Chapter 9 Mathematically rigorous closure of spatially filtered NS PDE systems
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A. J. Baker
Libretto
Error freed CFD mathematics alterations of NS/RaNS/LES PDE systems annihilateannihilate space-time discretization-generated truncation error algebraic instability and scalar member phase aliasing.
Herein rigorously derived analytical closure of spatially filtered NS PDE systems is the transformational alteration to, “… stagnationstagnation of CFD capability advancement … exists.”
As the derivation never invokes the word turbulentturbulent, analytically closed spatially filtered NS PDE systems are pertinent for arbitrary Reynolds number (Re) specification.
This error-freederror-freed CFD mathematics advancement renders obsolete the host of LES algorithms that replace resolved-unresolved scale interaction and unresolved scales mathematical rigor with heuristic “physics-based” subgrid scale tensor models.
Libretto
Error freed CFD mathematics alterations of NS/RaNS/LES PDE systems annihilateannihilate space-time discretization-generated truncation error algebraic instability and scalar member phase aliasing.
Herein rigorously derived analytical closure of spatially filtered NS PDE systems is the transformational alteration to, “… stagnationstagnation of CFD capability advancement … exists.”
As the derivation never invokes the word turbulentturbulent, analytically closed spatially filtered NS PDE systems are pertinent for arbitrary Reynolds number (Re) specification.
This error-freederror-freed CFD mathematics advancement renders obsolete the host of LES algorithms that replace resolved-unresolved scale interaction and unresolved scales mathematical rigor with heuristic “physics-based” subgrid scale tensor models.
Kapitel in diesem Buch
- Frontmatter I
- Dedication V
- Contents VII
- Prologue 1
- Chapter 1 Why this monograph? 3
- Chapter 2 A brief pertinent CFD chronology 6
- Chapter 3 Fluid mechanics conservation principles, PDE notation 13
-
Part A: Space-time discretization error annihilation, algebraic instability
- Chapter 4 Legacy CFD difference algebra derived stabilizations, O(h2) truncation error annihilation (TEA) theory, NS error freed PDE mathematics, monotonicity, stability 21
- Chapter 5 Navier-Stokes error freed CFD mathematics, continuous weak formulation, FE theory, asymptotic convergence, error estimates, validations, monotone continuum shock interpolation 42
- Chapter 6 Time-averaged (RaNS) Navier-Stokes error freed CFD weak formulation, theory, asymptotic convergence, validations 73
- Chapter 7 Annihilation of NS/RaNS PDE space-time discretization-induced O(m2, m3) phase dispersion and O(Δt3) truncation errors 97
- Chapter 8 Hypersonics, aerothermodynamics, radiation CFD issues 109
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Part B: Analytical closure of spatially filtered NS PDE systems
- Chapter 9 Mathematically rigorous closure of spatially filtered NS PDE systems 125
- Chapter 10 FaNS theory O(1;δ2) PDE system rendered bounded domain well-posed 139
- Chapter 11 Validation, FaNS, NS PDE systems same code/mesh predictions,100 < Re < 4,000 159
- Chapter 12 Validation, ∀ Re pertinent FaNS theory prediction of laminar BL profile O(1) velocity insipient transition, separation, turbulent BL profile reattachment, then relaminarization, Re ≈ 12,000 175
- Chapter 13 Epilogue, error freed CFD mathematics continuing impact 201
- Nomenclature
- Appendix A: The finite element toolbox 207
- Appendix B: Theory, weak formulation optimal continuous Galerkin FE p = 1,2,3 basis CFD algorithms 221
- Appendix C: Error freed CFD mathematics altered continuous Galerkin FE basis algorithm and Newton jacobian matrix statements 233
- Subject index 345
Kapitel in diesem Buch
- Frontmatter I
- Dedication V
- Contents VII
- Prologue 1
- Chapter 1 Why this monograph? 3
- Chapter 2 A brief pertinent CFD chronology 6
- Chapter 3 Fluid mechanics conservation principles, PDE notation 13
-
Part A: Space-time discretization error annihilation, algebraic instability
- Chapter 4 Legacy CFD difference algebra derived stabilizations, O(h2) truncation error annihilation (TEA) theory, NS error freed PDE mathematics, monotonicity, stability 21
- Chapter 5 Navier-Stokes error freed CFD mathematics, continuous weak formulation, FE theory, asymptotic convergence, error estimates, validations, monotone continuum shock interpolation 42
- Chapter 6 Time-averaged (RaNS) Navier-Stokes error freed CFD weak formulation, theory, asymptotic convergence, validations 73
- Chapter 7 Annihilation of NS/RaNS PDE space-time discretization-induced O(m2, m3) phase dispersion and O(Δt3) truncation errors 97
- Chapter 8 Hypersonics, aerothermodynamics, radiation CFD issues 109
-
Part B: Analytical closure of spatially filtered NS PDE systems
- Chapter 9 Mathematically rigorous closure of spatially filtered NS PDE systems 125
- Chapter 10 FaNS theory O(1;δ2) PDE system rendered bounded domain well-posed 139
- Chapter 11 Validation, FaNS, NS PDE systems same code/mesh predictions,100 < Re < 4,000 159
- Chapter 12 Validation, ∀ Re pertinent FaNS theory prediction of laminar BL profile O(1) velocity insipient transition, separation, turbulent BL profile reattachment, then relaminarization, Re ≈ 12,000 175
- Chapter 13 Epilogue, error freed CFD mathematics continuing impact 201
- Nomenclature
- Appendix A: The finite element toolbox 207
- Appendix B: Theory, weak formulation optimal continuous Galerkin FE p = 1,2,3 basis CFD algorithms 221
- Appendix C: Error freed CFD mathematics altered continuous Galerkin FE basis algorithm and Newton jacobian matrix statements 233
- Subject index 345
