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fixing tracing logic and adding inhomogenous, nonlinear wave eq test for staggered grid #353

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90ad3ea
fixing tracing logic and adding inhomogenous, nonlinear wave eq test
cmhyett Jan 13, 2024
f606486
dummy commit for CI
cmhyett Jan 14, 2024
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12 changes: 4 additions & 8 deletions src/discretization/staggered_discretize.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ function SciMLBase.discretize(pdesys::PDESystem,
sys, tspan = SciMLBase.symbolic_discretize(pdesys, discretization)
try
simpsys = structural_simplify(sys)
if tspan === nothing
if tspan === nothing
add_metadata!(get_metadata(sys), sys)
return prob = NonlinearProblem(simpsys, ones(length(simpsys.states));
discretization.kwargs..., kwargs...)
Expand All @@ -27,17 +27,13 @@ function symbolic_trace(prob, sys)
u2_var = get_var_from_state(states[findfirst(x->get_var_from_state(x)!=u1_var, states)]);
u1inds = findall(x->get_var_from_state(x)===u1_var, states);
u2inds = findall(x->get_var_from_state(x)===u2_var, states);
u1 = states[u1inds]
u2 = states[u2inds]
tracevec_1 = [i in u2inds ? states[i] : Num(0.0) for i in 1:length(states)] # maybe just 0.0
tracevec_2 = [i in u1inds ? states[i] : Num(0.0) for i in 1:length(states)]
du1 = prob.f(tracevec_1, nothing, 0.0);
du2 = prob.f(tracevec_2, nothing, 0.0);
tmp = prob.f(states, nothing, 0.0)
du1 = [i in u1inds ? tmp[i] : Num(0.0) for i in 1:length(states)];
du2 = [i in u2inds ? tmp[i] : Num(0.0) for i in 1:length(states)];
gen_du1 = eval(Symbolics.build_function(du1, states)[2]);
gen_du2 = eval(Symbolics.build_function(du2, states)[2]);
dynamical_f1(_du1,u,p,t) = gen_du1(_du1, u);
dynamical_f2(_du2,u,p,t) = gen_du2(_du2, u);
u0 = prob.u0;#[prob.u0[u1inds]; prob.u0[u2inds]];
return SplitODEProblem(dynamical_f1, dynamical_f2, u0, prob.tspan);
#return DynamicalODEProblem{false}(dynamical_f1, dynamical_f2, u0[1:length(u1)], u0[length(u1)+1:end], prob.tspan)
end
40 changes: 39 additions & 1 deletion test/pde_systems/wave_eq_staggered.jl
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Expand Up @@ -19,7 +19,7 @@ using OrdinaryDiffEq
bcs = [ρ(0,x) ~ initialFunction(x),
ϕ(0.0,x) ~ 0.0,
Dx(ρ(t,L)) ~ 0.0,
ϕ(t,-L) ~ 0.0];#-a^2*Dx(ρ(t,L))];
ϕ(t,-L) ~ 0.0];

domains = [t in Interval(0.0, tmax),
x in Interval(-L, L)];
Expand Down Expand Up @@ -106,3 +106,41 @@ end
@test maximum(sol[1:128,1] .- sol[1:128,test_ind]) < max(dx^2, dt)
@test maximum(sol[1:128,1] .- sol[1:128,2*test_ind]) < 10*max(dx^2, dt)
end

@testset "1D inhomogenous nonlinear wave equation, staggered grid, Mixed BC" begin
@parameters x
@variables t, ρ(..), ϕ(..)
Dt = Differential(t);
Dx = Differential(x);

β = 0.11/(2*0.01);
a = 0.5;
L = 1.0;
dx = 1/2^7;
tspan = (0.0, 6.0)

function RHS(ρ, ϕ)
return -β*(ϕ^2)*sign(ϕ)/ρ
end

eqs = [Dt(ρ(t,x)) + Dx(ϕ(t,x)) ~ 0,
Dt(ϕ(t,x)) + a^2*Dx(ρ(t,x)) ~ RHS(ρ(t, x), ϕ(t,x))]
bcs = [ρ(0,x) ~ 50.0*exp(-((x-0.5)*20)^2) + 50.0,
ϕ(0,x) ~ 0.0,
Dx(ρ(t,L)) ~ 0.0,
ϕ(t,0.0) ~ 0.0]
domains = [t in Interval(tspan[1], tspan[end]),
x in Interval(0.0, L)]

@named pdesys = PDESystem(eqs, bcs, domains, [t,x], [ρ(t,x), ϕ(t,x)])
discretization = MOLFiniteDifference([x=>dx], t, grid_align=MethodOfLines.StaggeredGrid(), edge_aligned_var=ϕ(t,x));
prob = discretize(pdesys, discretization);
@time sol = solve(prob, SplitEuler(), dt=(dx/a)^2, adaptive=false)
@test sol.retcode == ReturnCode.Success
# p = plot()
# for i in 1:tspan[end]*((a/dx)^2)/10:length(sol)
# ind = floor(Int, i)
# plot!(p, sol.u[ind], label="t = $(@sprintf("%.2f", sol.t[ind]))")
# end
# p
end