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Gauss-Legendre DGSEM Solver: 2D TreeMesh Parabolic #2845

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ranocha merged 10 commits into from
Mar 4, 2026
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Gauss-Legendre DGSEM Solver: 2D TreeMesh Parabolic #2845

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DanielDoehring Mar 3, 2026
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Merge branch 'main' into GL_Parabolic_2D_Periodic
DanielDoehring Mar 3, 2026
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refactor
DanielDoehring Mar 3, 2026
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tests
DanielDoehring Mar 3, 2026
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Merge branch 'main' into GL_Parabolic_2D_Periodic
ranocha Mar 4, 2026
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Merge branch 'main' into GL_Parabolic_2D_Periodic
ranocha Mar 4, 2026
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Update test/test_parabolic_2d.jl
DanielDoehring Mar 4, 2026
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DanielDoehring Mar 4, 2026
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test bnds y
DanielDoehring Mar 4, 2026
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Merge branch 'GL_Parabolic_2D_Periodic' of github.com:DanielDoehring/…
DanielDoehring Mar 4, 2026
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1 change: 1 addition & 0 deletions examples/tree_2d_dgsem/elixir_navierstokes_viscous_shock.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -153,6 +153,7 @@ boundary_conditions_parabolic = (x_neg = boundary_condition_parabolic,

semi = SemidiscretizationHyperbolicParabolic(mesh, (equations, equations_parabolic),
initial_condition, solver;
solver_parabolic = ViscousFormulationBassiRebay1(),
boundary_conditions = (boundary_conditions,
boundary_conditions_parabolic))

Expand Down
146 changes: 82 additions & 64 deletions src/solvers/dgsem_tree/dg_2d.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -536,43 +536,43 @@ function prolong2interfaces!(cache, u, mesh::TreeMesh{2}, equations,

