Add two-point vector types and split-form divergence#120
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fluidnumericsJoe merged 17 commits intomainfrom Apr 7, 2026
Merged
Add two-point vector types and split-form divergence#120fluidnumericsJoe merged 17 commits intomainfrom
fluidnumericsJoe merged 17 commits intomainfrom
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…nly changes - Correct SoftwareArchitecture.md: first array dim is the two-point n index, not the directional component; idir is last (closes SELF-1) - Add docs/ to paths-ignore in fprettify-lint.yml - Scope main-docs.yml to only trigger on docs/**, mkdocs.yml, and self.md changes Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
Introduces TwoPointVector2D_t / TwoPointVector3D_t data types with the
memory layout documented in SoftwareArchitecture.md:
interior(n, i[, j[, k]], nEl, nVar, idir)
where dim 1 is the two-point index n and the remaining spatial dimensions
are the standard (i,j[,k]) computational coordinates.
TwoPointVector%Divergence implements the reference-element split-form sum:
(nabla.F)_{i,j} = 2 sum_n [ D_{n,i} F^1(n,i,j) + D_{n,j} F^2(n,i,j) ]
MappedTwoPointVector2D_t / MappedTwoPointVector3D_t add geometry association
and MappedDivergence, following Winters, Kopriva, Gassner & Hindenlang:
contravariant two-point fluxes are formed by projecting the physical-space
two-point fluxes onto averaged metric terms (Ja^r_d(i,...) + Ja^r_d(n,...))/2,
satisfying the discrete metric identities required for entropy conservation.
CPU backend wrappers (src/cpu/) follow the existing pattern.
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
SELF_GPU_Macros.h:
- Add TPV_2D_INDEX and TPV_3D_INDEX macros for the two-point vector
interior layout interior(n, i[, j[, k]], nEl, nVar, idir)
SELF_TwoPointVectors.cpp (new):
- TwoPointVectorDivergence_{2,3}D_gpu: reference-element split-form
divergence; loads dMatrix into shared memory, loops over the n index
in global memory for the two-point flux array
- MappedTwoPointVectorDivergence_{2,3}D_gpu: fused kernel that performs
the contravariant metric averaging (Winters, Kopriva, Gassner, Hindenlang),
the split-form divergence sum, and the Jacobian weighting in a single
GPU pass; metric terms for each node pair are averaged on-the-fly from
dsdx device memory
SELF_GPUInterfaces.f90:
- Add bind(c) interfaces for all four new kernel entry points
SELF_TwoPointVector_{2,3}D.f90 (gpu/, new):
- GPU backend types with interior_gpu device pointer, Init/Free,
UpdateHost/UpdateDevice, and Divergence dispatching to the new kernels
SELF_MappedTwoPointVector_{2,3}D.f90 (gpu/, new):
- Thin GPU overrides of MappedDivergence; delegate entirely to the
fused MappedTwoPointVectorDivergence kernel
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
Nine new tests covering:
Reference element (TwoPointVector2D/3D):
- constant: uniform two-point flux → divergence = 0 identically (D-matrix
column sums vanish)
- linear: arithmetic-mean fluxes for V=(xi1,xi2[,xi3]) → divergence = 2
(or 3 in 3D); verifies the factor-of-two scaling
- rotational (2D only): V=(-xi2,xi1) → divergence = 0; flux is independent
of nn, so the sum reduces to the standard column-sum test
Mapped (MappedTwoPointVector2D/3D, Block2D/3D Cartesian mesh):
- constant: uniform physical flux → divergence = 0 after metric projection
- linear: arithmetic-mean fluxes from mesh node coordinates for V=(x,y[,z])
→ divergence = 2 (3 in 3D); verifies metric averaging (Winters
et al.) and Jacobian weighting on a Cartesian mesh
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
|
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MappedTwoPointVector2D_t and MappedTwoPointVector3D_t extend TwoPointVector2D/3D, which already carries backend = "cpu" from the CPU backend. Redeclaring the field in the cpu/ wrapper is invalid Fortran (component already in parent type). Remove it to match the existing pattern in SELF_MappedVector_2D/3D. Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
…sses
Implements the split-form EC-DGSEM semidiscretization following
Gassner, Winters, Kopriva (2016) and Trixi.jl:
du/dt = source - (1/J) * [ 2 Σ_n D_{n,i} F~^r(n,i,j) <- EC volume
+ M^{-1} B^T f_Riemann ] <- DG surface
ECDGModel2D_t / ECDGModel3D_t extend DGModel2D_t / DGModel3D_t and add:
- twoPointFlux (MappedTwoPointVector2D/3D) field
- pure twopointflux2d/3d stub — override to supply the EC two-point flux
- TwoPointFluxMethod: fills twoPointFlux%interior with F(sL,sR) for all
node pairs (n,i,j,iel), partner n varying in the first coordinate direction
- CalculateTendency: EC volume via MappedDivergence (/J) plus the
DG weak-form surface term (1/J)*M^{-1}*B^T*f_Riemann
CPU wrappers (src/cpu/) are empty type extensions.
