Add test with units

test/pde_systems/units.jl

@@ -0,0 +1,70 @@
+using ModelingToolkit, MethodOfLines, LinearAlgebra, Test, OrdinaryDiffEq, DomainSets
+using ModelingToolkit: Differential
+using DynamicQuantities
+
+
+# Method of Manufactured Solutions
+u_exact = (x, t) -> exp.(-t) * cos.(x)
+
+# Parameters, variables, and derivatives
+@parameters begin
+    t, [unit = u"s"]
+    x, [unit = u"m"]
+    D_diff=1.0, [description = "Diffusion coefficient", unit = u"m^2/s"]
+end   
+@variables u(..) [unit = u"kg/m^3"]
+Dt = Differential(t)
+Dxx = Differential(x)^2
+
+# 1D PDE and boundary conditions
+eq = Dt(u(t, x)) ~ D_diff * Dxx(u(t, x))
+bcs = [
+    u(0, x) ~ cos(x),
+    u(t, 0) ~ exp(-t),
+    u(t, Float64(π)) ~ -exp(-t),
+]
+
+# Space and time domains
+domains = [
+    t ∈ Interval(0.0, 1.0),
+    x ∈ Interval(0.0, Float64(π)),
+]
+
+# PDE system
+@named pdesys = PDESystem(eq, bcs, domains, [t, x], [u(t, x)], [D_diff])
+
+# Method of lines discretization
+dx = range(0.0, Float64(π), length = 30)
+dx_ = dx[2] - dx[1]
+
+order = 2
+discretization = MOLFiniteDifference([x => dx_], t)
+discretization_edge = MOLFiniteDifference([x => dx_], t; grid_align = edge_align)
+# Explicitly specify order of centered difference
+discretization_centered = MOLFiniteDifference([x => dx_], t; approx_order = order)
+# Higher order centered difference
+discretization_approx_order4 = MOLFiniteDifference([x => dx_], t; approx_order = 4)
+
+for disc in [
+        discretization, discretization_edge,
+        discretization_centered, discretization_approx_order4,
+    ]
+    # Convert the PDE problem into an ODE problem
+    # Here we are disabling unit checks because MOL does not currently
+    # handle units correctly. In the future, we should add unit handling 
+    # and re-enable these checks.
+    prob = discretize(pdesys, disc; system_kwargs = [:checks => ~ModelingToolkit.CheckUnits])
+
+    # Solve ODE problem      # Solve ODE problem
+    sol = solve(prob, Tsit5(), saveat = 0.1)
+
+    x_disc = sol[x][2:(end - 1)]
+    t_disc = sol[t]
+    u_approx = sol[u(t, x)][:, 2:(end - 1)]
+
+    # Test against exact solution
+    for i in 1:length(sol)
+        exact = u_exact(x_disc, t_disc[i])
+        @test all(isapprox.(u_approx[i, :], exact, atol = 0.01))
+    end
+end

test/runtests.jl

@@ -148,4 +148,9 @@ const is_TRAVIS = haskey(ENV, "TRAVIS")
             include("pde_systems/wave_eq_staggered.jl")
         end
     end
+    if GROUP == "All" || GROUP == "Units"
+        @time @safetestset "Units" begin
+            include("pde_systems/units.jl")
+        end
+    end
 end