if orientations[interface] == 1
# interface in x-direction
for j in eachnode(dg), v in eachvariable(equations)
# Interpolate to the interfaces using a local variable for
# the accumulation of values (to reduce global memory operations).
interface_u_1 = zero(eltype(interfaces_u))
interface_u_2 = zero(eltype(interfaces_u))
for ii in eachnode(dg)
# Not += to allow `@muladd` to turn these into FMAs
# (see comment at the top of the file)
interface_u_1 = (interface_u_1 +
u[v, ii, j, left_element] *
boundary_interpolation[ii, 2])
interface_u_2 = (interface_u_2 +
u[v, ii, j, right_element] *
boundary_interpolation[ii, 1])
for j in eachnode(dg)
for v in eachvariable(equations)
# Interpolate to the interfaces using a local variable for
# the accumulation of values (to reduce global memory operations).
interface_u_1 = zero(eltype(interfaces_u))
interface_u_2 = zero(eltype(interfaces_u))
for ii in eachnode(dg)
# Not += to allow `@muladd` to turn these into FMAs
# (see comment at the top of the file)
interface_u_1 = (interface_u_1 +
u[v, ii, j, left_element] *
boundary_interpolation[ii, 2])
interface_u_2 = (interface_u_2 +
u[v, ii, j, right_element] *
boundary_interpolation[ii, 1])
end
interfaces_u[1, v, j, interface] = interface_u_1
interfaces_u[2, v, j, interface] = interface_u_2
end
interfaces_u[1, v, j, interface] = interface_u_1
interfaces_u[2, v, j, interface] = interface_u_2
end
else # if orientations[interface] == 2
# interface in y-direction
for i in eachnode(dg), v in eachvariable(equations)
# Interpolate to the interfaces using a local variable for
# the accumulation of values (to reduce global memory operations).
interface_u_1 = zero(eltype(interfaces_u))
interface_u_2 = zero(eltype(interfaces_u))
for jj in eachnode(dg)
# Not += to allow `@muladd` to turn these into FMAs
# (see comment at the top of the file)
interface_u_1 = (interface_u_1 +
u[v, i, jj, left_element] *
boundary_interpolation[jj, 2])
interface_u_2 = (interface_u_2 +
u[v, i, jj, right_element] *
boundary_interpolation[jj, 1])
for i in eachnode(dg)
for v in eachvariable(equations)
interface_u_1 = zero(eltype(interfaces_u))
interface_u_2 = zero(eltype(interfaces_u))
for jj in eachnode(dg)
interface_u_1 = (interface_u_1 +
u[v, i, jj, left_element] *
boundary_interpolation[jj, 2])
interface_u_2 = (interface_u_2 +
u[v, i, jj, right_element] *
boundary_interpolation[jj, 1])
end
interfaces_u[1, v, i, interface] = interface_u_1
interfaces_u[2, v, i, interface] = interface_u_2
end
interfaces_u[1, v, i, interface] = interface_u_1
interfaces_u[2, v, i, interface] = interface_u_2
end
end
end
Expand Down Expand Up @@ -713,52 +713,60 @@ function prolong2boundaries!(cache, u,
# boundary in x-direction
if neighbor_sides[boundary] == 1
# element in -x direction of boundary => interpolate to right boundary node (+1)
for l in eachnode(dg), v in eachvariable(equations)
# Interpolate to the boundaries using a local variable for
# the accumulation of values (to reduce global memory operations).
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
# Not += to allow `@muladd` to turn these into FMAs
# (see comment at the top of the file)
boundary_u = (boundary_u +
u[v, ii, l, element] *
boundary_interpolation[ii, 2])
for l in eachnode(dg)
for v in eachvariable(equations)
# Interpolate to the boundaries using a local variable for
# the accumulation of values (to reduce global memory operations).
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
# Not += to allow `@muladd` to turn these into FMAs
# (see comment at the top of the file)
boundary_u = (boundary_u +
u[v, ii, l, element] *
boundary_interpolation[ii, 2])
end
boundaries.u[1, v, l, boundary] = boundary_u
end
boundaries.u[1, v, l, boundary] = boundary_u
end
else # element in +x direction of boundary => interpolate to left boundary node (-1)
for l in eachnode(dg), v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
boundary_u = (boundary_u +
u[v, ii, l, element] *
boundary_interpolation[ii, 1])
for l in eachnode(dg)
for v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
boundary_u = (boundary_u +
u[v, ii, l, element] *
boundary_interpolation[ii, 1])
end
boundaries.u[2, v, l, boundary] = boundary_u
end
boundaries.u[2, v, l, boundary] = boundary_u
end
end
else # if orientations[boundary] == 2
# boundary in y-direction
if neighbor_sides[boundary] == 1
# element in -y direction of boundary => interpolate to right boundary node (+1)
for l in eachnode(dg), v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
boundary_u = (boundary_u +
u[v, l, ii, element] *
boundary_interpolation[ii, 2])
for l in eachnode(dg)
for v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for jj in eachnode(dg)
boundary_u = (boundary_u +
u[v, l, jj, element] *
boundary_interpolation[jj, 2])
end
boundaries.u[1, v, l, boundary] = boundary_u
end
boundaries.u[1, v, l, boundary] = boundary_u
end
else # element in +y direction of boundary => interpolate to left boundary node (-1)
for l in eachnode(dg), v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for ii in eachnode(dg)
boundary_u = (boundary_u +
u[v, l, ii, element] *
boundary_interpolation[ii, 1])
for l in eachnode(dg)
for v in eachvariable(equations)
boundary_u = zero(eltype(boundaries.u))
for jj in eachnode(dg)
boundary_u = (boundary_u +
u[v, l, jj, element] *
boundary_interpolation[jj, 1])
end
boundaries.u[2, v, l, boundary] = boundary_u
end
boundaries.u[2, v, l, boundary] = boundary_u
end
end
end
Expand Down Expand Up @@ -1113,6 +1121,16 @@ function calc_mortar_flux!(surface_flux_values,
return nothing
end

# For Gauss-Legendre DGSEM mortars are not yet implemented
function calc_mortar_flux!(surface_flux_values,
mesh::TreeMesh{2},
have_nonconservative_terms, equations,
mortar::Nothing, surface_integral,
dg::DGSEM{<:GaussLegendreBasis}, cache)
@assert isempty(eachmortar(dg, cache))
return nothing
end

@inline function calc_fstar!(destination::AbstractArray{<:Any, 2}, equations,
surface_flux, dg::DGSEM,
u_interfaces, interface, orientation)
Expand Down
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