Merge #127

127: Move ARS docs to new types, delete old imp r=charleskawczynski a=charleskawczynski

This PR:
 - Deletes the old ARS implementation
 - Moves the documentation of the tableaus to the new types
 - Adds the doc links for these types to the docs

Co-authored-by: Charles Kawczynski <kawczynski.charles@gmail.com>

docs/src/algorithms.md

@@ -88,7 +88,12 @@ ARK548L2SA2KennedyCarpenter
 
 ### ARS
 
-TODO: add `ARS111`, `ARS121`, and `ARS343` docs.
+```@docs
+ARS111
+ARS121
+ARS232
+ARS343
+```
 
 ## Multirate
 

src/ClimaTimeSteppers.jl

@@ -99,7 +99,6 @@ include("solvers/multirate.jl")
 include("solvers/lsrk.jl")
 include("solvers/ssprk.jl")
 include("solvers/ark.jl")
-# include("solvers/ars.jl") # previous implementations of ARS schemes
 include("solvers/mis.jl")
 include("solvers/wickerskamarock.jl")
 include("solvers/rosenbrock.jl")

src/solvers/imex_ark_tableaus.jl

@@ -1,5 +1,5 @@
 export AbstractIMEXARKTableau
-export ARS111, ARS121, ARS122, ARS233, ARS232, ARS222, ARS443
+export ARS111, ARS121, ARS122, ARS233, ARS232, ARS222, ARS343, ARS443
 export IMKG232a, IMKG232b, IMKG242a, IMKG242b, IMKG252a, IMKG252b
 export IMKG253a, IMKG253b, IMKG254a, IMKG254b, IMKG254c, IMKG342a, IMKG343a
 export DBM453, HOMMEM1
@@ -48,13 +48,31 @@ end
 # the number of explicit stages, and p is the order of accuracy
 
 # This algorithm is equivalent to OrdinaryDiffEq.IMEXEuler.
+
+"""
+    ARS111
+
+The Forward-Backward (1,1,1) implicit-explicit (IMEX) Runge-Kutta scheme of
+[ARS1997](@cite), section 2.1.
+
+This is equivalent to the `OrdinaryDiffEq.IMEXEuler` algorithm.
+"""
 struct ARS111 <: AbstractIMEXARKTableau end
 
 function tableau(::ARS111)
     IMEXARKTableau(; a_exp = @SArray([0 0; 1 0]), a_imp = @SArray([0 0; 0 1]))
 end
 
+"""
+    ARS121
+
+The Forward-Backward (1,2,1) implicit-explicit (IMEX) Runge-Kutta scheme of
+[ARS1997](@cite), section 2.2.
+
+This is equivalent to the `OrdinaryDiffEq.IMEXEulerARK` algorithm.
+"""
 struct ARS121 <: AbstractIMEXARKTableau end
+
 function tableau(::ARS121)
     IMEXARKTableau(; a_exp = @SArray([0 0; 1 0]), b_exp = @SArray([0, 1]), a_imp = @SArray([0 0; 0 1]))
 end
@@ -88,6 +106,12 @@ function tableau(::ARS233)
     )
 end
 
+"""
+    ARS232
+
+The Forward-Backward (2,3,2) implicit-explicit (IMEX) Runge-Kutta scheme of
+[ARS1997](@cite), section 2.5.
+"""
 struct ARS232 <: AbstractIMEXARKTableau end
 function tableau(::ARS232)
     γ = 1 - √2 / 2
@@ -122,6 +146,12 @@ function tableau(::ARS222)
     ]))
 end
 
+"""
+    ARS343
+
+The L-stable, third-order (3,4,3) implicit-explicit (IMEX) Runge-Kutta scheme of
+[ARS1997](@cite), section 2.7.
+"""
 struct ARS343 <: AbstractIMEXARKTableau end
 function tableau(::ARS343)
     γ = 0.4358665215084590