Numerical Computation of Compressible and Viscous Flow [Kietas viršelis]

  • Formatas: Hardback, 504 pages, aukštis x plotis x storis: 236x163x33 mm, weight: 1039 g
  • Serija: AIAA Education Series
  • Išleidimo metai: 20-Nov-2014
  • Leidėjas: American Institute of Aeronautics & Astronautics
  • ISBN-10: 1624102646
  • ISBN-13: 9781624102646
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 504 pages, aukštis x plotis x storis: 236x163x33 mm, weight: 1039 g
  • Serija: AIAA Education Series
  • Išleidimo metai: 20-Nov-2014
  • Leidėjas: American Institute of Aeronautics & Astronautics
  • ISBN-10: 1624102646
  • ISBN-13: 9781624102646
Kitos knygos pagal šią temą:
Numerical Computation of Compressible and Viscous is written for those who want to calculate compressible and viscous flow past aerodynamic bodies. As taught by Robert W. MacCormack at Stanford University, it allows readers to get started in programming for solving initial value problems. It facilitates understanding of numerical accuracy and stability, matrix algebra, finite volume formulations, and the use of flux split algorithms for solving the Euler and Navier-Stokes equations. Featuring step by step presentation of numerical procedures for solving for flows of complex inviscid/viscous physical interactions, the first five chapters present the building blocks of computational fluid dynamics (CFD). Additional chapters present The Murman-Cole method for solving the Transonic Small Disturbance equation Transformations required to transform the governing equations in physical Cartesian space into body fitted computational space Several algorithms for solving the Euler equations, using as a test case the shock tube problem Harten's TVD (Total Variation Diminishing) procedure for higher resolution in space and time Procedures for solving implicit sets of equations via matrix inversion General boundary conditions for fluid flow Several applications of numerical procedures for solving the one and quasi one dimensional Euler equations Extension of the presented algorithms for solving the Euler equations and the Navier-Stokes equations to two and three dimensions
Preface xv
Chapter 1 Equations Governing Fluid Flow 1(12)
1.1 Introduction
1(1)
1.2 Equation Hierarchy
1(1)
1.3 Navier—Stokes Equations
2(2)
1.4 Euler Equations
4(1)
1.5 Full Potential Equation
4(2)
1.6 Transonic Small Disturbance Equation
6(1)
1.7 Laplace-Like Equations
7(2)
1.8 Model Equations
9(1)
1.9 Solution Methods
10(1)
References
11(2)
Chapter 2 Integral and Conservation Law Form, Discontinuities, Jacobians, Linearization and Characteristic Relations 13(24)
2.1 Introduction
13(1)
2.2 Conservation Law Form
13(1)
2.3 Integral Form
14(1)
2.4 Relations at Discontinuities
15(2)
2.5 Discontinuity Examples
17(8)
2.6 Jacobians
25(2)
2.7 Linearization
27(1)
2.8 Characteristic Relations
28(7)
2.9 Hyperbolic Requirement
35(1)
2.10 Boundary Conditions for Hyperbolic Equations
35(1)
2.11 Concluding Remarks
36(1)
Chapter 3 Numerical Approximation 37(12)
3.1 Introduction
37(1)
3.2 Numerical Approximation on an Equally Spaced Mesh
37(2)
3.3 Numerical Approximation on a Nonequally Spaced Mesh
39(2)
3.4 Difference Operators
41(1)
3.5 Finite Difference Equations
42(4)
3.6 Time-Accurate and Steady-State Solutions
46(1)
