P. M. Gresho, R. L. Sani
Description
This comprehensive reference work covers all the important details regarding the application of the finite element method to incompressible flows. It
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addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection-diffusion equation in volume one. For both this equation and the equations of principal interest - the Navier-Stokes equations, covered in detail in volume two - detailed 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.
Together, this two volume work 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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