Make the deep hot Jupiter case stable

[dennissergeev]

• Reformulate forcing in theta instead of temperature and/or in terms of height instead of pressure - yes! See Tom's branch.
• Reduce reference_reset_time - seems to help
• Try capping dtheta - doesn't work
• Scale dtheta by a factor - works with 0.01 for example (but the resulting circulation is not quite right)
• Scale dtheta by a factor and increment it gradually - doesn't work
• Try filtering using the cartesian wind components - makes the model stable but the jet is retrograde. Trying with a scaling factor, doesn't really help
• Try Rayleigh damping - nope
• Divergence damping Add divergence damping #10
• Temperature diffusion Add temperature diffusion option #8 (needs extended mesh to avoid grid imprinting!)
• Try higher mesh resolutions Doesn't seem to help
• Try different vertical resolutions ditto
• Try stretched mesh ditto
• Try implicit timestepping (Backward Euler) for the temperature increment
• Try making sure we are consistent with our assumptions about which of density or exner is kept constant, which would mean either: (a) assuming that density is constant, so that we include the d(exner)/dt term in calculating the increment to theta, or (b) assuming that exner is constant, so that we then increment density
• Try extending SHJ to lower/higher pressures and stronger day-night gradient

Related: #28

LFRic-Apps ticket: https://code.metoffice.gov.uk/trac/lfric_apps/ticket/690

[dennissergeev]

The latest changes to dynamics might help 🤞
https://code.metoffice.gov.uk/trac/lfric_apps/ticket/28

(@stephenpcook you can test the DHJ setup using Tom's branch in that ticket, or wait till vn1.2 is released...)