Incompressible Flow and the Finite Element Method, Isothermal Laminar Flow
This comprehensive two-volume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution.
Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes equations (covered in detail in Volume Two) - a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. The important role played by the pressure, so confusing in the past, is carefully explained.
The book explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
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acceleration advection algorithm analysis applied approximation basis functions component computed constant continuity equation convergence corresponding DAE's derived Dirichlet BC's discretely divergence-free discussion divergence divergence-free divergence-free subspace domain eigenvalues eigenvectors error example Figure Finally finite element method Fortin GFEM gives global gradient Gresho grid IC's ill-posed incompressible flow initial integration iteration Lagrange multiplier least linear mass conservation mass matrix mathematical mesh momentum equation Navier-Stokes equations no-slip node non-linear normal velocity Note NS equations null space numerical obtain ODE's orthogonal penalty method potential flow present pressure modes problem projection method Q\Qo Remarks satisfy scalar scalar transport equation second-order Section simple solution solve specified spurious stability steady Stokes step Stokes equations Stokes flow term time-dependent transient vector viscous vortex sheet vorticity Vu)r weak form weak formulation well-posed well-posed problem zero