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ASPECT
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ASPECT
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Classes | |
| class | ParticleOutput |
Functions | |
| template<int dim> | |
| LinearAlgebra::BlockVector | compute_dirichlet_boundary_heat_flux_solution_vector (const SimulatorAccess< dim > &simulator_access) |
| template<int dim> | |
| std::vector< std::vector< std::pair< double, double > > > | compute_heat_flux_through_boundary_faces (const SimulatorAccess< dim > &simulator_access) |
| LinearAlgebra::BlockVector aspect::Postprocess::internal::compute_dirichlet_boundary_heat_flux_solution_vector | ( | const SimulatorAccess< dim > & | simulator_access | ) |
Compute the heat flux for boundaries with prescribed temperature (Dirichlet boundary conditions) using the consistent boundary flux method. The method is described in
Gresho, P. M., Lee, R. L., Sani, R. L., Maslanik, M. K., & Eaton, B. E. (1987). The consistent Galerkin FEM for computing derived boundary quantities in thermal and or fluids problems. International Journal for Numerical Methods in Fluids, 7(4), 371-394.
The implementation of the method is benchmarked in
Juliane Dannberg, Rene Gassmöller, Daniele Thallner, Frederick LaCombe, Courtney Sprain (2024). Changes in core–mantle boundary heat flux patterns throughout the supercontinent cycle, Geophysical Journal International, Volume 237, Issue 3, June 2024, Pages 1251–1274, https://doi.org/10.1093/gji/ggae075.
In summary, the method solves the temperature equation again on the boundary faces, with known temperatures and solving for the boundary fluxes that satisfy the equation. Since the equation is only formed on the faces and it can be solved using only diagonal matrices, the computation is cheap. Conceptually simpler methods like evaluating the temperature gradient on the face are significantly less accurate.
The function returns a solution vector, which contains the heat flux in the temperature block of the vector.
| std::vector<std::vector<std::pair<double, double> > > aspect::Postprocess::internal::compute_heat_flux_through_boundary_faces | ( | const SimulatorAccess< dim > & | simulator_access | ) |
This function computes the combined heat flux through each boundary face (conductive + advective). For reflecting boundaries the conductive heat flux is 0, for boundaries with prescribed heat flux (inhomogeneous Neumann boundary conditions) it is simply the integral of the prescribed heat flux over the face, and for boundaries with non-tangential velocities the advective heat flux is computed as the integral over the advective heat flux density. For boundaries with prescribed temperature (Dirichlet boundary conditions) the heat flux is computed using the compute_dirichlet_boundary_heat_flux_solution_vector() function.
The function returns a vector with as many entries as active cells. For each locally owned cell it contains a vector with one entry per face. Each of these entries contains a pair of doubles, containing the combined heat flux (first entry) and face area (second entry). This function is a helper function that unifies the complex heat flux computation necessary for several postprocessors.