Vector Invariant Formulation of the `ShallowWaterModel` #2522

simone-silvestri · 2022-05-05T14:23:56Z

As for now the ShallowWaterModel is implemented in a conservative form.

${\partial_t(uh)+\partial_x(hu^2+\frac{1}{2}gh^2)+\partial_y(huv)-fvh=0}$

${\partial_t(vh)+\partial_x(huv)+\partial_y(hv^2+\frac{1}{2}gh^2)+fuh=0}$

${\partial_th+\partial_x(hu)+\partial_y(hv)=0}$

This PR attempts to introduce a non-conservative form of the equation with a vector invariant formulation of advection

${\partial_tu-(\zeta+f)v+\partial_x(gh+k)=0}$

${\partial_tv+(\zeta+f)u+\partial_y(gh+k)=0}$

${\partial_th+\partial_x(hu)+\partial_y(hv)=0}$

such that we can treat the advection with high order WENO reconstruction.
We should also think about introducing bathymetric terms ( ${gh\partial_x h_B}$ and ${gh\partial_y h_B}$ ) and viscous term (#2403)

with @francispoulin

francispoulin · 2022-05-05T14:28:55Z

Wonderful to see @simone-silvestri ! Please let me know how I can help.

One question, could we change the name of this PR to Vector Invariant Formuation of ShallowWaterModel? It seems like a good quality to highlight.

Also, as a test problem, could we use the same initial conditions as we have in the Bickley Jet example? Might make for a good comparison.

simone-silvestri · 2022-05-05T14:30:41Z

sounds like a good idea!

glwagner · 2022-05-05T15:38:42Z

You probably also want to fix #1866

I think what makes the most sense is to store velocities (AbstractOperations) inside the ShallowWaterModel so

velocities = (u = uh / h, v = vh / h)

(these have the correct location as well, which can be checked)

then use velocities.u to advect the total transport solution.uh in the advection operator.

francispoulin

Looks great so far!

src/Models/ShallowWaterModels/shallow_water_advection_operators.jl

glwagner · 2022-05-05T18:22:59Z

Perhaps

if formulation isa ConservativeFormulation
        solution = (uh = XFaceField(grid),
                    vh = YFaceField(grid),
                     h = CenterField(grid))
     else
        solution = (u = XFaceField(grid),
                    v = YFaceField(grid),
                    h = CenterField(grid))
    end

simone-silvestri · 2022-05-05T19:58:55Z

@francispoulin I have implemented the vector invariant / non conservative form of the equations. I have also separated the advection between momentum / velocity, height and tracers.

Now we have to think at some nice test cases, I ll start with the bickley jet experiment

francispoulin · 2022-05-05T20:32:01Z

That is great news @simone-silvestri, and very fast!

Yes, I think the Bickley jet is a good place to start. I'll think of others that would be fun.

When we put in closure we could do a gyre with a Munk layer. For now, we could do bottom drag and get a Stommel layer. I can look for a reference to compare this too if you like the idea?

…iMA/Oceananigans.jl into ss-fjp/non-conservative-shallow-water

glwagner · 2022-05-05T21:24:13Z

src/Models/ShallowWaterModels/calculate_shallow_water_tendencies.jl

@@ -32,6 +32,8 @@ function calculate_tendencies!(model::ShallowWaterModel)
                                               model.grid,
                                               model.gravitational_acceleration,
                                               model.advection,
+                                               model.tracer_advection,
+                                               model.height_advection,


It might be better to use advection.tracers and advection.mass, so that we don't have to refactor this model too when we change the advection scheme implementations for nonhydrostatic and hydrostatic models in #2454

its ok if you don't want to, just trying to be lazy

francispoulin · 2022-05-05T21:30:57Z

examples/shallow_water_Bickley_jet.jl

@@ -115,7 +125,7 @@ compute!(ω)

 # and finally set the "true" initial condition with noise,

-set!(model, uh = uhⁱ)
+formulation isa VectorInvariantFormulation ? set!(model, u = uhⁱ) : set!(model, uh = uhⁱ)


In the case of vector invariant, should we set u = u^i and not the mass flux?

francispoulin · 2022-05-05T21:32:29Z

src/Models/ShallowWaterModels/calculate_shallow_water_tendencies.jl

@@ -77,19 +83,19 @@ function calculate_interior_tendency_contributions!(tendencies,

    barrier = Event(device(arch))

-    Guh_event = calculate_Guh_kernel!(tendencies.uh,
+    Guh_event = calculate_Guh_kernel!(tendencies[1],


Given that the only difference between the next 3 steps is the index, would it be more compact to put these in a for loop over 1,2,3?

