# Draft: Convection Model Operators, SUPG Stabilisation Operators, Elementwise DoFValueOperators (+Tests), Second derivatives for the Blending Maps, PETScHDF5 Function Saving, Projection subclasses for Smoothers and Restriction/Prolongation

**Preface: Our pipeline seems to be broken right now, so we should probably wait until it works again.**

This merge request contains several new operators and features aimed at the TerraNeo application.

A few comments on the content of the various diffs:

**composites/P2P1TaylorHoodCompStokesOperator.hpp:** Implements a P2P1 Block Operator for the compressible Stokes (both ALA and TALA are available) with potentially temperature dependent viscosity. It can also generate an appropriate right hand side. You can also activate or deactivate the frozen velocity approach (i.e. if the compressible term in the mass conservation equation is made explicit).

LHS velocity:
`2 \int_{\Omega} \eta(x,T) \sigma(u) : \sigma(v) \text{ } dx - \frac{2}{\text{dim}} \int_{\Omega}{\eta(x,T) (\nabla \cdot u) \cdot (\nabla \cdot v)} \text{ } dx - \int_{\Omega} \text{div}(v)p_d \text{ } dx - \int_\Omega \frac{\text{Di}}{\Gamma_0} \rho(x) (K_T)^{-1} p_d g \cdot v \text{ } dx`

RHS velocity:
`-\int_\Omega \frac{\text{Ra}}{\text{Pe}} \rho(x) \alpha T_d g \cdot v \text{ } dx`

LHS pressure (here without frozen velocity):

` -\int_\Omega \left (\frac{\nabla \rho(x)}{\rho(x)} \cdot u \right ) q \text{ } dx - \int_\Omega (\nabla \cdot u) q \text{ } dx`

RHS pressure: 0

**src/p2functionspace/P2CompTransportOperator.hpp:** Implements a P2 Operator for the time (in-)dependent energy conservation equation with optional SUPG Stabilisation. Various time stepping schemes (implicit Euler, BDF2, Crank-Nicolson) are available (some additional function calls from outside might be required, e.g. the operator provides a method to save the previous time step right hand side for crank nicolson). Can also be used for the diffusion solve step when using the MMOC operator splitting approach. It can also generate an appropriate right hand side.

LHS temperature (here for the adiabatic heat on the lhs, but can be also be made explicit):
`\int_\Omega \frac{\partial T}{\partial t} w \text{ } dx + \int_\Omega (u \cdot \nabla T) w \text{ } dx + \int_\Omega \frac{k }{\text{Pe} \text{ } C_p}\nabla T \cdot \nabla \left ( \frac{w}{\rho(x)} \right ) \text{ } dx - \int_\Omega \text{Di} \text{ } \frac{\alpha}{C_p} T (u \cdot g )w \text{ } dx + \text{SUPG Terms (if used)}`

RHS temperature:
`- \int_\Omega \frac{1}{C_p} H w \text{ } dx -\int_\Omega \frac{\text{Pe}}{\rho(x) C_p}\frac{\text{Di}}{\text{Ra}} \left (\tau\left (u,\eta\left (x,T \right )\right ) : {\varepsilon(u)}\right ) w \text{ } dx + \text{SUPG Terms (if used)}`

The lhs and rhs above are consequently also dependent on the chosen time discretisation.

**src/hyteg/p2functionspace/P2FullViscousTDependentOperator.hpp, src/hyteg/p2functionspace/P2GradRhoRho_P2_Operator.hpp, src/hyteg/p2functionspace/P2ScaledMassDiffusionOperator.hpp, src/hyteg/p2functionspace/P2VariableBlendingKMassScalarToVectorOperator.hpp, src/hyteg/gridtransferoperators/P2toP1GradRhoRho_P2_Operator.hpp, src/hyteg/gridtransferoperators/P1toP2VariableBlendingKMassScalarToVectorOperator.hpp:** Various operators that conveniently combine the usage of multiple other operators (e.g. if we apply one on every component).

