Advancement of shock capturing computational fluid dynamics methods : numerical flux functions in finite volume method


    • Kitamura, Keiichi


Advancement of shock capturing computational fluid dynamics methods : numerical flux functions in finite volume method

Keiichi Kitamura

Springer, c2020

大学図書館所蔵 件 / 3



Includes bibliographical references



This book offers a compact primer on advanced numerical flux functions in computational fluid dynamics (CFD). It comprehensively introduces readers to methods used at the forefront of compressible flow simulation research. Further, it provides a comparative evaluation of the methods discussed, helping readers select the best numerical flux function for their specific needs. The first two chapters of the book reviews finite volume methods and numerical functions, before discussing issues commonly encountered in connection with each. The third and fourth chapter, respectively, address numerical flux functions for ideal gases and more complex fluid flow cases- multiphase flows, supercritical fluids and magnetohydrodynamics. In closing, the book highlights methods that provide high levels of accuracy. The concise content provides an overview of recent advances in CFD methods for shockwaves. Further, it presents the author's insights into the advantages and disadvantages of each method, helping readers implement the numerical methods in their own research.


1. Introduction: Brief Review of Finite Volume Method in Computational Fluid Dynamics 2. Role and History of Numerical Flux Functions 2.1. Issue 1: Anomalous Solutions of Captured Shock and Heating at Hypersonic Speeds 2.2. Issue 2: Stiffness Problem at Low Speeds 3. Numerical Flux Functions for Ideal Gas 3.1. Godunov's Exact Riemann Solver 3.2. Central-difference formulas, and Lax-Friedrichs method 3.3. Flux Difference Splitting (FDS): Roe's Approximate Riemann Solver (and Entropy Fix) and Osher's Approximate Riemann Solver 3.4. Flux Vector Splitting (FVS): Steger-Warming, Van Leer, Hanel, Liou-Steffen (Original AUSM), Zha-Bilgen, and Toro-Vazquez methods 3.5. Harten-Lax-van Leer Family: HLL, HLLE, HLLEM, HLLC, HLLD, and HLLI 3.6. FDS/FVS Hybrid Advection-Upstream-Splitting-Method Family: AUSMDV, AUSM+, SHUS, LDFSS, AUSMPW+, AUSM+-up, SLAU, SD-SLAU, SLAU2, and HR-SLAU2 3.7. Others: Rotated Roe-HLL and Genuinely Multidimensional Splitting 4. Numerical Flux Functions Extended to Other Fluids 4.1. Multiphase Flows 4.2. Supercritical Fluids 4.3. Magnetohydrodynamics 5. Reconstruction and Slope Limiters 5.1. Monotone Upstream-centered Schemes for Conservation Laws, (Weighted) Least-Squares, Green-Gauss (G-G), and Green-Gauss/Least-Square methods 5.2. Conventional Limiters 5.3. Post Limiters

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