What is it about?
This is a post graduate level textbook with focus the analytical subject of CFD rigorously addressed via continuous Galerkin weak form theory. The theory predecessor burst onto the CFD scene in the early 1970s disguised as the weighted-residuals finite element (FE) alternative to finite difference (FD) CFD. Weighted-residuals obvious connections to variational calculus prompted mathematical formalization, whence emerged continuum weak form theory. It is this theory, discretely implemented, herein validated precisely pertinent to nonlinear (!) NS, and time averaged and space filtered alternatives, elliptic boundary value (EBV) partial differential equation (PDE) systems.
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Why is it important?
The text last chapter collates text content under the US National Academy of Sciences (NAS) large scale computing identification “Verification, Validation, Uncertainly Quantification” (VVUQ). Observed in context is replacement of legacy difference algebra derived CFD algorithm numerical diffusion formulations with proven continuum calculus implemented mPDE operands possessing superior performance in response to NAS-cited requirements: • error quantification • a posteriori error estimation • error bounding • spectral content accuracy extremization • phase selective dispersion error annihilation • monotone solution generation • error extremization optimal mesh quantification • mesh resolution inadequacy measure • efficient optimal radiosity theory with error bound which in summary address in completeness VVUQ.
Perspectives
I must acknowledge the content of this text is the result of collaborative activities conducted over three decades under the umbrella of UT CFD Lab, especially that resulting from PhD research. Content herein is originally published in the dissertations of Doctors Soliman (1978), Kim (1987), Noronha (1988), Iannelli (1991), Freels (1992), Williams (1993), Roy (1994), Wong (1995), Zhang (1995), Chaffin (1997), Kolesnikov (2000), Barton (2000), Chambers (2000), Grubert (2006), Sahu (2006), and Sekachev (2013), the last one completed in the third year of my retirement. Teams get the job done – this text is proof positive.
Professor emeritus A. J. Baker
CFD Laboratory;, University of Tennessee, USA
Read the Original
This page is a summary of: Optimal Modified Continuous Galerkin CFD, April 2014, Wiley,
DOI: 10.1002/9781118402719.
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