Numerical simulation of viscous shock layer flows (Q1383275)

This book, based to a great extent on the results obtained by the author and his colleagues at the Ioffe Physico-Technical Institute, St. Petersburg, Russia, presents a detailed description of the viscous shock layer models and numerical methods for their solution. The book comprises five chapters. In the introductory chapter 1: ``Simulation of supersonic flow around a body using the Navier-Stokes equations'', the author formulates the problem by using full Navier-Stokes equations with the corresponding initial and boundary conditions, discusses some similarity criteria, and shows how turbulence can be included in the analysis. Chapter 1 gives also a brief review of appropriate finite difference methods together with mesh generation techniques, and discusses the applicability of the continuum approach to the simulation of rarefied flows. Chapter 2: ``Viscous shock layer models and computational methods'' presents some simplified approximations which can be obtained from the full Navier-Stokes equations by omitting terms which are expected to be small (in particular, reduced and parabolized Navier-Stokes equations). It is shown how these simplified equations can be solved numerically by time-marching, space-marching and global relaxation and multisweep algorithms. Chapter 2 concludes with an asymptotic derivation of the thin viscous shock layer model and with a discussion of the solution of Navier-Stokes equations on the stagnation streamline. Chapter 3: ``Application to plane and axisymmetric flows'' and chapter 4: ``Simulation of three-dimensional flows'' demonstrate how the developed above methods can be applied to concrete problems (flows around a blunted body in the aerodynamic wake, flow from a supersonic source around spherical bluntness, flows with mass blowing, flows around ellipsoids, delta-wings, elongated, spinning and combined bodies). The final chapter 5: ``Physical and chemical effects'' describes various models relevant to hypersonic reentry flows (non-equilibrium chemically reacting and weakly ionized flows, radiating flows). The results of numerous simulations show the ranges of validity of the models presented. In summary, this is an excellent research book which is intended not only for specialists, but also for graduate students which spezialize in the computational fluid dynamics.