Numerical Solutions Applied to Heat Transfer with the SPH Method

A Verification of Approximations for Speed and Accuracy
1. Auflage 2023
ISBN: 978-3-031-28945-3
Verlag: Springer International Publishing

Buch, Englisch, 119 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 236 g

Reihe: SpringerBriefs in Mathematics

This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models. Techniques described in this book aim to speed up the convergence of numerical solutions and increase their accuracy by significantly reducing the discretization error.
In their quest, the authors shed light on new sources of numerical error that are specific to the SPH method and, through them, they identify the characteristics of the solutions influenced by such errors. The accuracy of numerical solutions is also improved with the application of advanced tools like the repeated Richardson extrapolation (RRE) in quadruple precision, which was adapted to consider fixed or moving particles. The book finishes with the conclusion that the qualitative and quantitative verification of numerical solutions through coherence tests andmetrics are currently a methodology of excellence to treat computational heat transfer problems.
Mathematicians in applied fields and engineers modelling and solving real physical phenomena can greatly benefit from this work, as well as any reader interested in numerical methods for differential equations.

Zielgruppe

Research

Autoren/Hrsg.

Pereira Da Silva, Luciano

Marchi, Carlos Henrique

Meneguette Junior, Messias

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction.- Numerical Modeling of Heat Diffusion.- Numerical error analysis and heat diffusion models.- SPH applied to computational heat transfer problems.- Conclusion.

Über Autor(innen)

Luciano Pereira da Silva holds a PhD in Numerical Methods in Engineering (2022) from the Federal University of Paraná, Brazil, and a Master's degree in Computational and Applied Mathematics (2017) from the São Paulo State University (UNESP), Brazil. His research interests lie in numerical methods for partial differential equations, notably geometric and algebraic multigrid methods to accelerate the convergence of numerical solutions.
Messias Meneguette Junior is a Professor at the São Paulo State University, Brazil. He holds a PhD in Numerical Analysis (1987) and a Master's degree in Mathematical Modelling and Numerical Analysis (1983), both from the University of Oxford, UK. He also has a Master's degree in Mathematics (1981) from the University of São Paulo/ICMC São Carlos, Brazil. 

Carlos Henrique Marchi has a PhD in Mechanical Enginering (2001) and a Master's degree (1992), both from the Federal University of Santa Catarina, Brazil. His research activities focus on variational principles and numerical methods.