Error Freed CFD Mathematics analytically derives and validates nonlinear continuum calculus alterations to Navier-Stokes partial differential equation systems that completely annihilate the legacy CFD theory/practice intrinsic error mechanisms� spatial-temporal discretization generated instabilitydiscrete algebra theorization limitationsphysics-based isotropic Reynolds stress tensor modeling weak linear algebra admitted non-convergence that persist to compromise physics of fluids prediction fidelity. �Weak formulation continuous Galerkin finite element (FE) basis theorization identifies cubically nonlinear continuum calculus tensor product functionals that totally eliminate the need for code phake physics stabilization. also stabilized shock capture. ��Resultant is classic tri-diagonal stencil equivalent generation of strictly monotone discrete approximations that are 4th order accurate in physical space, wave number space and implicit time on any mesh.� Summarily, matrix differential calculus identifies all nonlinear contributions to the quadratic convergent Newton iteration algorithm to eliminate generation of non-converged solutions. covers incompressible/compressible laminar, turbulent, transitional thermal-fluid dynamics processes in multiply connected domains with shocks, contact surfacesrigorous theory derived asymptotic convergence, local and global error estimates, error quantification, stopping criterion for regular solution adapted nonuniform mesh refinement "on-the-fly" code execution at the optimal mesh solution �mathematical complexity of TEA theory� unstagnation advancements are keyed to ready alteration of current practice finite volume commercial/government and FE CFD codes.

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Bibliographic Details

Title: Error Freed CFD Mathematics
Publisher: De Gruyter, DE
Publication Date: 2025
Language: English
ISBN 10: 3119147761
ISBN 13: 9783119147767
Binding: Hardback
Condition: New
Dimensions: 16.99 centimeters width by 1.6 centimeters height by 24.41 centimeters depth
Weight: 500 grams

About this title

Synopsis

Error Freed CFD Mathematics analytically derives and validates nonlinear continuum calculus alterations to Navier-Stokes partial differential equation systems that completely annihilate the legacy CFD theory/practice intrinsic error mechanisms

spatial-temporal discretization generated instability
discrete algebra theorization limitations
physics-based isotropic Reynolds stress tensor modeling
weak linear algebra admitted non-convergence

that persist to compromise physics of fluids prediction fidelity. Weak formulation continuous Galerkin finite element (FE) basis theorization identifies cubically nonlinear continuum calculus tensor product functionals that totally eliminate the need for code phake physics stabilization. also stabilized shock capture. Resultant is classic tri-diagonal stencil equivalent generation of strictly monotone discrete approximations that are 4^th order accurate in physical space, wave number space and implicit time on any mesh. Summarily, matrix differential calculus identifies all nonlinear contributions to the quadratic convergent Newton iteration algorithm to eliminate generation of non-converged solutions.

covers incompressible/compressible laminar, turbulent, transitional thermal-fluid dynamics processes in multiply connected domains with shocks, contact surfaces
rigorous theory derived asymptotic convergence, local and global error estimates, error quantification, stopping criterion for regular solution adapted nonuniform mesh refinement “on-the-fly” code execution at the optimal mesh solution
mathematical complexity of TEA theory unstagnation advancements are keyed to ready alteration of current practice finite volume commercial/government and FE CFD codes

About the Author

A. J. Baker, PhD, PE, Professor Emeritus, MAE, University of Tennessee, Knoxville TN

Professional Preparation:

Union College, Schenectady, NY, Mechanical Engineering, BME, 1958

State University of New York/Buffalo, Engineering Science, MSc, 1968

State University of New York/Buffalo, Engineering Science, PhD, 1970

Professional Appointments:

2010-present: Professor Emeritus, University of Tennessee/Knoxville

2010-2013: Member, Technical Staff, Trideum Inc., Huntsville AL

1982-2013: Director, UT CFD Laboratory, University of Tennessee/Knoxville

1979-2010: Professor, MAE/Engineering Science, University of Tennessee/Knoxville

6/2003: Visiting Scientist, National Computing Center, Taipei, Taiwan

1/2001: Visiting Professor, Mechanical Engineering, Northwest University, Potchefstroom, South Africa

1975-1997: President and Chief Scientist, Computational Mechanics Corp., Knoxville TN

9/1995: Visiting Professor, Civil Engineering, Chuo University, Tokyo, Japan

3/1983: Lecturer, von Karman Institute of Fluid Dynamics, Brussels, Belgium

1975-1979: Associate Professor, Engineering Science & Mechanics, University of Tennessee, Knoxville TN

1974-1975: Visiting Professor, Mechanical Engineering, Old Dominion University, and Visiting Scientist, NASA Langley Research Center, Hampton, VA

1971-1973: Visiting Scientist (summers), Institute for Computer Applications in Science & Engineering (ICASE), NASA Langley, Hampton, VA

1970-1974: Principal Research Scientist, Computational Fluid Mechanic, Textron/Bell Aerospace Inc., Buffalo, NY

1965-1970: Instructor, Engineering Faculty, SUNY/Buffalo

1958-1964: Mechanical Engineer, Union Carbide Corp., Buffalo NY

Graduate Degree Production, 17 PhD (major professor), 18 MSc (thesis advisor)

Research Contract Support: ~$11 M during UT professorship as PI

Professional Honors and Associations:

Fellow (elected 2001), US Association for Computational Mechanics (USACM)

Fellow (elected 2002), International Association for Computational Mechanics (IACM)

Associate Fellow (elected 1974), American Institute Aeronautics and Astronautics

Research Fellow Award, UT College of Engineering, 2003

Excellence in Technology Transfer Award, University of Tennessee, 1993

Chancellor’s Research Scholar Award, University of Tennessee, 1983

NASA Tech Brief Awards, 1984, 1976

Professional Engineer, New York and Tennessee

Journal Associate Editorships (now Emeritus): Computer Methods in Applied Mechanics and Engineering, Progress in Computational Fluid Dynamics, Numerical Heat Transfer, Numerical Methods in Fluids

James D. Freels PhD, PE, Senior Research Staff (retired 2018), UT-Battelle, ORNL,

Adjunct Faculty member, MAE, University of Tennessee, Knoxville, TN

Professional Preparation: BS Nuclear Engineering, University of TN, 1977

MS Nuclear Engineering, University of TN, 1979

PhD Engineering Science and Mechanics, Univ TN, 1992

Professional Experience:

1979-1983: Staff Scientist, Science Applications, Inc, Oak Ridge, TN

1983-1988: Senior Engr, Technology for Energy Corporation, Knoxville, TN

1988-1991: Senior Staff Scientist/Division Manager,

Science Applications International Corporation, Oak Ridge, TN

1991-2017: Senior Research Staff, Nuclear Safety Group, Research Reactors Division,

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN

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