Solving for the singular values, power spectral density and the \(\mathcal{H}_\infty\) norm of the linearized Navier stokes equations. We reproduce Figure 4.10 in [5] using spectral integration with the linearized Navier-Stokes equations in primitive variables. More...
Detailed Description
Solving for the singular values, power spectral density and the \(\mathcal{H}_\infty\) norm of the linearized Navier stokes equations. We reproduce Figure 4.10 in [5] using spectral integration with the linearized Navier-Stokes equations in primitive variables.
The we plot the power spectral density:
Lastly notice that the largest singular value is somewhere near \(-0.5\); the exact value can be calculated using the fast algorithm by Bruinsma and Steinbuch [1] that is implemented in our codes.
Definition in file Ex_12.cpp.
Go to the source code of this file.
Macros | |
| #define | EIGEN_USE_BLAS |
| #define | SIS_USE_LAPACK |
Typedefs | |
| typedef complex< double > | Cd_t |
| typedef valarray< complex< double > > | Vcd_t |
Functions | |
| complex< double > | ii (0.0, 1.0) |
| int | main () |
Macro Definition Documentation
◆ EIGEN_USE_BLAS
◆ SIS_USE_LAPACK
Typedef Documentation
◆ Cd_t
◆ Vcd_t
Function Documentation
◆ ii()
| complex<double> ii | ( | 0. | 0, |
| 1. | 0 | ||
| ) |
Referenced by main().
◆ main()
| int main | ( | ) |
Definition at line 27 of file Ex_12.cpp.
References sis::Linop< T >::coef, sis::SingularValueDecomposition< T >::compute(), sis::GeneralizedEigenSolver< T >::eigenvalues, sis::BcMat< T >::eval, ii(), sis::BcMat< T >::L, sis::N, std::pow(), std::real(), sis::LinopMat< T >::resize(), sis::setChebPts(), sis::sis_setup(), and sis::y().
