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waves
Basic FE playground
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Formulation of nonlinear potential equation residuals. More...
#include <wPotentialResidual.h>
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static Eigen::MatrixXd | buildFixed (tbox::Element const &e, std::vector< double > const &phi, Medium const &fluid) |
Build the residual matrix for a fixed-point iteration, on one element. More... | |
static Eigen::VectorXd | build (tbox::Element const &e, tbox::Element const &eU, std::vector< double > const &phi, Medium const &fluid, double muC, double mCO) |
Build the residual vector, on one element. More... | |
static std::tuple< Eigen::MatrixXd, Eigen::MatrixXd > | buildGradientFlow (tbox::Element const &e, tbox::Element const &eU, std::vector< double > const &phi, Medium const &fluid, double muC, double mCO) |
Build the gradient of the residual vector with respect to the flow variable (jacobian), on one element. More... | |
static std::tuple< Eigen::MatrixXd, Eigen::MatrixXd > | buildGradientMesh (tbox::Element const &e, tbox::Element const &eU, std::vector< double > const &phi, Medium const &fluid, int nDim, double muC, double mCO) |
Build the gradient of the residual vector with respect to the nodes, on one element. More... | |
Formulation of nonlinear potential equation residuals.
mu as F0ElMu?
split stabilization terms from subsonic terms?
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Build the residual vector, on one element.
b = \int ( (1-mu)*rho + mu*rhoU ) * grad_phi * grad_psi dV
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Build the residual matrix for a fixed-point iteration, on one element.
A = \int rho * grad_phi * grad_psi dV
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Build the gradient of the residual vector with respect to the flow variable (jacobian), on one element.
A = \int d( (1-mu)*rho + mu*rhoU ) * grad_phi * grad_psi dV = \int (1-mu)*drho * grad_phi * grad_psi dV
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Build the gradient of the residual vector with respect to the nodes, on one element.
A = d( \int ( (1-mu)*rho + mu*rhoU ) * grad_phi * grad_psi dV ) = \int (1-mu)*drho * grad_phi * grad_psi dV