Advancement of Shock Capturing Computational Fluid Dynamics Methods: Numerical Flux Functions in Finite Volume Method

ISBN-13: 9789811590139 / Angielski / Miękka / 2021 / 150 str.

Keiichi Kitamura

Opis

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.

Spis treści

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, Hänel, 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

O autorze

Keiichi Kitamura is an Associate Professor at Yokohama National University. His work focuses on developing numerical methods in computational fluid dynamics for high-speed, low-speed, and multiphase/supercritical/MHD flows, and he has proposed numerical flux functions, e.g., SLAU2 and Post Limiter.

He received his doctor of engineering from Nagoya University in 2008. After serving as a postdoctoral researcher at JAXA and Glenn Research Center, NASA, he was appointed an Assistant Professor at Nagoya University in 2012. Since 2014, he has served in his current position. He was honored with young researcher awards by the Japan Society for Aeronautical and Space Sciences in 2012, by the Society for Promotion of Space Science in 2018, and by the Japan Society of Fluid Mechanics in 2018. He was also awarded the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (The Young Scientist’s Prize) in Japan, and the Frontier Commendation from Fluids Engineering Division, The Japan Society of Mechanical Engineers, both in 2019.