I like it written out personally!

I am happy either way. Just a thought.

francispoulin · 2022-05-05T21:33:25Z

src/Models/ShallowWaterModels/rk3_substep_shallow_water_model.jl

-        U.uh[i, j, k] += Δt * (γⁿ * Gⁿ.uh[i, j, k] + ζⁿ * G⁻.uh[i, j, k])
-        U.vh[i, j, k] += Δt * (γⁿ * Gⁿ.vh[i, j, k] + ζⁿ * G⁻.vh[i, j, k])
-        U.h[i, j, k]  += Δt * (γⁿ * Gⁿ.h[i, j, k]  + ζⁿ * G⁻.h[i, j, k])
+        U[1][i, j, k] += Δt * (γⁿ * Gⁿ[1][i, j, k] + ζⁿ * G⁻[1][i, j, k])


Could loop over these three too, right?

francispoulin · 2022-05-05T21:33:37Z

src/Models/ShallowWaterModels/rk3_substep_shallow_water_model.jl

-        U.uh[i, j, k] += Δt * γ¹ * G¹.uh[i, j, k]
-        U.vh[i, j, k] += Δt * γ¹ * G¹.vh[i, j, k]
-        U.h[i, j, k]  += Δt * γ¹ * G¹.h[i, j, k]
+        U[1][i, j, k] += Δt * γ¹ * G¹[1][i, j, k]


I like it written out.

The main thing to fix here are the errors in units in advection terms etc

francispoulin

Look great! This will be very easy to use and build on to add topography and closure schemes.

francispoulin · 2022-06-01T22:37:24Z

Should we merge this PR if all tests pass? Is there any other outstanding issues?

Regarding bathymetry properly included in ConservativeFormulation(), if there is more work needed there perhaps it belongs to a different PR (given the title of this PR)?

I agree that we should not wait to get bathymetry working with ConservativeFormulation().

@simone-silvestri and I were playing with a realistic global ocean model using the VectorInvariantForm and had some success. There were some issues when we included realistic topography, but I don't think that should hold us back. That is a hard problem and will take more time. This is a great addition and should allow for some very interesting simulations!

And we have 208 comments. That must be a record?

navidcy · 2022-06-01T23:16:58Z

OK, when test pass let's merge. And let's open an issue or PR for proper treatment of bathymetry in conservative formulation.

navidcy · 2022-06-01T23:21:04Z

Should we export

Oceananigans.jl/src/Models/ShallowWaterModels/shallow_water_model.jl

Lines 54 to 56 in d7588de

    
           struct ConservativeFormulation end 
        
           struct VectorInvariantFormulation end

?

francispoulin · 2022-06-01T23:26:52Z

Should we export

Oceananigans.jl/src/Models/ShallowWaterModels/shallow_water_model.jl

Lines 54 to 56 in d7588de

struct ConservativeFormulation end

struct VectorInvariantFormulation end

?

If we don't export it then the user needs to import them manually?

I am fine either way but have a slight preference for exporting it, so it makes things a little easier for the user.

navidcy · 2022-06-01T23:36:15Z

I agree. So I pushed 8eaf216. If there are opposing opinions we can undo this.

With this export we can do:

julia> ShallowWaterModel(; gravitational_acceleration=1, grid, formulation=VectorInvariantFormulation(), momentum_advection = VectorInvariant())

instead of

julia> ShallowWaterModel(; gravitational_acceleration=1, grid, formulation=Oceananigans.Models.ShallowWaterModels.VectorInvariantFormulation(), momentum_advection = VectorInvariant())

navidcy · 2022-06-02T07:47:26Z

is there anything wrong with the regression?

src/Models/ShallowWaterModels/shallow_water_model.jl

Co-authored-by: Gregory L. Wagner <wagner.greg@gmail.com>

simone-silvestri · 2022-06-02T22:30:18Z

I am not sure why it's not passing. I ll fix it, when it passes we can merge!

