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Copy pathShallowWaterThetaMethodFullNewton.jl
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ShallowWaterThetaMethodFullNewton.jl
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# Generate initial monolothic solution
function uhqF₀(u₀,h₀,q₀,F₀,X,Y,dΩ; mass_matrix_solver=Gridap.Algebra.BackslashSolver())
a((u,p,r,u2),(v,q,s,v2))=∫(v⋅u+q*p+s*r+v2⋅u2)dΩ
b((v,q,s,v2))=∫( v⋅u₀+ q*h₀ + s*q₀ + v2⋅F₀ )dΩ
fes=FESolver(mass_matrix_solver)
solve(fes,AffineFEOperator(a,b,X,Y))
end
"""
Solves the nonlinear rotating shallow water equations
T : [0,T] simulation interval
N : number of time subintervals
θ : Theta-method parameter [0,1)
τ : APVM method stabilization parameter (dt/2 is typically a reasonable value)
"""
function shallow_water_theta_method_full_newton_time_stepper(
nls::Gridap.Algebra.NonlinearSolver,
model, order, degree, h₀, u₀, f₀, topography, g, θ, T, N, τ;
mass_matrix_solver::Gridap.Algebra.LinearSolver=Gridap.Algebra.BackslashSolver(),
matrix_type::Type{<:AbstractSparseMatrix}=SparseMatrixCSC{Float64,Int},
vector_type::Type{<:AbstractVector}=Vector{Float64},
write_diagnostics=true,
write_diagnostics_freq=1,
dump_diagnostics_on_screen=true,
am_i_root=true,
write_solution=false,
write_solution_freq=N/10,
output_dir="nswe_ncells_$(num_cells(model))_order_$(order)_theta_method_full_newton")
Ω = Triangulation(model)
n = get_normal_vector(Ω)
dΩ = Measure(Ω,degree)
dω = Measure(Ω,degree,ReferenceDomain())
# Setup the trial and test spaces
R, S, U, V, P, Q = setup_mixed_spaces(model, order)
if (write_diagnostics)
# assemble the mass matrices
H1MM, _, L2MM, H1MMchol, RTMMchol, L2MMchol =
setup_and_factorize_mass_matrices(dΩ, R, S, U, V, P, Q;
mass_matrix_solver=mass_matrix_solver)
end
Y = MultiFieldFESpace([V,Q,S,V])
X = MultiFieldFESpace([U,P,R,U])
fes=FESolver(mass_matrix_solver)
a1(u,v)=∫(v⋅u)dΩ
l1(v)=∫(v⋅u₀)dΩ
assem=SparseMatrixAssembler(matrix_type,vector_type,U,V)
un=solve(fes,AffineFEOperator(a1,l1,U,V,assem))
a2(u,v)=∫(v*u)dΩ
l2(v)=∫(v*h₀)dΩ
assem=SparseMatrixAssembler(matrix_type,vector_type,P,Q)
hn=solve(fes,AffineFEOperator(a2,l2,P,Q,assem))
a3(u,v)=∫(v*u)dΩ
l3(v)=∫(v*f₀)dΩ
assem=SparseMatrixAssembler(matrix_type,vector_type,R,S)
fn=solve(fes,AffineFEOperator(a3,l3,R,S,assem))
unv,hnv,fnv=get_free_dof_values(un,hn,fn)
b = interpolate(topography,P)
# Compute:
# - Initial potential vorticity (q₀)
# - Initial volume flux (F₀)
# - Initial full solution
q₀=clone_fe_function(R,fn)
compute_potential_vorticity!(q₀,H1MM,H1MMchol,dΩ,R,S,hn,un,fn,n,assem)
F₀=clone_fe_function(V,un)
compute_mass_flux!(F₀,dΩ,V,RTMMchol,un*hn)
ΔuΔhqF=uhqF₀(un,hn,q₀,F₀,X,Y,dΩ; mass_matrix_solver=mass_matrix_solver)