**src/elementwiseoperators:** Added all combinations of P1/P2 ElementwiseDoFValueOperator classes. These operators can be inherited from and provide a way (via the DoFValues_ vector) to access the DoFs of another FEM function during the evaluation of a form. This allows us for the creation of operators like an advection operator that takes a velocity field as an additional input.
Added a setConstantScaling function to all elementwise operators. This can be used to scale your operators by a constant on the fly (without having to create for example a linear combination form).
There are some bug fixes and the ability to use a custom form for P2ToP1 and P1ToP2 elementwise operators included.

**src/elementwiseoperators/generated:** Folder containing all of the generated ElementwiseDoFValueOperators. In particular it adds operators for adiabatic heating, advection, diffusion (only supg), temperature dep. stokes, the grad(rho)/rho * u compressible term in the mass conservation equation, div_k_grad scaled by rho^-1, mass(only supg), shear heat and respective SUPG Stabilisation terms.

**src/p1functionspace/VertexDoFFunction, src/edgedofspace/EdgeDoFFunction, src/functions/DoFValueFunctions:** Added a DoFValueFunction class that both VertexDoFFunction and EdgeDoFFunction inherit from. No previous functionality of VertexDoFFunction and EdgeDoFFunction was changed, I just implemented the additional functions defined in the DoFValueFunction base class. The defined functions are required for the DoFValueOperators to work.

**src/hyteg/composites/VelocityOperator_T_Wrapper, src/hyteg/solvers/SubstituteSolver.hpp:** Some convenient wrappers, allowing you to wrap a operator with a different VelocityOperator_T type and to use a solver for a different operator type (e.g. if you want to solve Laplace as a preconditioner, but the preconditioner is expected to be a solver for a different operator).

**src/petsc/PETScHDF5FunctionSave.hpp:** Functions that allow you to save functions and paramters via creating a PETSc Vector and saving it in parallel to a binary file via HDF5. Has some limitations since you can only reload your functions in the same configuration as you saved it.

**src/solvers/preconditioners/stokes:** Two preconditioner classes used for benchmarks and the convection model

**src/solvers/solvertemplates/StokesSolverTemplates.hpp:** Pulled over some changes to the StokesSolverTemplates solver used in the other Terraneo branches. No functionality is changed but you can now distinguish between absolute and relative tolerance.

**src/solvers/ChebyshevSmoother.hpp:** Added a subclass of the Chebyshev Smoother that contains a normal projection at an appropriate spot for the freeslip boundary conditions.

**src/solvers/GMRESSolver.hpp:** Serveral bug fixes and additional functions from Andreas Wagner to the GMRES solver which we found during our testing of the GMRES.

**src/solvers/MinResSolver.hpp:** Pulled over some changes to the MinRes solver used in the other Terraneo branches. No functionality is changed but you can now define an absolute tolerance.

**src/solvers/UzawaSmoother.hpp, /src/hyteg/composites/P2P1UzawaDampingFactorEstimationOperator.hpp:** Added functions for the estimation of the Uzawa Omega paramter also in case of the P2CompStokesOperator and added a subclass of the UzawaSmoother that contains a normal projection at an appropriate spot for the freeslip boundary conditions.

**src/hyteg/gridtransferoperators/P2P1StokesToP2P1StokesProlongation.hpp, src/hyteg/gridtransferoperators/P2P1StokesToP2P1StokesRestriction.hpp:** Restriction and Prolongation operator subclasses that contains a normal projection at an appropriate spot for the freeslip boundary conditions.

**data/meshes:** Just some additional meshes which are offset from the origin (are used for testing with the sphericalCoordinateMap blending map.

**src/forms:** Just some additional generated blending forms.

**src/geometry:** Added second derivative functions (needed for SUPG Stabilisiation) for all blending maps and a new spherical coordinate map.

**tests/hyteg/operators:** Added tests checking if the various DoFValueOperators are calculating the correct integrals and if the diagonal calculation for the temperature dependent stokes works.

Hopefully I haven't forgotten anything and these are all changes.