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Mesh Adaptation for Computational Fluid Dynamics, Volume 2
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Mesh Adaptation for Computational Fluid Dynamics, Volume 2
by Alain Dervieux, Frederic Alauzet, Adrien Loseille, Bruno Koobus
Mesh Adaptation for Computational Fluid Dynamics, Volume 2
Cover
Title Page
Copyright Page
Acknowledgments
Introduction
1 Nonlinear Corrector for CFD
2 Multi-scale Adaptation for Unsteady Flows
3 Multi-rate Time Advancing
4 Goal-Oriented Adaptation for Inviscid Steady Flows
5 Goal-Oriented Adaptation for Viscous Steady Flows
6 Norm-Oriented Formulations
7 Goal-Oriented Adaptation for Unsteady Flows
8 Third-Order Unsteady Adaptation
References
Index
Summary of Volume 1
Other titles from iSTE in Numerical Methods in Engineering
End User License Agreement
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Title Page
Table of Contents
Cover
Title Page
Copyright Page
Acknowledgments
Introduction
1 Nonlinear Corrector for CFD
1.1. Introduction
1.2. Two correctors for the Poisson problem
1.3. RANS equations
1.4. Nonlinear functional correction
1.5. Example: supersonic flow
1.6. Concluding remarks
1.7. Notes
2 Multi-scale Adaptation for Unsteady Flows
2.1. Introduction
2.2. Mesh adaptation efficiency
2.3. Transient fixed-point mesh adaptation scheme
2.4. 2D bi-fluid example
2.5. Example: impact of a 3D water column on a obstacle
2.6. Conclusion
2.7. Appendix: remarks about the adaptation of the time step
2.8. Notes
3 Multi-rate Time Advancing
3.1. Introduction
3.2. Multi-rate time advancing by volume agglomeration
3.3. Elements of analysis
3.4. Applications
3.5. Conclusion
3.6. Notes
4 Goal-Oriented Adaptation for Inviscid Steady Flows
4.1. Introduction
4.2. A more accurate nonlinear error analysis
4.3. The case of the steady Euler equations
4.4. Error model minimization
4.5. Adaptative strategy
4.6. Numerical outputs
4.7. Conclusion
4.8. Notes
5 Goal-Oriented Adaptation for Viscous Steady Flows
5.1. Introduction
5.2. Case of an elliptic problem
5.3. Error analysis for Navier–Stokes problem
5.4. From theory to practice
5.5. An example of application to a turbulent flow
5.6. Conclusion
5.7. Notes
6 Norm-Oriented Formulations
6.1. Introduction
6.2. A summary of previous analyses
6.3. Norm-oriented approach
6.4. Numerical elliptic examples
6.5. Application to flows
6.6. Conclusion
6.7. Notes
7 Goal-Oriented Adaptation for Unsteady Flows
7.1. Introduction
7.2. Formal error analysis
7.3. Unsteady Euler models
7.4. Optimal unsteady adjoint-based metric
7.5. Theoretical mesh convergence analysis
7.6. From theory to practice
7.7. Numerical experiments
7.8. Conclusion
7.9. Notes
8 Third-Order Unsteady Adaptation
8.1. Introduction
8.2. Higher order interpolation and reconstruction
8.3. CENO approximation for the 2D Euler equations
8.4. Error analysis
8.5. Metric-based error estimate
8.6. Optimal metric
8.7. From theory to practical application
8.8. A numerical example: acoustic wave
8.9. Conclusion
8.10. Notes
References
Index
Summary of Volume 1
Other titles from iSTE in Numerical Methods in Engineering
End User License Agreement
List of Tables
Chapter 2
Table 2.1.
2D falling water column.The
x
-location of the bottom of the colum
...
Chapter 3
Table 3.1.
Circular cylinder at Reynolds number
8
.
4 × 10
6
. Time step factor
...
Table 3.2.
Mesh adaptative propagation of a contact discontinuity: Time step
...
Chapter 7
Table 7.1.
Mesh characteristics of the 3D blast wave calculation. For anisot
...
Chapter 8
Table 8.1.
Noise propagation in a rectangular box: mesh convergence for the
...
List of Illustrations
Chapter 1
Figure 1.1.
Examples of linear accumulation process when the h/
2
-mesh vertex
...
Figure 1.2.
Reconstruction of a smoother solution (dashed curve) from a disc
...
Figure 1.3.
Second AIAA Sonic Boom prediction workshop. Left: C25D geometry.
...
Figure 1.4.
Second AIAA Sonic Boom prediction workshop. Pressure difference
...
Chapter 2
Figure 2.1.
