weakThermalLinGeomSolid

This page documents the weakly coupled thermal linear-geometry solid model. The runtime type is:

weakThermalLinearGeometry

The model assumes small strains and small rotations. It solves the energy equation for temperature T to convergence, then solves the momentum equation for total displacement D once, with no outer iterations between the two. This one-way coupling is what "weak" refers to.

The stress is computed by the run-time selectable mechanical law.

User Guide

What this model solves

weakThermalLinGeomSolid:

• solves the transient heat equation rhoC*ddt(T) == laplacian(k, T), with no mechanical work term;
• then hands over to linGeomTotalDispSolid for the momentum equation, from which it inherits;
• takes C and k from a thermalModel, configured in constant/thermalProperties.

Use this model when the temperature field drives the deformation but the deformation does not appreciably change the temperature field, which covers most thermoelastic problems. Use thermalLinGeomSolid if the coupling needs to be converged within each time step.

Supported solution algorithms

The heat equation is always solved with a segregated implicit loop. The momentum equation is solved by linGeomTotalDispSolid, so the solutionAlgorithm entry applies to it as usual: implicitSegregated (default), PETScSNES or explicit.

Model options

absoluteTemperatureTolerance is an absolute change in degrees: once the temperature stops moving by more than this between outer iterations, the thermal loop is considered converged.

All of the linGeomTotalDispSolid and base solidModel options apply as well; see that page for the full list. The entries most relevant to the thermal loop are:

The temperature loop always performs at least two iterations, and converges when the absolute change in T falls below absoluteTemperatureTolerance, or when the solver and relative residuals meet solutionTolerance or alternativeTolerance.

Required input files

• T and D in the time directory;
• constant/solidProperties;
• constant/thermalProperties, providing the thermal sub-dictionary;
• constant/mechanicalProperties;
• constant/g.

T is MUST_READ, so a case that omits it will fail at construction.

Example constant/thermalProperties:

thermal
{
    type            constant;
    C               C [0 2 -2 -1 0 0 0] 434;
    k               k [1 1 -3 -1 0 0 0] 250;
}

Recommended dictionary setup

Minimal example for constant/solidProperties:

solidModel        weakThermalLinearGeometry;

weakThermalLinearGeometryCoeffs
{
    solutionAlgorithm            implicitSegregated;

    nCorrectors                  10000;
    solutionTolerance            1e-06;
    alternativeTolerance         1e-07;
    materialTolerance            1e-05;
    absoluteTemperatureTolerance 1e-06;
    infoFrequency                100;
}

fvSchemes must provide laplacian(k,T) in addition to the entries linGeomTotalDispSolid needs, and fvSolution must provide solvers for T and D.

Boundary conditions

Displacement boundaries use the standard solids4foam patch types. Temperature boundaries use the usual OpenFOAM scalar patch types, plus thermalConvection for a convective heat-transfer boundary.

Unlike thermalLinGeomSolid and thermalSolid, this model does not implement the setTemperatureAndHeatFlux() interface, so it cannot be used as the solid side of a thermal fluid-solid interface.

Field glossary

• T: temperature; written each output time.
• grad(T): temperature gradient, used to report the heat flux.
• heatFlux: -k*grad(T), constructed and written by writeFields().
• rhoC: product of density and specific heat capacity.
• All the fields of linGeomTotalDispSolid: D, DD, pointD, pointDD, grad(D), grad(DD), U, sigma.

Each write also prints the maximum and minimum temperature and the maximum magnitude of the heat flux.

Developer Notes

Class role

weakThermalLinGeomSolid inherits from linGeomTotalDispSolid rather than from solidModel directly, and adds a thermalModel member. That inheritance is the whole design: the thermal part is a prefix to an otherwise unmodified mechanical solve.

• D remains the primary solution variable;
• nonLinGeom() returns LINEAR_GEOMETRY;
• the heat equation is uncoupled from the stress state, so there is no sigma && grad(U) term.

Construction

The constructor calls the linGeomTotalDispSolid constructor, constructs the thermalModel from the mesh, builds rhoC_ as thermal.C()*mechanical().rho() and k_ from thermal.k(), reads T (MUST_READ), creates grad(T), reads absoluteTemperatureTolerance, and forces creation of T.oldTime().

evolve()

1. Loop on the heat equation rhoC*ddt(T) == laplacian(k, T): store T, relax and solve, relax T, update grad(T); repeat until the private converged() overload is satisfied or nCorrectors is reached.
2. Call linGeomTotalDispSolid::evolve() to solve the momentum equation.

There is no outer loop around the two, which is the difference from thermalLinGeomSolid. evolve() always returns true.

writeFields()

Reports the temperature range, constructs and writes the heatFlux field, and then calls linGeomTotalDispSolid::writeFields().

Extension points

• evolve() if the heat equation needs source terms or a different coupling;
• the private converged() overload for a different thermal criterion.

Because the class derives from linGeomTotalDispSolid, any change to that model's momentum solve is inherited here automatically.

Tutorials

No tutorial selects weakThermalLinearGeometry by default. It is offered as a commented alternative in the thermoelasticity cases, which are the natural places to try it:

• solids/thermoelasticity/hotCylinder
• solids/thermoelasticity/hotSphere
• solids/thermoelasticity/slabCooling

Those cases run thermalLinearGeometry as shipped; switching the solidModel entry to weakThermalLinearGeometry is a one-line change.