rk2 coefficients

Author: milankl

src/Constants.jl

@@ -25,9 +25,13 @@ end
 """Generator function for the mutable struct Constants."""
 function Constants{T,Tprog}(P::Parameter,G::Grid) where {T<:AbstractFloat,Tprog<:AbstractFloat}
 
-    # Runge-Kutta 3rd/4th order coefficients including time step Δt
-    # (which includes the grid spacing Δ too)
-    if P.RKo == 3     # version 2
+    # Runge-Kutta 2nd/3rd/4th order coefficients including time step Δt and grid spacing Δ
+    # a are the coefficents to sum the rhs on the fly, such that sum=1
+    # b are the coefficents for the update that used for a new evaluation of the RHS
+    if P.RKo == 2     # Heun's method
+        RKaΔt = Tprog.([1/2,1/2]*G.dtint/G.Δ)
+        RKbΔt = Tprog.([1]*G.dtint/G.Δ)
+    elseif P.RKo == 3     # version 2 / Heun's 3rd order
         RKaΔt = Tprog.([1/4,0.,3/4]*G.dtint/G.Δ)
         RKbΔt = Tprog.([1/3,2/3]*G.dtint/G.Δ)
     elseif P.RKo == 4

src/DefaultParameters.jl

@@ -118,7 +118,7 @@
     @assert topo_width > 0.0    "topo_width has to be >0, $topo_width given."
     @assert t_relax > 0.0       "t_relax has to be >0, $t_relax given."
     @assert η_refw > 0.0        "η_refw has to be >0, $η_refw given."
-    @assert RKo in [3,4]        "RKo has to be 3 or 4, $RKo given."
+    @assert RKo in [2,3,4]        "RKo has to be 2,3 or 4, $RKo given."
     @assert Ndays > 0.0         "Ndays has to be >0, $Ndays given."
     @assert nstep_diff > 0      "nstep_diff has to be >0, $nstep_diff given."
     @assert nstep_advcor >= 0   "nstep_advcor has to be >=0, $nstep_advcor given."
@@ -191,8 +191,8 @@ Creates a Parameter struct with following options and default values
     wk::Real=10e3                       # width [m] in y of Gaussian used for surface forcing
 
     # TIME STEPPING OPTIONS
-    RKo::Int=4                          # Order of the RK time stepping scheme (3 or 4)
-    cfl::Real=1.0                       # CFL number (1.0 recommended for RK4, 0.6 for RK3)
+    RKo::Int=4                          # Order of the RK time stepping scheme (2,3 or 4)
+    cfl::Real=1.0                       # CFL number (1.0 recommended for RK4, 0.6 for RK3, 0.1 for RK2)
     Ndays::Real=10.0                    # number of days to integrate for
     nstep_diff::Int=1                   # diffusive part every nstep_diff time steps.
     nstep_advcor::Int=0                 # advection and coriolis update every nstep_advcor time steps.