Defect Correction Methods for Fluid Flows at High Reynolds Numbers

Alexander Labovsky, Alexander E. Labovsky

• Publisher: Chapman and Hall/CRC
• Year: 2025
• eBook ISBN: 9781040370544
• Edition: 0
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Defect Correction Methods for Fluid Flows at High Reynold's Numbers presents the mathematical development of defect correction methods (DCM) in application to fluid flow problems in various settings. We will show several approaches to applying the DCM ideas in computational fluid dynamics (CFD) – from a basic idea of controlling the flow by the means of increased diffusion, to the state-of-the-art family of novel, DCM-based turbulence models. The main idea of the methods presented in this book, is to use defect correction in turbulence modelling; additionally, several methods will also be presented, that aim at reducing the time discretization error.

Features

· Provides a road map, starting from the ideas of minimally invasive controlling of turbulent flows, to the ways of improving the existing regularization techniques with DCM, to the ideas of 'full defect correction' in both space and time and, finally, to the more complex embedding of the DCM into turbulence modelling by the 'correction' of the whole turbulence model

· Can be used for teaching a topics course on a Masters or Ph.D. level. It is even more suitable as a reference for CFD theorists and practitioners, with most of the methods being minimally invasive and, therefore, easy to implement in the existing/legacy codes

· Discusses the current challenges in turbulence modelling with defect correction, showing several possible directions for future developments. Two source codes are provided – one for a regularization technique and another for a novel turbulence model – in order to give an interested researcher a quick start to the topic of DCM in CFD.

Table of contents

• Cover Page
• Half-Title Page
• Series Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface and Acknowledgments
• Chapter 1 ◾ Introduction
• Chapter 2 ◾ Artificial Viscosity and Defect Correction
• Chapter 3 ◾ Deferred Correction in MagnetoHydroDynamics
• Chapter 4 ◾ Deferred Correction with a Turbulence Model
• Chapter 5 ◾ Can Defect Correction Replace a Turbulence Model?
• Chapter 6 ◾ Deferred Correction for a Fluid–Fluid Interaction Problem
• Chapter 7 ◾ Large Eddy Simulation with Correction (LES-C)
• Chapter 8 ◾ Scale Truncation and the Energy Balance of the ADC
• Chapter 9 ◾ Defect-Deferred Correction
• Chapter 10 ◾ The Full ADC Model for Magnetohydrodynamics
• Chapter 11 ◾ Another LES-C Model for a Fluid–Fluid Interaction Problem
• Bibliography
• Index