Optimal MODIFIED CONTINUOUS Galerkin CFD, John Wiley and Sons, London (2014), thoroughly details the maturation of 4+ decades of academic research on weak formulations for computational fluid dynamics (CFD) exhibiting optimal performance in the discrete peer group. This textbook, written at post graduate level, replaces the author's pioneering publication Finite Element Computational Fluid Mechanics, McGraw-Hill/Hemisphere, New York (1983). Galerkin CFD content and organization is the consequence of graduate level academic course developments in computational fluid-thermal systems including turbulence closure theorization. It fully supports pedagogical content of these CFD-specific lecture series now Internet-accessible.
In brief, fluid dynamics weak form theorization is performed and completed(!) addressing the continuum partial differential equation (PDE) systems. Thereby, calculus and vector field theory precisely convert the ubiquitous nonlinearities pervading the Navier-Stokes (NS) PDE system and pertinent manipulations to computable form. The sole post-theory decision is selection of the trial space supporting NS/RaNS/LES PDE system state variable approximation spatial distributions. Herein is selected, detailed and validated optimal a (finite element) trial space basis. Alternative discretizations, e.g., finite difference, finite volume, are admitted by continuum theorization; however, Galerkin CFD content quantitatively validates their non-Galerkin weak form equivalents lead to sub-optimal performance.
A truly fundemantal attribute of weak form continuum theorization enables modifying the classic appearance of NS/RaNS/LES PDE statements to mPDE systems. These manipulations engender trial space basis implementations validated to annihilate! dominant order space and time discretization-induced dispersion error mechanisms. Weak formulations are supported by a rich theory progressively detailed in Galerkin CFD development to accurately predict NS/RaNS/LES CFD algorithm performance. This broadly encompassing theory additionally supports quantitative validation of the assertion that mPDE continuous Galerkin weak form trial space basis implementation is optimal in the peer group, as text title inferred.
At millenium turn the author began moving from the classic blackboard lecture environment to an Internet modality. The end result morphed into a totally time/distance-inconsequential environment for graduate academic CFD content outreach. Follow the links below to access edits of these semester length courses containing full color graphic data to support and hopefully enrich Galerkin CFD text readership experiences.
Computational Fluid-Thermal Systems - ES 552w:
A first level graduate exposure to CFD algorithm generation for incompressible-thermal Navier-Stokes statements via weak form theorization. Thoroughly develops the rich theory supporting trial space basis implementations validated optimal within the discrete peer group. Content addresses laminar NS and time averaged (RaNS) NS PDE/mPDE systems across a wide spectrum of statements in thermal-fluid systems.
Topics in Computation of Turbulence - ES 645w:
An advanced graduate level exposure to a range of mathematical physics theorizations characterizing the incompressible-thermal fluid dynamics continuum phenomenon of turbulence. Theorizations transition to computable weak formulations with lecture focus identification of attributes/limitations of closure modeling performance for resultant CFD algorithms. Courseware content (no lectures) concludes with a recently derived amd validated completely analytical closure theory for the tensor/vector quadruples identified in rigorous space filtering of incompressible-thermal NS PDE/mPDE systems.
Readers whose recall of calculus and vector field theory is rusty will find course mathematics context perhaps tough going. Baccalauriat level coverage of weak form trial space basis implementations across a wide spectrum of computational engineering sciences topics is a suggested entrance modality.