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@xtalax xtalax commented Jul 20, 2022

fixes #102
fixes #136
fixes #143
fixes #141

TODO:

  • Implement Basic Scheme.
  • Handle Boundaries:
    • Handle periodic
    • Extrapolate with high order scheme to ensure equation balance/validity.
  • Extend interface to provide WENO as an option for 1st order derivatives.
  • Test.
  • Document.

Any comments on possible Interface designs or boundary handling welcome.

Stretch:

  • Generate WENO stencils with fornberg.
  • Directly calculate WENO parameter Formulae (for betas).
  • Extend to nonuniform case.
  • Extend to arbitrary derivative order.

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codecov bot commented Jul 22, 2022

Codecov Report

Merging #138 (97dadce) into master (cc34081) will increase coverage by 0.84%.
The diff coverage is 93.92%.

@@            Coverage Diff             @@
##           master     #138      +/-   ##
==========================================
+ Coverage   88.56%   89.41%   +0.84%     
==========================================
  Files          23       25       +2     
  Lines        1067     1228     +161     
==========================================
+ Hits          945     1098     +153     
- Misses        122      130       +8     
Impacted Files Coverage Δ
src/interface/MOLFiniteDifference.jl 88.88% <ø> (ø)
src/MOL_discretization.jl 82.11% <69.23%> (-2.24%) ⬇️
src/MOL_utils.jl 82.85% <75.00%> (+4.75%) ⬆️
...discretization/generate_finite_difference_rules.jl 90.90% <83.33%> (-9.10%) ⬇️
src/discretization/schemes/WENO/WENO.jl 92.85% <92.85%> (ø)
src/discretization/generate_bc_eqs.jl 81.60% <96.77%> (+0.74%) ⬆️
src/discretization/differential_discretizer.jl 100.00% <100.00%> (ø)
src/discretization/discretize_vars.jl 86.41% <100.00%> (ø)
...hemes/centered_difference/centered_diff_weights.jl 100.00% <100.00%> (ø)
...rc/discretization/schemes/extrapolation_weights.jl 100.00% <100.00%> (ø)
... and 6 more

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@xtalax
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xtalax commented Aug 5, 2022

@ChrisRackauckas Can you review?

Corners are still 0, I will extrapolate them in a seperate PR

@xtalax xtalax changed the title [ WIP ] Implement WENO Scheme [ Awaiting Review ] Implement WENO Scheme Aug 5, 2022
"""
`generate_extrap_eqs`
Pads the boundaries with extrapolation equations, extrapolated with 6th order lagrangian polynomials.
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Why 6th?

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To maintain 5th order accuracy for weno, it is used in the spec.

Comment on lines -94 to +147
@testset "Test 01: Burger's Equation 2D" begin
@parameters x y t
@variables u(..) v(..)
Dt = Differential(t)
Dx = Differential(x)
Dy = Differential(y)
Dxx = Differential(x)^2
Dyy = Differential(y)^2
# @testset "Test 01: Burger's Equation 2D" begin
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?

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This has never passed, I'm not sure its even correct.

@xtalax xtalax requested a review from ChrisRackauckas August 8, 2022 15:39
@ChrisRackauckas ChrisRackauckas merged commit 0c6474c into SciML:master Aug 8, 2022
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