…iMA/Oceananigans.jl into ss-fjp/non-conservative-shallow-water

test/regression_tests/shallow_water_bickley_jet_regression.jl

navidcy · 2022-06-03T03:53:56Z

omg, there is only one test pending...

smells like merging is close by...

visualize.jl

glwagner · 2022-06-03T16:15:50Z

Vorticity in ShallowWaterModel:

near_global_lat_lon_1440_600__fine_surface.6.mp4

and a single-layer HydrostaticFreeSurfaceModel:

near_global_lat_lon_1440_600_1_fine_surface.2.mp4

both with flat bathymetry. The free surface model is using the implicit free surface solver with a long time-step. Note the difference in the color scale.

(via @simone-silvestri and @francispoulin)

simone-silvestri · 2022-06-03T16:35:20Z

The hydrostatic simulation was done by @francispoulin

simone-silvestri · 2022-06-03T18:25:15Z

I 'll merge when the last test passes

navidcy · 2022-06-03T23:08:34Z

Omg

first commit

f56fa20

simone-silvestri changed the title ~~[WIP] Non conservative form of the ShallowWaterModel~~ [WIP] Vector Invariant Formulation of the ShallowWaterModel May 5, 2022

simone-silvestri added the numerics 🧮 So things don't blow up and boil the lobsters alive label May 5, 2022

simone-silvestri added 2 commits May 5, 2022 12:47

added new formulation

a0889a7

added vector invariant advectino

28b5ed5

francispoulin reviewed May 5, 2022

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src/Models/ShallowWaterModels/shallow_water_advection_operators.jl Outdated Show resolved Hide resolved

src/Models/ShallowWaterModels/shallow_water_advection_operators.jl Outdated Show resolved Hide resolved

glwagner mentioned this pull request May 5, 2022

Re-implementing the HydrostaticFreeSurfaceModel with Generalized Vertical Coordinates (GVC) #1679

Open

simone-silvestri added 3 commits May 5, 2022 15:43

added tracer and height advection

bc1ee2e

should be finished?

6edc14a

reverteed manifest

0bed1fb

simone-silvestri added 2 commits May 5, 2022 16:20

compiles...

8f9f8a3

we HAVE to move to Julia 1.7...

1e4598b

simone-silvestri added 4 commits May 5, 2022 16:32

leaving bugs here and there...

3ed4fc2

Merge branch 'ss-fjp/non-conservative-shallow-water' of github.com:Cl…

144b74c

…iMA/Oceananigans.jl into ss-fjp/non-conservative-shallow-water

bugs..

9ee87b5

more bugs fixing

eb84dee

glwagner reviewed May 5, 2022

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francispoulin reviewed May 5, 2022

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francispoulin approved these changes May 5, 2022

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simone-silvestri added 2 commits May 5, 2022 17:43

more bug fixes

1504f32

more bug fixes

6f824e8

navidcy added 2 commits June 2, 2022 09:02

fix admonition

9558e03

better momentum_advection validation message

d904274

new line in error message

d7588de

export shallow water model formulations

8eaf216

change warning title

4e51229

glwagner reviewed Jun 2, 2022

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src/Models/ShallowWaterModels/shallow_water_model.jl Outdated Show resolved Hide resolved

better phrasing

48e8e21

Co-authored-by: Gregory L. Wagner <wagner.greg@gmail.com>

simone-silvestri added 4 commits June 2, 2022 19:11

fixed regression?

b073184

Merge branch 'ss-fjp/non-conservative-shallow-water' of github.com:Cl…

772b54c

…iMA/Oceananigans.jl into ss-fjp/non-conservative-shallow-water

fixed regression?

ac4a3ca

test passed

c81ae07

navidcy reviewed Jun 3, 2022

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test/regression_tests/shallow_water_bickley_jet_regression.jl Outdated Show resolved Hide resolved

new initial condition

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navidcy reviewed Jun 3, 2022

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navidcy and others added 2 commits June 3, 2022 21:12

Delete visualize.jl

616ec7c

Merge branch 'main' into ss-fjp/non-conservative-shallow-water

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simone-silvestri merged commit 9ebe5d6 into main Jun 3, 2022

simone-silvestri deleted the ss-fjp/non-conservative-shallow-water branch June 3, 2022 19:14

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Vector Invariant Formulation of the `ShallowWaterModel` #2522

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Vector Invariant Formulation of the ShallowWaterModel #2522

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