Linear form for the TALA/PDA compressibility term in compressible Stokes. More...

#include <inv_rho_grad_rho_dot_u.hpp>

Public Types
using	DstVectorType = linalg::VectorQ1Scalar< ScalarT >

using	ScalarType = ScalarT

Public Member Functions
	InvRhoGradRhoDotU (const grid::shell::DistributedDomain &domain, const grid::Grid3DDataVec< ScalarT, 3 > &grid, const grid::Grid2DDataScalar< ScalarT > &radii, const linalg::VectorQ1Scalar< ScalarT > &rho, const linalg::VectorQ1Vec< ScalarT, VelocityVecDim > &velocity, const linalg::OperatorApplyMode operator_apply_mode=linalg::OperatorApplyMode::Replace, const linalg::OperatorCommunicationMode operator_communication_mode=linalg::OperatorCommunicationMode::CommunicateAdditively)

void	apply_impl (DstVectorType &dst)

void	operator() (const int local_subdomain_id, const int x_cell, const int y_cell, const int r_cell) const
	Kokkos kernel: per-cell contribution to \( f_i = \int_E \frac{1}{\rho} \nabla\rho \cdot \mathbf{u} \, \phi_i \, \mathrm{d}x \).

Detailed Description

template<typename ScalarT, int VelocityVecDim = 3>
class terra::fe::wedge::linearforms::shell::InvRhoGradRhoDotU< ScalarT, VelocityVecDim >

Linear form for the TALA/PDA compressibility term in compressible Stokes.

Given a scalar FE function \(\rho\) (density) and a vectorial FE function \(\mathbf{u}\) (velocity), this linear form evaluates

\[ f_i = \int_\Omega \frac{1}{\rho} \nabla\rho \cdot \mathbf{u} \, \phi_i \, \mathrm{d}x \]

into a scalar finite element coefficient vector, where \(\phi_i\) are the scalar Q1 test functions on the spherical shell mesh.

This term arises in the pressure equation of the Truncated Anelastic Liquid Approximation (TALA) and the Projected Density Approximation (PDA) for compressible Stokes flow in geodynamics. See the Stokes documentation for the full context.

Note: The sign convention at the call site depends on the (2,1) block of the Stokes operator. The Divergence block computes \(-(q, \mathrm{div}\, u)\), so the mass conservation equation \(-(q, \mathrm{div}\, u) = f_p\) requires \(f_p = +\frac{1}{\rho}\nabla\rho\cdot\mathbf{u}\) term (positive sign).; \(\rho\) must not vanish in the domain; no singular-value protection is applied.

Concept. This class satisfies terra::linalg::LinearFormLike. Evaluation writes the assembled coefficient vector into dst via linalg::apply:

InvRhoGradRhoDotU< double > L( domain, grid, radii, rho, velocity );
linalg::VectorQ1Scalar< double > g( domain );
linalg::apply( L, g );   // fills g_i = ∫ (1/ρ) ∇ρ·u φ_i dx

The default OperatorApplyMode::Replace zeroes dst before accumulation. Pass OperatorApplyMode::Add to add into an existing vector instead.