The governing equations for the perturbations

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Table of contents

1 Introduction and Motivation 
2 Problem Definition 
2.1 The governing equations for the base flow
2.2 The governing equations for the perturbations
2.3 The adjoint governing equations for the perturbations
2.4 Receptivity and sensitivity
3 Numerical Approach 
3.1 The pressure form of the Navier-Stokes equations
3.2 Computational domain and discretization
3.3 Validation
3.4 Considerations on domain size and grid size
4 Multigrid 
4.1 A generic iterative solver
4.2 Ingredients of a multigrid solver
4.3 Relaxation
4.4 Correction Scheme – the linear equation
4.5 Full Approximation Scheme – the non-linear equation
4.6 Test cases
5 Global analysis 
5.1 Base flow
5.2 Global analysis of the direct operator
5.3 Adjoint field
5.4 The wavemaker
6 Conclusions and Perspectives 
A Matlab multigrid code