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7932 results in Fluid dynamics and solid mechanics

Page 27 of 397

Modelling Turbulence in Engineering and the Environment
  • Rational Alternative Routes to Closure
  • 2nd edition
  • Kemal Hanjalić, Brian Launder
  • Published online:
    03 November 2022
    Print publication:
    24 November 2022
  • Modelling transport and mixing by turbulence in complex flows are huge challenges for computational fluid dynamics (CFD). This highly readable book introduces readers to modelling levels that respect the physical complexity of turbulent flows. It examines the hierarchy of Reynolds-averaged Navier-Stokes (RANS) closures in various situations ranging from fundamental flows to three-dimensional industrial and environmental applications. The general second-moment closure is simplified to linear eddy-viscosity models, demonstrating how to assess the applicability of simpler schemes and the conditions under which they give satisfactory predictions. The principal changes for the second edition reflect the impact of computing power: a new chapter devoted to unsteady RANS and another on how large-eddy simulation, LES, and RANS strategies can be effectively combined for particular applications. This book will remain the standard for those in industry and academia seeking expert guidance on the modelling options available, and for graduate students in physics, applied mathematics and engineering entering the world of turbulent flow CFD.

  • 9 - Finite Volume Methods for Viscous Incompressible Flows

  • from Part III - The Finite Volume Method
  • J. N. Reddy, Texas A & M University, N. K. Anand, Texas A & M University, P. Roy, Lawrence Livermore National Laboratory, California
  • Book:
    Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
    Published online:
    27 January 2023
    Print publication:
    27 October 2022, pp 295-346

  • Summary

    In this chapter, we will focus on solving the PDEs governing laminar flows of viscous incompressible fluids using the FVM (this chapter is a counterpart of Chapter 6 on FEM, where velocity–pressure and penalty finite element models of two dimensional flows of viscous incompressible fluids were presented). These equations are expressed in terms of the primitive variable, namely, the velocity field and the pressure. To begin with, we will consider isothermal flows (flows without the presence of the temperature effect), and demonstrate the use of the FVM for two-dimensional laminar flows of viscous incompressible fluids. Then cases of non-isothermal flows with both forced convection and natural convection will be considered in the sequel.

  • 5 - The Finite Element Method: Unsteady Heat Transfer

  • from Part II - The Finite Element Method
  • J. N. Reddy, Texas A & M University, N. K. Anand, Texas A & M University, P. Roy, Lawrence Livermore National Laboratory, California
  • Book:
    Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
    Published online:
    27 January 2023
    Print publication:
    27 October 2022, pp 153-178

  • Summary

    In Chapter 4 we considered finite element analysis of steady state heat transfer. When external stimuli (e.g., boundary conditions and internal heat generation) are independent of time, heat transfer in a medium may attain a steady state; otherwise, the temperature field changes with time (i.e., unsteady state). The governing equations of unsteady heat transfer are obtained using the principle of balance of energy. When unsteady equations are solved the temperature field reaches a steady state if the external stimuli are independent of time (i.e., the time dependence decays with time).

  • 3 - Solution Methods for Algebraic Equations

  • from Part I - Preliminaries
  • J. N. Reddy, Texas A & M University, N. K. Anand, Texas A & M University, P. Roy, Lawrence Livermore National Laboratory, California
  • Book:
    Finite Element and Finite Volume Methods for Heat Transfer and Fluid Dynamics
    Published online:
    27 January 2023
    Print publication:
    27 October 2022, pp 63-90

  • Summary

    All numerical methods, including the FEM and FVM, ultimately result in a set of linear or nonlinear algebraic equations, relating the values of the dependent variables at the nodal points of the mesh. These algebraic equations can be linear or nonlinear in the nodal values of the primary variables, depending on whether the governing differential equations being solved are linear or nonlinear. When the algebraic equations are nonlinear, we linearize them using certain assumptions and techniques, such as the Picard method or Newton’s method.

Page 27 of 397