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flow::KuttaResidual Class Reference

Formulation of Kutta residuals. More...

#include <wKuttaResidual.h>

Static Public Member Functions

static Eigen::MatrixXd buildFixed (KuttaElement const &ke, std::vector< double > const &phi)
 Build the residual matrix for a fixed-point iteration, on one Kutta element. More...
 
static Eigen::VectorXd build (KuttaElement const &ke, std::vector< double > const &phi)
 Build the residual vector, on one Kutta element. More...
 
static Eigen::MatrixXd buildGradientFlow (KuttaElement const &ke, std::vector< double > const &phi)
 Build the gradient of the residual vector with respect to the flow variable (jacobian), on one Kutta element. More...
 
static std::tuple< Eigen::MatrixXd, Eigen::MatrixXd > buildGradientMesh (KuttaElement const &ke, std::vector< double > const &phi)
 Build the gradient of the residual vector with respect to the nodes, on one Kutta element. More...
 

Detailed Description

Formulation of Kutta residuals.

Member Function Documentation

◆ build()

Eigen::VectorXd KuttaResidual::build ( KuttaElement const &  ke,
std::vector< double > const &  phi 
)
static

Build the residual vector, on one Kutta element.

b = \int psi * (grad_phi)^2 dS

◆ buildFixed()

Eigen::MatrixXd KuttaResidual::buildFixed ( KuttaElement const &  ke,
std::vector< double > const &  phi 
)
static

Build the residual matrix for a fixed-point iteration, on one Kutta element.

A = \int psi * v_u*grad_phi dS

◆ buildGradientFlow()

Eigen::MatrixXd KuttaResidual::buildGradientFlow ( KuttaElement const &  ke,
std::vector< double > const &  phi 
)
static

Build the gradient of the residual vector with respect to the flow variable (jacobian), on one Kutta element.

A = \int psi * 2*(grad_phi_u)*dgrad_phi_u dS

◆ buildGradientMesh()

std::tuple< Eigen::MatrixXd, Eigen::MatrixXd > KuttaResidual::buildGradientMesh ( KuttaElement const &  ke,
std::vector< double > const &  phi 
)
static

Build the gradient of the residual vector with respect to the nodes, on one Kutta element.

A = d( \int psi * (grad_phi)^2 dS ) = \int psi * d(grad_phi)^2 dS

  • \int psi * (grad_phi)^2 ddS

The documentation for this class was generated from the following files: