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Viscous terms from entropy gradients #1202

Merged
merged 19 commits into from
Sep 6, 2022
Merged

Viscous terms from entropy gradients #1202

merged 19 commits into from
Sep 6, 2022

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andrewwinters5000
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Computation of viscous fluxes in the compressible Navier-Stokes equations computed using the gradients of the entropy variables. New functions are marked with "TODO: parabolic; entropy stable viscous terms".

Currently, the default behavior is to use the entropy gradients for the viscous terms. So tests will not pass. For now it is setup this way for everyone to see how the new functionality works.

@andrewwinters5000 andrewwinters5000 marked this pull request as draft August 10, 2022 13:22
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codecov bot commented Aug 10, 2022

Codecov Report

Merging #1202 (0bf359e) into dev (a6db7a1) will increase coverage by 13.90%.
The diff coverage is 100.00%.

@@             Coverage Diff             @@
##              dev    #1202       +/-   ##
===========================================
+ Coverage   82.90%   96.81%   +13.90%     
===========================================
  Files         326      326               
  Lines       24996    25047       +51     
===========================================
+ Hits        20722    24247     +3525     
+ Misses       4274      800     -3474     
Flag Coverage Δ
unittests 96.81% <100.00%> (+13.90%) ⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files Coverage Δ
...les/dgmulti_2d/elixir_navier_stokes_convergence.jl 100.00% <ø> (ø)
.../tree_2d_dgsem/elixir_navier_stokes_convergence.jl 100.00% <ø> (ø)
src/Trixi.jl 70.00% <ø> (ø)
src/solvers/dgsem_tree/dg_2d_parabolic.jl 99.54% <ø> (ø)
src/equations/compressible_navier_stokes_2d.jl 98.99% <100.00%> (+10.10%) ⬆️
src/equations/shallow_water_2d.jl 99.38% <0.00%> (+0.31%) ⬆️
src/equations/acoustic_perturbation_2d.jl 100.00% <0.00%> (+0.78%) ⬆️
src/callbacks_step/summary.jl 94.55% <0.00%> (+0.91%) ⬆️
src/equations/ideal_glm_mhd_3d.jl 100.00% <0.00%> (+0.92%) ⬆️
src/solvers/dgsem/basis_lobatto_legendre.jl 88.89% <0.00%> (+1.01%) ⬆️
... and 56 more

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@andrewwinters5000
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I am suspicious that the entropy_timederivative analysis computation is working correctly for the hyperbolic + parabolic solver combo. The reason I say this is if I run the elixir from this PR elixir_navier_stokes_es.jl but change the solver to be

volume_flux = flux_ranocha
solver = DGSEM(polydeg=3, surface_flux=flux_ranocha,
               volume_integral=VolumeIntegralFluxDifferencing(volume_flux))

then the output at the final time (as well as during the time integration) says that the entropy time derivative is on the order of double precision roundoff, e.g., at the final time I get

 ∑∂S/∂U ⋅ Uₜ :   1.22496211e-16

This seems wrong because I set the Reynolds number to be 1600 in this elixir. So some dissipation should presumably be happening.

@jlchan
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jlchan commented Aug 10, 2022

Yeah, that sounds like the parabolic rhs is getting incorporated...

It looks like the entropy timederivative analyzer is called using

du_ode = first(get_tmp_cache(integrator))

I checked with a short example, and the SplitODE integrator cache seems like it is incorporating both RHS terms...

@ranocha
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ranocha commented Aug 11, 2022

It looks like the entropy timederivative analyzer is called using

du_ode = first(get_tmp_cache(integrator))

This is just to get some temporary vector to write the RHS to. In the next line, the RHS is computed using

@notimeit timer() rhs!(du_ode, integrator.u, semi, t)

I would have expected to get the full hyperbolic+parabolic RHS here...

@ranocha
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ranocha commented Aug 11, 2022

But I can reproduce the problem with

trixi_include("examples/tree_2d_dgsem/elixir_advection_diffusion.jl", surface_flux=flux_central)

on dev 😥

@ranocha
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ranocha commented Aug 11, 2022

Okay, understood. I will make a PR to fix this

This was referenced Aug 11, 2022
@ranocha
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ranocha commented Aug 11, 2022

Should be fixed once #1205 is merged into main and dev & this branch are updated.

@andrewwinters5000
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I checked with a short example, and the SplitODE integrator cache seems like it is incorporating both RHS terms...

Curiouser and curiouser...I will keep experimenting with the implementation. It could just be a bug on my end.

@ranocha
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ranocha commented Aug 11, 2022

I checked with a short example, and the SplitODE integrator cache seems like it is incorporating both RHS terms...

Curiouser and curiouser...I will keep experimenting with the implementation. It could just be a bug on my end.

No, it isn't - it will be fixed by #1205

@andrewwinters5000
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No, it isn't - it will be fixed by #1205

Sorry, I missed part of the conversation (forgot to refresh the github page). Thanks for the fix!

@jlchan
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jlchan commented Aug 16, 2022

I've added a draft of the GradientVariablesPrimitive and GradientVariablesEntropy type parameter in b876b9d. The implementation is taken from my paper https://doi.org/10.1016/j.jcp.2021.110723.

I'm hoping to test this before I leave.

@jlchan
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jlchan commented Aug 16, 2022

OK, I have the entropy variables with boundary conditions working now. To test, run with

trixi_include(joinpath(examples_dir(), "dgmulti_2d", "elixir_navier_stokes_convergence.jl"), gradient_variables=GradientVariablesEntropy())

or

trixi_include(joinpath(examples_dir(), "tree_2d_dgsem", "elixir_navier_stokes_convergence.jl"), gradient_variables=GradientVariablesEntropy())

I introduced some steps which can probably be made more efficient. These are marked with TODO.

@jlchan jlchan changed the title WIP: Viscous terms from entropy gradients Viscous terms from entropy gradients Aug 23, 2022
@jlchan jlchan marked this pull request as ready for review August 23, 2022 14:50
@jlchan jlchan requested a review from sloede August 23, 2022 15:05
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jlchan commented Aug 24, 2022

@sloede should be ready to review for merging into dev now

@ranocha ranocha self-requested a review September 6, 2022 14:04
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Thank you all! This looks mostly good to me. Do we have some docs for this functionality?

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@jlchan
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jlchan commented Sep 6, 2022

Thank you all! This looks mostly good to me. Do we have some docs for this functionality?

Only the docstrings - we don't yet have a can add a Literate.jl tutorial. I've added it as an item to #1147. Would you be OK if I were to make a separate PR for that?

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Sure, we can merge this PR as it is (when tests pass) . Thanks!

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jlchan commented Sep 6, 2022

Thanks!

@jlchan jlchan closed this Sep 6, 2022
@jlchan jlchan reopened this Sep 6, 2022
@jlchan jlchan merged commit 550d279 into dev Sep 6, 2022
@jlchan jlchan deleted the entropy-gradients branch September 6, 2022 21:43
ranocha added a commit that referenced this pull request Oct 11, 2022
* Parabolic terms for DGMulti (#1136)

* minor formatting

* adding multi-term semidiscretization

* fixing bug and adding test

* changing name

* changing name, importing SplitODEFunction

* fixing test by adding norm

* trying another test fix

* adding norm back

* adjusting tol

* try to fix test again

* syntax error

* removing norm frm test

* adding cache to parabolic terms (enable reuse of inviscid cache)

* generalize dgmulti iterators

* fix typo

* generalizing reset_du! for dgmulti

* WIP gradient and divergence computations

* fix name

* more generalization

* divergence + remove repeated code

* adding cache

* remove test

* update diffusion test

* update diffusion rhs

* moving routines around

* fix multiple includes

* removing time dependence for now from viscous rhs

* export ScalarDiffusion2D

* fix test

* working periodic advection RHS

* cleanup and comments

* making periodic advection-diffusion example

* trim whitespace

* adding t back in to parabolic rhs


add t back in

* refactoring boundary condition code

* update elixir with BCs

* change default DGMulti interface flux behavior

same as in #1139

* cleanup

* renaming variables

* BC prepping

* cleanup of elixir

* more name fixing

* Update src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* adding Neumann BCs

* switching to weak form


weak form


more weak form


weak form

* fixing cache variable names

* simplified parabolic boundary flux treatement

* updated elixir with different types of BCs

* Update src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update src/equations/equations.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* rhs! -> rhs_parabolic!

* move Gradient/Divergence types

* add "no boundary condition" BC

* rename ScalarDiffusion -> LaplaceDiffusion


r


r

* rhs -> rhs_parabolic! again

* comments

* moving tests around

* scalarDiffusion -> LaplaceDiffusion

* tuple-based constructor

* updating examples

* add ScalarPlotData2D docstring (#1145)

Co-authored-by: Jesse Chan <[email protected]>

* Apply suggestions from code review

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>

* renaming for consistency

parabolic_equations -> equations_parabolic
no_boundary_condition -> boundary_condition_do_nothing

* move Neumann BCs into equations.jl

* renaming, e.g., ParabolicEquations -> EquationsParabolic, etc

* rename test module

* generalize LaplaceDiffusion2D to any number of variables

* removing saveat times and standardizing `tol` names

* parabolic_cache -> cache_parabolic


cache

* renaming `create_cache` -> `create_cache_parabolic`

avoids conflicts when using dg::DGMultiFluxDiff

* Update examples/dgmulti_2d/elixir_advection_diffusion.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update src/equations/equations.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Update src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* parabolic_boundary_conditions -> boundary_conditions_parabolic

similarly for hyperbolic
d

* Update src/semidiscretization/semidiscretization_hyperbolic_parabolic.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* add equations as field to LaplaceDiffusion2D

* moving Neumann BCs into equations.jl and adding default BC behavior

* running parabolic tests, adding integration test

* adding parabolic tests to ci

* missing comma

* Update src/equations/laplace_diffusion_2d.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* fix test

* fix test typo

* fix tests (for real this time)

* improve test coverage

Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Additional work on parabolic terms  (#1148)

* make "do nothing BC" a struct, move it to basic_types

* add varnames for LaplaceDiffusion

* add forgotten @threaded

* update comment

* Revert "add forgotten @threaded"

This reverts commit 1564501.

* add @threaded (without enumerate)

* remove periodic advection diffusion elixir (redundant)

* adding test

* one more test

* Update src/basic_types.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>

* Reorganization of boundary conditions (#1152)

* moving "default" boundary conditions back into equations file

* add periodic advection_diffusion back in

* updating test

* update test

* Apply suggestions from code review

Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>

* Adding parabolic solver option (#1153)

* adding parabolic solver types

* incorporating parabolic solver types into dg_parabolic penalties

* specializing parabolic solver options in LaplaceDiffusion2D

* moving things around to fix CI

* dropped arg in test

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* renaming files and ViscousFlux solvers


renaming files


rename


rename

* Added TODO note for penalty term

* ViscousFlux___ -> ViscousFormulation___

* move function def around

Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>

* rearrange include order

* Add support for hyperbolic-parabolic systems to TreeMesh2D (#1156)

* Add prototype for advection-diffusion elixir for TreeMesh2D

* Initial implementation of `calc_gradient!` for TreeMesh{2}

* First complete implementation of the parabolic rhs operator for TreeMesh

* Make it work

* Add first elixir that works

* Clean up elixir

* first draft of container for Navier-Stokes constants and fluxes

* remove unneeded temperature computation

* draft of elixir with possible boundary condition structure

* added manufactured solution and source term

* fix typo in function name for MMS

* update variable names for consistency. improve comments

* fix dumb typos in new equation system name

* actually export new equations

* add comment near variable_mapping declaration.

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* parabolic equations now exported separately

* change name to CompressibleNavierStokesEquations2D

* export NS with proper name

* explicitly require compressible Euler in the type parameter

* name kinematic viscosity nu for consistency with Lattice-Boltzmann

* add promotion in constructor

* make Reynolds, Prandtl, Mach, and kappa keyword arguments

* update constructor call in elixir

* reduce computation by exploiting stress tensor symmetry

* fix unpacking of flux

* modifying parabolic cache creation

in cache, we assume we take the gradient of all hyperbolic variables. since the number of parabolic variables can differ from the number of hyperbolic variables, we pass in the hyperbolic equations to `create_cache_parabolic` now

* comments

* comments

* formatting and renaming equations to equations_hyperbolic


formatting comments

* fix unpacking of gradients in flux

* adding CNS BCs

* adding lid-driven cavity elixir

* adding variable transform, editing cons2prim for CNS

* add prim2cons for NS (inconsistent right now)

* add draft of DGMulti Navier Stokes convergence elixir

* converging solution using elixir for TreeMesh with BCs

* fixing DGMulti advection diffusion elixir convergence

* naming equations as parabolic/hyperbolic

* generalizing transform_variables

* add TODO


more todos

* additional checks on get_unsigned_normal

* adding isothermal BC

* commenting out unused CNS functions for now

* fix call to transform_variables

* comments and cleanup

* changing default solver and Re for cavity

* adding more advection diffusion tests

* label tests

* add gradient_variables field to SemidiscretizationHyperbolicParabolic

* Revert "add gradient_variables field to SemidiscretizationHyperbolicParabolic"

This reverts commit 063b602.

