Laminar Flow past a Sphere

5.4.4Laminar Flow around a Delta Wing

5.4.5Turbulent Flat Plate Boundary Layer

5.5Conclusions

6Summary and Future work

References

Published Papers

Acknowledgements