Δu,Δh,q,F = ΔuΔhqF
h_tmp = copy(hnv)
w_tmp = copy(fnv)
function run_simulation(pvd=nothing)
dt = T/N
τ = dt/2 # APVM stabilization parameter
hc = CellField(h₀,Ω)
uc = CellField(u₀,Ω)
if (write_diagnostics)
ϕ = clone_fe_function(Q,hn)
wn = clone_fe_function(S,fn)
diagnostics_file = joinpath(output_dir,"nswe_diagnostics_theta_method_full_newton.csv")
if (am_i_root)
initialize_csv(diagnostics_file,
"time", "mass", "vorticity", "kinetic", "potential", "power")
end
end
for step=1:N
function residual((Δu,Δh,qvort,F),(v,q,s,v2))
one_m_θ = (1-θ)
uiΔu = un + one_m_θ*Δu
hiΔh = hn + one_m_θ*Δh
hbiΔh = hn + b + one_m_θ*Δh
∫((1.0/dt)*v⋅(Δu)-(∇⋅(v))*(g*hbiΔh + 0.5*uiΔu⋅uiΔu)+
(qvort-τ*(uiΔu⋅∇(qvort)))*(v⋅⟂(F,n)) + # eq1
(1.0/dt)*q*(Δh))dΩ + ∫(q*(DIV(F)))dω + # eq2
∫(s*qvort*hiΔh + ⟂(∇(s),n)⋅uiΔu - s*fn + # eq3
v2⋅(F-hiΔh*uiΔu))dΩ # eq4
end
function jacobian((Δu,Δh,qvort,F),(du,dh,dq,dF),(v,q,s,v2))
one_m_θ = (1-θ)
uiΔu = un + one_m_θ*Δu
hiΔh = hn + one_m_θ*Δh
uidu = one_m_θ*du
hidh = one_m_θ*dh
∫((1.0/dt)*v⋅du + (dq - τ*(uiΔu⋅∇(dq)+uidu⋅∇(qvort)))*(v⋅⟂(F ,n))
+ (qvort - τ*( uiΔu⋅∇(qvort)))*(v⋅⟂(dF,n))
- (∇⋅(v))*(g*hidh +uiΔu⋅uidu) + # eq1
(1.0/dt)*q*dh)dΩ + ∫(q*(DIV(dF)))dω + # eq2
∫(s*(qvort*hidh+dq*hiΔh) + ⟂(∇(s),n)⋅uidu + # eq3
v2⋅(dF-hiΔh*uidu-hidh*uiΔu))dΩ # eq4
end
# Solve fully-coupled monolithic nonlinear problem
# Use previous time-step solution, ΔuΔhqF, as initial guess
# Overwrite solution into ΔuΔhqF
assem = SparseMatrixAssembler(matrix_type,Vector{Float64},X,Y)
op=FEOperator(residual,jacobian,X,Y,assem)
solver=FESolver(nls)
solve!(ΔuΔhqF,solver,op)
# Update current solution
unv .= unv .+ get_free_dof_values(Δu)
hnv .= hnv .+ get_free_dof_values(Δh)
if (write_diagnostics && write_diagnostics_freq>0 && mod(step, write_diagnostics_freq) == 0)
compute_diagnostic_vorticity!(wn, dΩ, S, H1MMchol, un, n)
compute_bernoulli_potential!(ϕ,dΩ,Q,L2MMchol,un⋅un,hn,g)
dump_diagnostics_shallow_water!(h_tmp, w_tmp,
model, dΩ, dω, S, L2MM, H1MM,
hn, un, wn, ϕ, F, g, step, dt,
diagnostics_file,
dump_diagnostics_on_screen,
am_i_root)
end
if (write_solution && write_solution_freq>0 && mod(step, write_solution_freq) == 0)
if (!write_diagnostics || write_diagnostics_freq != write_solution_freq)
compute_diagnostic_vorticity!(wn, dΩ, S, H1MMchol, un, n)
end
pvd[dt*Float64(step)] = new_vtk_step(Ω,joinpath(output_dir,"n=$(step)"),hn,un,wn)
end
end
hn, un, num_free_dofs(Y)
end
if (am_i_root && (write_diagnostics || write_solution))
rm(output_dir,force=true,recursive=true)
mkdir(output_dir)
end
if (write_solution)
pvdfile=joinpath(output_dir,
"nswe_ncells_$(num_cells(model))_order_$(order)_theta_method_full_newton")
paraview_collection(run_simulation,pvdfile)
else
run_simulation()
end
end