3.7 Conservation Form of the Difference Equations
47(1)
References
48(1)
Chapter 4 Numerical Stability 49(14)
4.1 Introduction
49(1)
4.2 Fundamental Numerical Requirements
49(1)
4.3 Numerical Stability
49(1)
4.4 von Neumann Stability Analysis
50(12)
4.5 Concluding Remarks
62(1)
References
62(1)
Chapter 5 Algorithms for the Model Equations 63(26)
5.1 Introduction
63(1)
5.2 Model Hyperbolic Equation
63(11)
5.3 Model Elliptic Equation
74(8)
5.4 Panel Method for Solving the Linear Potential Flow Equation
82(2)
5.5 Numerical Method for Model Parabolic Equation
84(4)
5.6 Concluding Remarks
88(1)
References
88(1)
Chapter 6 Solution of the Transonic Small Disturbance Equation 89(14)
6.1 Introduction
89(1)
6.2 Murman—Cole Method
89(3)
6.3 Stability of the Murman—Cole Method
92(2)
6.4 Application of the Murman—Cole Method
94(6)
6.5 Correction Change or Delta Form of the Algorithm
100(1)
6.6 Concluding Remarks
101(1)
Reference
101(2)
Chapter 7 Transformations and the Finite Volume Approach 103(22)
7.1 Introduction
103(1)
7.2 Computational Meshes and Transformations
103(1)
7.3 Transformations of the Stationary Case
104(2)
7.4 Transformations of the Nonstationary Case
106(2)
7.5 Finite Volume Formulation
108(5)
7.6 Equivalence of Finite Difference and Finite Volume Forms
113(3)
7.7 A Common Formulation for Both Approximations
116(3)
7.8 A Common Computational Mesh for Finite Approaches
119(6)
Chapter 8 Algorithms for the Full Potential Equation 125(30)
8.1 Introduction
125(1)
8.2 Jameson's Rotated Difference Method
125(3)
8.3 Hoist's Method for the Full Potential Equation in Conservation Law Form
128(9)
8.4 Applications
137(16)
8.5 Concluding Remarks
153(1)
References
153(2)
Chapter 9 Algorithms for the Euler Equations 155(50)
9.1 Introduction
155(1)
9.2 Shock Tube Problem
155(4)
9.3 MacCormack Method
159(3)
9.4 Beam—Warming Method
162(8)
9.5 Jameson's Runge—Kutta Method
170(2)
9.6 Steger—Warming's Flux Split Method
172(9)
9.7 Conservative Difference Equations in Generic Form
181(1)
9.8 Modified Steger—Warming Method
181(4)
9.9 Roe Flux Difference Vector Splitting Method
185(3)
9.10 Comparison of the Split Fluxes in Generic Form
188(2)
9.11 Extensions to Higher Order for the Flux Split Algorithms
190(6)
9.12 Implicit Modified-Steger—Warming and Roe Methods
196(4)
9.13 Higher Order Time Accuracy
200(3)
9.14 Concluding Remarks
203(1)
References
203(2)
Chapter 10 Higher Resolution in Space and Time—The TVD Method 205(24)
10.1 Introduction
205(1)
10.2 Harten's TVD Method
206(10)
10.3 TVD for the Euler Equations
216(8)
10.4 Implicit TVD Methods
224(4)
10.5 Concluding Remarks
228(1)
References
228(1)
Chapter 11 Solution of Implicit Sets of Equations 229(18)
11.1 Introduction
229(1)
11.2 Generic Implicit Algorithm
229(2)
11.3 1-D Implicit Algorithm
231(3)
11.4 2-D Implicit Algorithm
234(2)
11.5 Gauss—Seidel Line Relaxation
236(2)
11.6 Approximate Factorization
238(2)
11.7 DDADI Algorithm
240(3)
11.8 Removal of Decomposition Error
243(1)
11.9 Implicit Algorithm in General Curvilinear Coordinates
244(1)
11.10 Concluding Remarks
245(1)
References
245(2)
Chapter 12 Boundary Conditions for Fluid Flow 247(22)
12.1 Introduction
247(1)
12.2 Impermeable Boundaries—Solid Walls or Streamlines
248(4)
12.3 Entrance and Exit Boundaries
252(1)
12.4 Subsonic Entrance Boundaries
253(7)