* allowing for specialization in transform_variables

adding a function `gradient_variable_transformation` which should get specialized if the gradient variables are not conservative variables

* formatting and comments

* reverting elixir

* comments

* standardizing time tol

* minor fix to CNS boundary flux for convenience

make it so that the density state is computed correctly, even though it's not used

* formatting + comments

* using primitive variables in viscous flux instead of conservative

* minor formatting

* add CNS tests

* fix test

* testing if scoping issues fix TreeMesh tests

* decreasing timestep tol for TreeMesh parabolic test

* enabling periodic BCs for TreeMesh + more tests

* fix density BC flux (unused, but could be useful)

* adding non-working TreeMesh elixirs

* adding AD checks

* standardizing parameters in convergence elixirs

* minor cleanup

* revert DGMulti CNS elixir setup back to the one used in tests

* adding TreeMesh CNS convergence test

* removing redundant elixir

* add more tests

* add more test

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* set version to v0.4.43

* set development version to v0.4.44-pre

* add YouTube links to JuliaCon presentations (#1192)

* add YouTube links to JuliaCon presentations

* Apply suggestions from code review

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* improved readability of equation docstrings in compressible Euler files

* Navier-Stokes in 2D on DGMulti and TreeMesh (#1165)

* first draft of container for Navier-Stokes constants and fluxes

* remove unneeded temperature computation

* draft of elixir with possible boundary condition structure

* added manufactured solution and source term

* fix typo in function name for MMS

* update variable names for consistency. improve comments

* fix dumb typos in new equation system name

* actually export new equations

* add comment near variable_mapping declaration.

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* parabolic equations now exported separately

* change name to CompressibleNavierStokesEquations2D

* export NS with proper name

* explicitly require compressible Euler in the type parameter

* name kinematic viscosity nu for consistency with Lattice-Boltzmann

* add promotion in constructor

* make Reynolds, Prandtl, Mach, and kappa keyword arguments

* update constructor call in elixir

* reduce computation by exploiting stress tensor symmetry

* fix unpacking of flux

* modifying parabolic cache creation

in cache, we assume we take the gradient of all hyperbolic variables. since the number of parabolic variables can differ from the number of hyperbolic variables, we pass in the hyperbolic equations to `create_cache_parabolic` now

* comments

* comments

* formatting and renaming equations to equations_hyperbolic


formatting comments

* fix unpacking of gradients in flux

* adding CNS BCs

* adding lid-driven cavity elixir

* adding variable transform, editing cons2prim for CNS

* add prim2cons for NS (inconsistent right now)

* add draft of DGMulti Navier Stokes convergence elixir

* converging solution using elixir for TreeMesh with BCs

* fixing DGMulti advection diffusion elixir convergence

* naming equations as parabolic/hyperbolic

* generalizing transform_variables

* add TODO


more todos

* additional checks on get_unsigned_normal

* adding isothermal BC

* commenting out unused CNS functions for now

* fix call to transform_variables

* comments and cleanup

* changing default solver and Re for cavity

* adding more advection diffusion tests

* label tests

* add gradient_variables field to SemidiscretizationHyperbolicParabolic

* Revert "add gradient_variables field to SemidiscretizationHyperbolicParabolic"

This reverts commit 063b602.

* allowing for specialization in transform_variables

adding a function `gradient_variable_transformation` which should get specialized if the gradient variables are not conservative variables

* formatting and comments

* reverting elixir

* comments

* standardizing time tol

* minor fix to CNS boundary flux for convenience

make it so that the density state is computed correctly, even though it's not used

* formatting + comments

* using primitive variables in viscous flux instead of conservative

* minor formatting

* add CNS tests

* fix test

* testing if scoping issues fix TreeMesh tests

* decreasing timestep tol for TreeMesh parabolic test

* enabling periodic BCs for TreeMesh + more tests

* fix density BC flux (unused, but could be useful)

* adding non-working TreeMesh elixirs

* adding AD checks

* standardizing parameters in convergence elixirs

* minor cleanup

* revert DGMulti CNS elixir setup back to the one used in tests

* adding TreeMesh CNS convergence test

* removing redundant elixir

* add more tests

* add more test

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* add docstrings

Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>

* add docstring for CNS equations

* removing some addressed TODOs

* adjust definition of the kappa constant

* avoid overwriting u_grad with viscous_flux results

* remove old TODOs

* clarify TODOs for later

* removing let statements

* rearrange main docstring. Fix typos in math environment causing it to not parse

* update TODO notes

* Apply suggestions from code review

Co-authored-by: Andrew Winters <[email protected]>

* update TODO notes

* Apply suggestions from code review

Co-authored-by: Andrew Winters <[email protected]>

* update TODO notes

* changing diffusivity names

Auto stash before merge of "parabolic-treemesh" and "origin/parabolic-treemesh"

