Numerical Techniques for Direct and Large-Eddy Simulations

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Features

  • Presents numerical methods for compressible and incompressible three-dimensional flows, such as high-order discretization schemes, high-fidelity boundary conditions, and coupling aspects
  • Gives sample numerical simulation results that exemplify the practical application of the methods
  • Discusses advanced topics and current challenges, including detached eddy simulation, SGS modeling, and multiscale flow simulations
  • Includes sample FORTRAN programs in the appendix to illustrate the implementation of finite difference numerical schemes

Summary

Compared to the traditional modeling of computational fluid dynamics, direct numerical simulation (DNS) and large-eddy simulation (LES) provide a very detailed solution of the flow field by offering enhanced capability in predicting the unsteady features of the flow field. In many cases, DNS can obtain results that are impossible using any other means while LES can be employed as an advanced tool for practical applications. Focusing on the numerical needs arising from the applications of DNS and LES, Numerical Techniques for Direct and Large-Eddy Simulations covers basic techniques for DNS and LES that can be applied to practical problems of flow, turbulence, and combustion.

After introducing Navier–Stokes equations and the methodologies of DNS and LES, the book discusses boundary conditions for DNS and LES, along with time integration methods. It then describes the numerical techniques used in the DNS of incompressible and compressible flows. The book also presents LES techniques for simulating incompressible and compressible flows. The final chapter explores current challenges in DNS and LES.

Helping readers understand the vast amount of literature in the field, this book explains how to apply relevant numerical techniques for practical computational fluid dynamics simulations and implement these methods in fluid dynamics computer programs.

Table of Contents

Introduction

Governing Equations: Compressible and Incompressible Formulations

Turbulence and Direct Numerical Simulation (DNS)

Large-Eddy Simulation (LES)

Numerical Treatment of Boundary Conditions

Inflow and Outflow Boundary Conditions

Wall Boundary Conditions

Other Boundary Conditions

Discrete Time Integration Methods

High-Order Runge–Kutta (RK) Methods

Linear Multistep Methods: Adams–Bashforth and Adams–Moulton Methods

Other Time Integration Methods

DNS of Incompressible Flows

Sample Results: DNS of Channel Flows

Numerical Features: DNS of Incompressible Flows

DNS of Compressible Flows

Sample Results: DNS of Compressible Jet Flows

Numerical Features: High-Order Schemes for Spatial Discretization

LES of Incompressible Flows

Sample Results: LES of Incompressible Flows in Complex Geometries

Subgrid Scale Modeling of Incompressible Flows

Numerical Features: LES on Unstructured Grids and Immersed Boundary Technique for Complex Geometries

LES of Compressible Flows

Sample Results of LES of Compressible Flows

Subgrid-Scale Modeling of Compressible Flows and Implicit Large-Eddy Simulation (ILES)

Further Topics and Challenges in DNS and LES

Multiscale Flow Simulations

Challenges in DNS and LES: Complex Geometry and SGS Modeling

Hybridization: Detached Eddy Simulation (DES)

Appendix: Supplementary Material: FORTRAN 90 Routines of the Finite Difference Schemes

Index

References appear at the end of each chapter.

Author Bio(s)

Xi Jiang is Senior Lecturer of Mechanical Engineering in the School of Engineering and Design at Brunel University.

Choi-Hong Lai is Professor of Numerical Mathematics in the School of Computing and Mathematical Sciences at the University of Greenwich.

Editorial Reviews

The book can be recommended to CFD practitioners at the early stage of their academic career, such as postgraduate students and junior researchers, to understand the vast literature in the field and to apply the relevant numerical techniques.
Zentralblatt MATH 1185