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Numerical Solutions Applied to Heat Transfer with the SPH Method
Luciano Pereira da SilvaMessias Meneguette JuniorCarlos Henrique Marchi
其他書名
A Verification of Approximations for Speed and Accuracy
出版Springer Nature, 2023-09-09
主題Mathematics / Counting & NumerationScience / Mechanics / ThermodynamicsMathematics / Mathematical AnalysisMathematics / AppliedMathematics / Numerical AnalysisMathematics / Probability & Statistics / Stochastic ProcessesMathematics / Calculus
ISBN30312894639783031289460
URLhttp://books.google.com.hk/books?id=9hfQEAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.