* Reynolds/Prandtl number name changes for consistency

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Michael Schlottke-Lakemper <[email protected]>
Co-authored-by: Andrew Winters <[email protected]>

* fixing bug introduced by GH code review

* moving manufactured solution into the CNS equations file

* fix allocation issue

* get_diffusivity -> diffusivity

* removing cruft code, adding comment on messy prim2cons routine

* moving manufactured solution back into elixirs

* Update examples/dgmulti_2d/elixir_advection_diffusion_nonperiodic.jl

* TODO -> Todo, and .6 -> 0.6


d

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* adding note to Adiabatic/Isothermal BCs

* replacing CompressibleNavierStokesEquations with ...Diffusion

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* documenting Jacobian sign flip

* remove extra arg to `gradient_variable_transformation`

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* change warning to error

* fix bug introduced by search/replace

* dg_parabolic -> parabolic_scheme

* BoundaryConditionViscousWall -> BoundaryConditionNavierStokesWall

* u_grad -> gradients

* fix test

* renaming

* update comment

* converting to signature `flux(u, gradients, orientation, equations)`

* using prolong2interfaces/boundaries

* unpacking `gradients` and `flux_viscous`

* using calc_surface_integral!

* adding @muladd

* Apply suggestions from code review

* update comments

* Rename grad_u -> gradients

* Update src/equations/compressible_navier_stokes_2d.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* Rename remaining grad_u/u_grad -> gradients

* Refactor into prolong2interfaces!

* Refactor calc_volume_integral!

* Refactor calc_interface_flux

* Refactor prolong2boundaries!

* Refactor calc_divergence!

* Formatting consistency

* Remove dispatch on volume integral type

* Add comment on why surface_integral is passed to prolong2interfaces!

* Explicitly use weak form volume integral to allow easy overriding in test

* Add flux differencing test for CNS test

* Remove erroneous P4estMesh{2} dispatch

* Remove non-cons terms from parabolic solver

Co-authored-by: Andrew Winters <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>

* Add commentary on reuse of interfaces/boundaries data structures (#1199)

* Add comments on storing flux values in `u`

* Rearrange function names for consistency

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Hendrik Ranocha <[email protected]>

* Update src/solvers/dgsem_tree/dg_2d_parabolic.jl

Co-authored-by: Andrew Winters <[email protected]>

Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Andrew Winters <[email protected]>

* Adding parabolic term description to NEWS.md (#1207)

* Add Literate docs for advection-diffusion (#1208)

* adding literate docs for advection-diffusion

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* rename "adding parabolic terms" -> "parabolic terms"

Co-authored-by: Hendrik Ranocha <[email protected]>

* Adding a tutorial on adding new parabolic terms (#1209)

* Viscous terms from entropy gradients (#1202)

* first draft of entropy stable gradients

* update TODOs

* added elixir with discontinuous solution for ES testing

* forgot one TODO marker

* adding GradientVariables**** type parameter

* fix bug (missing type param in constructor)

* add elixir with periodic CNS manufactured solution

* fix gradient conversion

* fix entropy variables w/BCs

* updating elixirs with `gradient_variables=GradientVariablesPrimitive()`

* Update src/equations/compressible_navier_stokes_2d.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* removing unused routines

* removing specialized entropy2cons and cons2entropy routines

* adding more tests

* removing unused elixirs

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>

* adding docs/warning for gradient variable type

* extracting w_inner[4] into a more clearly named variable

Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Michael Schlottke-Lakemper <[email protected]>
Co-authored-by: Jesse Chan <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>

* adding some minor documentation (#1214)

* fix parabolic PID (#1224)

* fix parabolic PID

* activate analysis_callback in Navier-Stokes convergence test

* fix typo

* Rescale compressible Navier-Stokes (#1230)

* remove the nondimensionalization and update the docstring for CNS

* update TreeMesh elixirs and test values

* update the elixirs and test values for DGMulti

* fix unbalanced parentheses

* file renaming for consistency

* update file names in the parabolic test script

* remove the gas constant as a parameter and update comments

* rename viscosity to dynamic_viscosity

* add comment about units in the docstring

* Update src/equations/compressible_navier_stokes_2d.jl

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* unify notation to call the viscosity mu

* fix undefined variable

Co-authored-by: Michael Schlottke-Lakemper <[email protected]>

* improve type stability of semidiscretize for parabolic semi (#1231)

* Apply suggestions from code review

Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Michael Schlottke-Lakemper <[email protected]>
Co-authored-by: Hendrik Ranocha <[email protected]>
Co-authored-by: Andrew Winters <[email protected]>
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4 participants