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 and metrics 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.
Introduction.- Numerical Modeling of Heat Diffusion.- Numerical error
analysis and heat diffusion models.- SPH applied to computational heat
transfer problems.- Conclusion.
Luciano Pereira da Silva holds a PhD in Numerical Methods in Engineering (2022) from the Federal University of Paranį, Brazil, and a Master's degree in Computational and Applied Mathematics (2017) from the Sćo 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 Sćo 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 Sćo Paulo/ICMC Sćo 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.
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