Finite element methods for fluids
Introduces the formulation of problems in fuild mechanics and dynamics, and shows how they can be analyzed and resolved using finite element methods. This practical book also discusses the equations of fluid mechanics and investigates the problems to which these equations can be applied, as well as how they can be analyzed and solved. Contains illustrations of computer simulations using the methods described in the book and features numerous illustrations.
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momentum energy and the state equation
Irrotational and weakly irrotational flows
5 other sections not shown
algorithm AMD-BA applied approximation artificial viscosity basis functions Benque boundary conditions boundary layers calculate compressible Navier-Stokes computation conjugate gradient method constraints construct continuous convection convection-diffusion convergence deduce defined denotes diffusion dimension discontinuous discretisation domain entropy error estimate Euler equations example exists Figure finite difference finite element method fluid mechanics G Jh given Glowinski GMRES incompressible Navier-Stokes equations integral interpolation iteration Jn Jn L2 norm linear system MacFEM Mach number mass lumping Math matrix Navier-Stokes equations nodes norm notation obtain P1 conforming Pironneau polynomial positive POTENTIAL FLOWS Proof Proposition quadrature formula Remark Reynolds number satisfied shallow water equations simulation solve space Springer stability stationary Stokes problem studied in chapter subsonic symmetric term test problem theorem total derivative transonic Transonic flow triangles turbulence unique solution variational formulation vector velocity vertex viscosity zero divergence