12.5 Subsonic or Supersonic Exit Boundaries
260(3)
12.6 Boundary Conditions for the Navier—Stokes Equations
263(2)
12.7 Boundary Conditions to Avoid
265(1)
12.8 Order of Accuracy Required for Boundary Conditions
266(1)
12.9 Concluding Remarks
267(1)
Reference
268(1)
Chapter 13 Solution of 1-D Euler Equations 269(40)
13.1 Introduction
269(1)
13.2 Supersonic Inlet Problem
269(13)
13.3 Converging—Diverging Nozzle Problem
282(6)
13.4 Piston Flow Problem
288(5)
13.5 Expansion Flow Problem
293(8)
13.6 Compression Flow Problem
301(7)
13.7 Concluding Remarks
308(1)
Reference
308(1)
Chapter 14 Algorithms for Euler Equations in General Curvilinear Coordinates 309(50)
14.1 Introduction
309(1)
14.2 Transformation to Curvilinear Coordinates
309(7)
14.3 2-D Applications
316(23)
14.4 Euler Equations in Arbitrary Axisymmetric Coordinates
339(11)
14.5 Axisymmetric Applications
350(8)
14.6 Concluding Remarks
358(1)
References
358(1)
Chapter 15 Navier—Stokes and Reynolds-Averaged Navier—Stokes (RANS) Equations 359(14)
15.1 Introduction
359(1)
15.2 Navier—Stokes Equations
359(1)
15.3 Time Averaging for RANS Equations
360(2)
15.4 Favre Averaging for Compressible Flow
362(1)
15.5 Boussinesq Eddy Viscosity
363(1)
15.6 Prandtl—van Driest Turbulence Model—Near Walls
364(1)
15.7 Cebeci—Smith Turbulence Model
364(2)
15.8 Baldwin—Lomax Model
366(1)
15.9 Other Turbulence Models
367(2)
15.10 Summary
369(1)
References
370(3)
Chapter 16 Algorithms for the Navier—Stokes Equations in 2-D Cartesian Coordinates 373(50)
16.1 Introduction
373(1)
16.2 Thin-Layer Navier—Stokes Equations
373(2)
16.3 Implicit Algorithm for Thin-Layer Navier—Stokes Equations
375(1)
16.4 Couette Flow
376(13)
16.5 Blasius Boundary Layer
389(5)
16.6 Thin-Layer Navier—Stokes Equations Application
394(11)
16.7 Full Navier—Stokes Equations
405(2)
16.8 Implicit Algorithm for the Navier—Stokes Equations
407(1)
16.9 Stability Analysis for the Implicit Navier—Stokes Algorithm
408(2)
16.10 Navier—Stokes Equations Application
410(9)
16.11 Time-Step Size, Time Accuracy, and CFL Number
419(2)
16.12 Concluding Remarks
421(1)
References
421(2)
Chapter 17 Algorithms for Navier—Stokes Equations in 2-D Arbitrary Curvilinear Coordinates 423(48)
17.1 Introduction
423(1)
17.2 Transformed Navier—Stokes Equations
423(2)
17.3 Euler Flux Terms and Rotated Jacobians
425(1)
17.4 Viscous Flux Terms
425(2)
17.5 Navier—Stokes Flux Vectors
427(1)
17.6 Implicit Algorithm for the Full Navier—Stokes Equations
428(2)
17.7 Evaluation of the Metric and Flow Derivative Terms
430(3)
17.8 Implicit Boundary Conditions at Solid Walls
433(4)
17.9 Application 1—Viscous Flow Past a Compression Corner
437(15)
17.10 Application 2—Viscous Flow Past a Circular Arc Airfoil
452(12)
17.11 Application 3—Viscous Flow Past a Blunt Body
464(6)
17.12 Concluding Remarks
470(1)
References
470(1)
Chapter 18 Algorithms for Navier—Stokes Equations in 3-D Arbitrary Curvilinear Coordinates 471(38)
18.1 Introduction
471(1)
18.2 Transformations in 3-D
471(2)
18.3 Stationary Coordinate Transformation
473(9)
18.4 Nonstationary Coordinate Transformation
482(1)
18.5 All You Need is F' and A'
483(1)
18.6 Implicit Algorithm for Navier—Stokes Equations in 3-D
484(6)
18.7 Application—Flow Past a Blunt Body
490(18)
18.8 Concluding Remarks
508(1)
References
508(1)
Index 509(14)
Supporting Materials 523