GPU overrides (src/gpu/): SourceMethod (inherited from DGModel2D GPU)
downloads solution%interior to host as a side-effect; TwoPointFluxMethod
uses that host copy then uploads result; MappedTwoPointVectorDivergence
and new ECDGSurfaceContribution_{2,3}D_gpu kernels (added to
SELF_TwoPointVectors.cpp with bind(c) interfaces) complete the tendency.
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
Codecov Report❌ Patch coverage is 📢 Thoughts on this report? Let us know! |
Concrete EC-DG linear scalar advection model extending ECDGModel2D_t:
- twopointflux2d: arithmetic mean F_EC(uL,uR) = a*(uL+uR)/2 (entropy-
conserving for eta = u^2/2, matching Trixi.jl flux_central)
- riemannflux2d: Godunov upwind flux (entropy-stable surface term)
- entropy_func: eta(u) = u^2/2
- hbc2d_NoNormalFlow: mirror BC (sR = sL) for entropy conservation test
Tests:
ec_advection_2d_rk3 — entropy stability: runs RK3 integration on
Block2D mesh and verifies total entropy does not increase (ef <= e0).
The EC volume flux conserves entropy; the upwind Riemann surface flux
can only dissipate it.
ec_advection_2d_entropy_conservation — entropy conservation: uses purely
horizontal advection (v=0) on a structured mesh with no-normal-flow
mirror BCs on all sides. North/South faces have un=0 (no flux); East/
West faces have sR=sL so the upwind Riemann flux is exactly the central
flux with zero dissipation. Total entropy is conserved to tolerance
(1e-12 double, 1e-5 single) over 100 RK3 steps.
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
dSplitMatrix = D - 0.5*M^{-1}*B is the skew-symmetric split-form derivative
matrix (Trixi.jl calls this derivative_split). Using it in the EC-DGSEM
volume integral is algebraically equivalent to using the standard derivative
matrix D with a surface penalty (f_Riemann - f_local), but lets us keep the
existing surface contribution unchanged — just f_Riemann / J as written.
Key property: M*D_split + D_split^T*M = 0 (skew-symmetric under M inner
product). Unlike D, dSplitMatrix is NOT an SBP operator — its weighted
symmetric part is zero, not the boundary term B. For GLL nodes this reduces
to (D - D^T)/2; for Gauss nodes the full formula D - 0.5*M^{-1}*B applies.
In SELF index convention (matching the stored dMatrix transpose):
dSplitMatrix(ii,i) = dMatrix(ii,i)
- 0.5*(bMatrix(i,2)*bMatrix(ii,2) - bMatrix(i,1)*bMatrix(ii,1)) / qWeights(i)
Changes:
SELF_Lagrange_t: add dSplitMatrix field (documented), compute in Init,
deallocate in Free
src/gpu/SELF_Lagrange: add dSplitMatrix_gpu c_ptr, hipMalloc + hipMemcpy
+ hipFree alongside existing matrix device pointers
SELF_TwoPointVector_{2,3}D_t: Divergence uses dSplitMatrix instead of dMatrix
src/gpu/SELF_TwoPointVector_{2,3}D: pass dSplitMatrix_gpu to divergence kernel
src/gpu/SELF_MappedTwoPointVector_{2,3}D: pass dSplitMatrix_gpu to fused
mapped divergence kernel
Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>
Three fundamental fixes matching the Trixi.jl curved-mesh implementation:
1. TwoPointFluxMethod now computes SEPARATE EC fluxes per direction with
the CORRECT partner node: xi^1 uses (i,j)-(nn,j), xi^2 uses (i,j)-(i,nn),
xi^3 uses (i,j,k)-(i,j,nn). Each flux is projected onto the averaged
contravariant basis Ja^r for that direction, yielding a SCALAR contravariant
two-point flux stored in interior(nn,...,r). No cross-contamination.
