Numerical methods for the Navier-Stokes equations

This work covers a range of advanced computational methods for fluid dynamics, particularly focusing on the Navier-Stokes equations. It includes reliable finite volume methods, parallel computing techniques, and multigrid solutions on adaptive unstructured meshes. The text discusses Newton-Krylov-Schwarz methods in computational fluid dynamics (CFD) and presents PASTIS-3D, a parallel finite element projection code for time-dependent incompressible flows. It explores coupled solutions for steady compressible flows and turbulence equations using relaxation methods, as well as aspects of finite element discretizations for the Boussinesq approximation. The study examines extended flow separation on parallel machines and operator splitting methods for compressible Euler and Navier-Stokes equations. It introduces an efficient algorithm for velocity-vorticity in 3D unsteady flows and discusses stabilized methods for incompressible flows. The text also addresses adaptive computation of compressible flow fields, defect correction for convection-dominated flows, and error control in CFD. Additional topics include parallel grid adaptation, numerical simulations of turbulent flows, high-resolution flux splitting schemes, and Chimera grid schemes for complex geometries. It also presents multi-domain algorithms for spectral solutions and robust smoothers for incompressible flow problems, alongside nonconforming finite element methods and