Implicit solver enhancements

[juliasloan25]

Purpose

In milestone O2.3.6, we have implemented implicit solvers for RichardsModel, EnergyHydrologyModel, and SoilCanopyModel. As we developed these, we identified some areas for improvement that we want to address at some point, as well as ideas for improved stability that may or may not be necessary. These are documented here.

Cost/benefits/risks

costs: developer time
benefits: increased simulation stability, decreased code duplication, more robust code
risks: potential regressions if we alter equations

Producers

@juliasloan25 @kmdeck

Components

• more accurate jacobian approximations for increased simulation stability
• code cleanup

Inputs

Implicit solvers introduced in #135

Results and deliverables

Maintain or improve stability of implicitly-stepped experiments

Reviewers

@juliasloan25 @kmdeck @dennisYatunin (PRs)
@tapios @cmbengue (SDI review)

Tasks

general implicit stepping

Beta Give feedback

1. Reduce code duplication in jacobian functions #659
   enhancement +1
2. Generalize variable names in Jacobian initialization #661
   enhancement +1

SoilCanopyModel

Beta Give feedback

1. improve canopy temp jacobian #782
   enhancement +1

EnergyHydrologyModel

Beta Give feedback

1. Update ozark conservation test for IMEX stepping #662
   enhancement +1
2. include boundary condition contributions (if needed)
3. include contribution from drhoe_int / dtheta_l (if needed)
4. understand how to treat soil phase change implicitly

RichardsModel

Beta Give feedback

1. smooth derivative dPsi/dtheta at theta = \nu (if needed)

[tapios]

This looks good and thorough to me (though I say that without being familiar with all items here).