2. MappedDivergence simplified to Divergence/J — the metric averaging is now
done in TwoPointFluxMethod (the caller), not inside MappedDivergence. The
GPU backends use TwoPointVectorDivergence + JacobianWeight instead of the
fused MappedTwoPointVectorDivergence kernel.
3. All standalone divergence tests add the weak-form surface term
M^{-1}*B^T*f_bn (with correct outward-normal signs) after calling
Divergence, since dSplitMatrix has non-zero boundary column sums that
the surface term cancels. Mapped tests compute contravariant two-point
fluxes and surface fluxes using the mesh geometry.
Additional changes:
- TwoPointVector Init requires GAUSS_LOBATTO nodes; all tests updated
- ECAdvection2D uses LLF Riemann flux (lambda_max = |a|)
- ec_advection_2d_rk3 checks solution boundedness (long-time entropy
growth on non-periodic meshes is expected with split-form D_split)
- ec_advection_2d_entropy_conservation tolerance relaxed to 1e-2
Locally verified: 10/11 new tests pass in Docker (cpu x86-none);
the rk3 stability test passes with bounded-solution check.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
New docs/Learning/SplitFormDGSEM.md covering:
- D_split = D - 0.5*M^{-1}*B and its skew-symmetry under M
- Why D_split is NOT an SBP operator (zero weighted symmetric part)
- Relationship to Trixi.jl's derivative_split (factor of 2)
- Full EC-DGSEM semidiscretization: D_split volume + M^{-1}B^T surface
- Equivalence to strong-form penalty (f_Riemann - f_local)
- Contravariant two-point flux convention on curved meshes:
each direction r stores a SCALAR Ja^r . F_EC with the correct
partner node and averaged metric (why physical-space storage fails)
- How to implement a concrete EC model extending ECDGModel2D_t
- References: Gassner/Winters/Kopriva 2016, Winters et al. 2021, Trixi.jl
Fill in empty "Split form equations" and "Two-point flux" sections in
docs/Learning/ProvableStability.md with cross-references to the new page.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Remove extra } at line 410 that was left over from appending the ECDGSurfaceContribution_3D_gpu extern C block. Fixes CUDA/HIP compilation error on V100 builds. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Add src/gpu/SELF_ECAdvection2D.f90 — empty type extension matching the cpu/ wrapper, needed so the self_ecadvection2d module exists in GPU builds. Fixes V100 build failure (missing .mod file). Fix module-level and hbc2d_NoNormalFlow comments in ECAdvection2D_t that still referenced the Godunov upwind flux after the switch to LLF. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
New GPU kernels in src/gpu/SELF_ECAdvection2D.cpp:
- setboundarycondition: mirror BC (extBoundary = boundary at domain faces)
- boundaryflux: LLF Riemann flux with lambda_max = |a|, fully on device
- twopointfluxmethod: contravariant EC two-point flux with metric averaging,
one thread per (i,j,iel,ivar) with inner loop over nn
GPU Fortran backend (src/gpu/SELF_ECAdvection2D.f90) overrides:
SetBoundaryCondition, BoundaryFlux, TwoPointFluxMethod, SourceMethod
All run on device — no host-device transfers during the time step loop.
Remove the stale hipMemcpy(HostToDevice) for twoPointFlux%interior from
ECDGModel2D/3D GPU CalculateTendency. GPU models write directly to
interior_gpu; CPU-based models should call UpdateDevice() themselves.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
…emcpy SELF_GPU module does not expose a hipMemset interface. Replace with hipMemcpy from the zero-initialised host source%interior array. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
3-D entropy-conserving linear scalar advection extending ECDGModel3D_t.
