PERK2 constructor consistence (#2184)

* Make `PairedExplicitRK2` constructors consistent

* Make PERK2 constructor consistent

* changes

* Update NEWS.md

* prevent readdlm error for S=2

* fix merge errors

* fix errors

---------

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

Author: DanielDoehring

NEWS.md

@@ -15,6 +15,9 @@ for human readability.
   [RecursiveArrayTools.jl](https://github.com/SciML/RecursiveArrayTools.jl)
   for `DGMulti` solvers ([#2150]). You can use `Base.parent` to unwrap
   the original data.
+- The `PairedExplicitRK2` constructor with second argument `base_path_monomial_coeffs::AbstractString` requires 
+  now `dt_opt`, `bS`, `cS` to be given as keyword arguments ([#2184]).
+  Previously, those where standard function parameters, in the same order as listed above.
 - The `AnalysisCallback` output generated with the `save_analysis = true` option now prints
   floating point numbers in their respective (full) precision. 
   Previously, only the first 8 digits were printed to file.

src/time_integration/paired_explicit_runge_kutta/methods_PERK2.jl

@@ -50,7 +50,7 @@ function compute_PairedExplicitRK2_butcher_tableau(num_stages, eig_vals, tspan,
                                                           dteps,
                                                           eig_vals; verbose)
 
-    if num_stages != consistency_order
+    if coeffs_max > 0
         monomial_coeffs = undo_normalization!(monomial_coeffs, consistency_order,
                                               num_stages)
         num_monomial_coeffs = length(monomial_coeffs)
@@ -81,24 +81,26 @@ function compute_PairedExplicitRK2_butcher_tableau(num_stages,
     a_matrix = zeros(2, coeffs_max)
     a_matrix[1, :] = c[3:end]
 
-    path_monomial_coeffs = joinpath(base_path_monomial_coeffs,
-                                    "gamma_" * string(num_stages) * ".txt")
+    if coeffs_max > 0
+        path_monomial_coeffs = joinpath(base_path_monomial_coeffs,
+                                        "gamma_" * string(num_stages) * ".txt")
 
-    @assert isfile(path_monomial_coeffs) "Couldn't find file"
-    monomial_coeffs = readdlm(path_monomial_coeffs, Float64)
-    num_monomial_coeffs = size(monomial_coeffs, 1)
+        @assert isfile(path_monomial_coeffs) "Couldn't find file"
+        monomial_coeffs = readdlm(path_monomial_coeffs, Float64)
+        num_monomial_coeffs = size(monomial_coeffs, 1)
 
-    @assert num_monomial_coeffs == coeffs_max
-    A = compute_a_coeffs(num_stages, stage_scaling_factors, monomial_coeffs)
+        @assert num_monomial_coeffs == coeffs_max
+        A = compute_a_coeffs(num_stages, stage_scaling_factors, monomial_coeffs)
 
-    a_matrix[1, :] -= A
-    a_matrix[2, :] = A
+        a_matrix[1, :] -= A
+        a_matrix[2, :] = A
+    end
 
     return a_matrix, c
 end
 
 @doc raw"""
-    PairedExplicitRK2(num_stages, base_path_monomial_coeffs::AbstractString, dt_opt = nothing,
+    PairedExplicitRK2(num_stages, base_path_monomial_coeffs::AbstractString; dt_opt = nothing,
                       bS = 1.0, cS = 0.5)
     PairedExplicitRK2(num_stages, tspan, semi::AbstractSemidiscretization;
                       verbose = false, bS = 1.0, cS = 0.5)
@@ -144,7 +146,7 @@ struct PairedExplicitRK2 <: AbstractPairedExplicitRKSingle
 end
 
 # Constructor that reads the coefficients from a file
-function PairedExplicitRK2(num_stages, base_path_monomial_coeffs::AbstractString,
+function PairedExplicitRK2(num_stages, base_path_monomial_coeffs::AbstractString;
                            dt_opt = nothing,
                            bS = 1.0, cS = 0.5)
     # If the user has the monomial coefficients, they also must have the optimal time step