Continuous adjoint approach to the Spalart–Allmaras turbulence model for incompressible flows

2009 ◽  
Vol 38 (8) ◽  
pp. 1528-1538 ◽  
Author(s):  
A.S. Zymaris ◽  
D.I. Papadimitriou ◽  
K.C. Giannakoglou ◽  
C. Othmer
Keyword(s):  
Turbulence Model ◽  
Incompressible Flows ◽  
Adjoint Approach ◽  
Continuous Adjoint

The continuous adjoint approach to thek–ε turbulence model for shape optimization and optimal active control of turbulent flows

2014 ◽  
Vol 47 (3) ◽  
pp. 370-389 ◽  
Author(s):  
E.M. Papoutsis-Kiachagias ◽  
A.S. Zymaris ◽  
I.S. Kavvadias ◽  
D.I. Papadimitriou ◽  
K.C. Giannakoglou
Keyword(s):  
Shape Optimization ◽  
Turbulent Flows ◽  
Active Control ◽  
Turbulence Model ◽  
Adjoint Approach ◽  
Continuous Adjoint

scholarly journals Derivation of the Adjoint Drift Flux Equations for Multiphase Flow

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 31 ◽  
Author(s):  
Shenan Grossberg ◽  
Daniel S. Jarman ◽  
Gavin R. Tabor
Keyword(s):  
Multiphase Flow ◽  
Objective Function ◽  
Settling Velocity ◽  
Flow Problem ◽  
Adjoint System ◽  
Drift Flux ◽  
Adjoint Approach ◽  
Continuous Adjoint ◽  
First Time ◽  
Mathematical Derivation

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multiphase flow modeled by the commonly used drift flux equations, together with the adjoint boundary conditions necessary to solve a generic multiphase flow problem. The objective function is defined for such a system, and specific examples derived for commonly used settling velocity formulations such as the Takacs and Dahl models. We also discuss the use of these equations for a complete optimisation process.

Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids

AIAA Journal ◽  
2007 ◽  
Vol 45 (9) ◽  
pp. 2125-2139 ◽  
Author(s):  
Carlos Castro ◽  
Carlos Lozano ◽  
Francisco Palacios ◽  
Enrique Zuazua
Keyword(s):  
Unstructured Grids ◽  
Aerodynamic Design ◽  
Adjoint Approach ◽  
Continuous Adjoint

scholarly journals Continuous Adjoint Approach for the Spalart-Allmaras Model in Aerodynamic Optimization

AIAA Journal ◽  
2012 ◽  
Vol 50 (3) ◽  
pp. 631-646 ◽  
Author(s):  
Alfonso Bueno-Orovio ◽  
Carlos Castro ◽  
Francisco Palacios ◽  
Enrique Zuazua
Keyword(s):  
Aerodynamic Optimization ◽  
Adjoint Approach ◽  
Continuous Adjoint

scholarly journals A complexity-driven framework for waveform tomography with discrete adjoints

2020 ◽  
Vol 223 (2) ◽  
pp. 1247-1264
Author(s):  
Alexandre Szenicer ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Adjoint Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Frequency Scaling ◽  
Seismic Waveform ◽  
Discrete Adjoint ◽  
Continuous Adjoint Method ◽  
Adjoint Approach ◽  
Pseudo Spectral Method ◽  
Continuous Adjoint

Summary We develop a new approach for computing Fréchet sensitivity kernels in full waveform inversion by using the discrete adjoint approach in addition to the widely used continuous adjoint approach for seismic waveform inversion. This method is particularly well suited for the forward solver AxiSEM3D, a combination of the spectral-element method (SEM) and a Fourier pseudo-spectral method, which allows for a sparse azimuthal wavefield parametrization adaptive to wavefield complexity, leading to lower computational costs and better frequency scaling than conventional 3-D solvers. We implement the continuous adjoint method to serve as a benchmark, additionally allowing for simulating off-axis sources in axisymmetric or 3-D models. The kernels generated by both methods are compared to each other, and benchmarked against theoretical predictions based on linearized Born theory, providing an excellent fit to this independent reference solution. Our verification benchmarks show that the discrete adjoint method can produce exact kernels, largely identical to continuous kernels. While using the continuous adjoint method we lose the computational advantage and fall back on a full-3-D frequency scaling, using the discrete adjoint retains the speedup offered by AxiSEM3D. We also discuss the creation of a data-coverage based mesh to run the simulations on during the inversion process, which would allow to exploit the flexibility of the Fourier parametrization and thus the speedup offered by our method.

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