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waves
Basic FE playground
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Formulation of Kutta residuals. More...
#include <wKuttaResidual.h>
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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... | |
Formulation of Kutta residuals.
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Build the residual vector, on one Kutta element.
b = \int psi * (grad_phi)^2 dS
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Build the residual matrix for a fixed-point iteration, on one Kutta element.
A = \int psi * v_u*grad_phi dS
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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
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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