Schematic presentation of the transient fixed-point mesh adaptat
...
Figure 2.2.
Transient fixed-point mesh adaptation algorithm applied to the a
...
Figure 2.3.
Adaptation to the interface, that is, to the
0
value of a level
...
Figure 2.4.
2D falling water column. Interfaces at
t = 0
and
t = 2
and mesh
...
Figure 2.5.
2D falling water column. The x-location of the bottom of the col
...
Figure 2.6.
3D falling water column on a obstacle. Left, the simulation geom
...
Figure 2.7.
3D falling water column on a obstacle. Comparison between the in
...
Figure 2.8.
3D falling water column on a obstacle. Comparison between the in
...
Figure 2.9.
3D falling water column on a obstacle. Mesh adaptation based on
...
Chapter 3
Figure 3.1.
Sketch (in 2D) of the agglomeration of four cells into a macro-c
...
Figure 3.2.
Circular cylinder at Reynolds number
8
.
4 × 10
6
. Instantaneous Q-
...
Figure 3.3.
Circular cylinder at Reynolds number
8
.
4 × 10
6
. Zoom of the lift
...
Figure 3.4.
Mesh adaptative calculation of a traveling contact discontinuity
...
Chapter 4
Figure 4.1.
Cut planes through the final adapted meshes for the adjoint-base
...
Figure 4.2.
Pressure signature along x axis in the observation plane Adjoint
...
Chapter 5
Figure 5.1.
HL-CRM
16
◦
case. Left: Convergence history of the total li
...
Figure 5.2.
HL-CRM
16
◦
case. Cut plane x
= 50
. The 5M vertices adapted
...
Figure 5.3.
HL-CRM
16
◦
case. Cut plane y
= 15
.
5
(near the flap). The 5M
...
Figure 5.4.
HL-CRM
16
◦
case. Cut plane y
= 15
.
5
(near the slat). The 5M
...
Figure 5.5.
HL-CRM
16
◦
case. Cut plane in the region where the slat tip
...
Figure 5.6.
HL-CRM
16
◦
case. Cut plane x
= 38
(near the gap between the
...
Chapter 6
Figure 6.1.
Fully 2D boundary layer test case: sketch of the solution. For a
...
Figure 6.2.
Fully 2D boundary layer test case. Left: Comparison of the a pri
...
Figure 6.3.
Fully 2D boundary layer test case: convergence of the error norm
Figure 6.4.
Poisson problem with discontinuous coefficient: sketch of exact
...
Figure 6.5.
Poisson problem with discontinuous coefficient. Views of final m
...
Figure 6.6.
Poisson problem with discontinuous coefficient. Convergence of t
...
Figure 6.7.
Feature-based adaptation for minimizing the L
1
norm of the inter
...
Figure 6.8.
Feature-based adaptation for minimizing the L
1
norm of the inter
...
Figure 6.9.
Adaptation for minimizing the norm
||
W
−
Wh
||
L
2
with the norm-or
...
Figure 6.10.
Top: Mach solution field. Bottom: final adapted mesh. Shape: co
...
Chapter 7
Figure 7.1.
Memory issue for computing an unsteay adjoint. When state equati
...
Figure 7.2.
The memory issue for computing an unsteady adjoint is solved by
...
Figure 7.3.
Initial blast solution (about center of bottom) and location of
...
Figure 7.4.
2D city blast solution state evolution. From left to right and t
...
Figure 7.5.
2D city blast adjoint state evolution. From left to right and to
...
Figure 7.6.
Global transient fixed-point algorithm for unsteady goal-oriente
...
Figure 7.7.
Propagation in a box: sketch of geometry. An acoustic source pro
...
Figure 7.8.
Propagation of acoustic waves: density field evolving in time on
...
Figure 7.9.
3D City test case geometry and location of target surface
Γ
(sur
...
Figure 7.10.
3D Blast wave propagation: adjoint-based adapted surface (left)
...
Chapter 8
Figure 8.1.
Dual cell and two reconstruction molecules
Figure 8.2.
Sketch of the interface ∂C
i
∩
∂Ck between cell Ci and cell
...
Figure 8.3.
Improvement of the CENO scheme for the advection of a 2D Gauss
-
s
...
Figure 8.4.
Acoustic waves traveling in a box from bottom (5th mesh in time)
...
Figure 8.5.
Noise propagation in a box: mesh convergence of the spatial inte
...
Guide
Cover Page
Title Page
Copyright Page
Acknowledgments
Introduction
Table of Contents
Begin Reading
References
Index
Summary of Volume 1
Other titles from iSTE in Numerical Methods in Engineering
WILEY END USER LICENSE AGREEMENT
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