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Reformulate hydrostatic model timestepping #4811
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    …ns.jl into ss/remove-matrix-solver
…/reformulate-hydrostatic-model-2
              
                    glwagner
  
              
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                    Sep 23, 2025 
                  
              
              
            
            
        
          
                src/Models/HydrostaticFreeSurfaceModels/HydrostaticFreeSurfaceModels.jl
              
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…/Oceananigans.jl into ss/reformulate-hydrostatic-model-2
…/Oceananigans.jl into ss/reformulate-hydrostatic-model-2
…/Oceananigans.jl into ss/reformulate-hydrostatic-model-2
…/Oceananigans.jl into ss/reformulate-hydrostatic-model-2
  
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      Labels
      
    benchmark performance
  runs preconfigured benchamarks and spits out timing 
  
    numerics 🧮
  So things don't blow up and boil the lobsters alive 
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This is a work-in-progress PR that aims to reformulate the timestepping scheme of the
HydrostaticFreeSurfaceModeltomake sure that three numerical properties are satisfied:
This is easier to achieve with an explicit discretization of the free surface (
ExplicitFreeSurfaceandSplitExplicitFreeSurface) rather than an implicit free surface discretization and with RK3 rather than AB2.However, this PR reformulates much of the timestepping algorithm, so it will be a lengthy WIP that will need to be thoroughly validated for all combinations of barotropic and baroclinic timestepping schemes.
More changes are performed to correctly abstract the timestepping schemes, which, at the moment, are tailored specifically to the
NonhydrostaticModel(for example, the timesteppers include acompute_pressure_correction!or acorrect_velocitiesfunction, which are meaningful only for a non-hydrostatic Navier Stokes solver)Edit: another objective I have is to remove any timestepping from the
update_state!function. We should be able to callupdate_state!multiple times in a row without problems and timestepping insideupdate_state!negates this possibility.TODO:
Remove timestepping fromIn another PRupdate_state!DistributedGridsImplement a semi - conservative method for AB2In another PRAddress precision errors that tend to destroy conservation for constant fieldsIn another PR