Numerical Techniques for Direct and Large-Eddy Simulations

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.

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.

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.