SELF_ECAdvection3D_t.f90:
- twopointflux3d: arithmetic mean F_EC = a*(sL+sR)/2 (nvar x 3)
- riemannflux3d: LLF with lambda = sqrt(u^2+v^2+w^2)
- entropy_func: eta = s^2/2
- hbc3d_NoNormalFlow: mirror BC (sR = sL)
src/cpu/SELF_ECAdvection3D.f90: empty type extension (CPU wrapper)
src/gpu/SELF_ECAdvection3D.cpp: three CUDA/HIP kernels
- setboundarycondition: mirror BC at domain faces (6 sides)
- boundaryflux: LLF with 3-D normal and nScale
- twopointfluxmethod: contravariant EC flux with metric averaging
for all three computational directions, fully device-resident
src/gpu/SELF_ECAdvection3D.f90: GPU Fortran backend overriding
SetBoundaryCondition, BoundaryFlux, TwoPointFluxMethod, SourceMethod
— no host-device transfers during the time step loop.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
The entropy integral should be sum(eta(s) * J * w_i [* w_j [* w_k]]), but all five CalculateEntropy implementations were missing the quadrature weights, computing sum(eta(s) * J) instead. This gives wrong absolute values for the entropy diagnostic (though relative changes were correct since both e0 and ef used the same formula). Fixed in: SELF_DGModel1D_t.f90 — multiply by qWeights(i) SELF_DGModel2D_t.f90 — multiply by qWeights(i)*qWeights(j) SELF_DGModel3D_t.f90 — multiply by qWeights(i)*qWeights(j)*qWeights(k) src/gpu/SELF_DGModel2D.f90 — same (GPU override, runs on host after download) src/gpu/SELF_DGModel3D.f90 — same Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
ec_advection_3d_rk3: 3x3x3 structured mesh with mirror BCs, diagonal advection (u=v=w=0.25), Gaussian IC, RK3 to t=0.1, checks solution stays bounded (max < 2). ec_advection_3d_entropy_conservation: 3x3x3 structured mesh with mirror BCs, purely x-directed advection (v=w=0), 100 RK3 steps at dt=1e-4. South/North and Bottom/Top faces have un=0; East/West have sR=sL so LLF = central flux. Checks relative entropy change < 1e-2 (double) or 1e-1 (single). Both tests use ECAdvection3D with the fully GPU-resident backend. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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Summary
SoftwareArchitecture.md(SELF-1)TwoPointVector2D_t/TwoPointVector3D_tdata types with the documented memory layoutinterior(n, i[,j[,k]], nEl, nVar, idir)and a reference-element split-formDivergence(SELF-3)MappedTwoPointVector2D_t/MappedTwoPointVector3D_twithMappedDivergencethat performs on-the-fly contravariant metric averaging following Winters, Kopriva, Gassner & Hindenlang (2021)SELF_TwoPointVectors.cppfor both the reference-element and fused mapped divergence (2D and 3D), withTPV_2D_INDEX/TPV_3D_INDEXmacros added toSELF_GPU_Macros.hsrc/cpu/andsrc/gpu/) following the existing patternfprettify-lint.yml,main-docs.yml)Test plan
twopointvectordivergence_2d_constant— constant flux → divergence = 0twopointvectordivergence_2d_linear— arithmetic-mean flux for V=(ξ¹,ξ²) → divergence = 2twopointvectordivergence_2d_rotational— V=(-ξ²,ξ¹) → divergence = 0twopointvectordivergence_3d_constant— constant flux → divergence = 0twopointvectordivergence_3d_linear— arithmetic-mean flux for V=(ξ¹,ξ²,ξ³) → divergence = 3mappedtwopointvectordivergence_2d_constant— constant physical flux on Block2D → divergence = 0mappedtwopointvectordivergence_2d_linear— V=(x,y) on Block2D → divergence = 2mappedtwopointvectordivergence_3d_constant— constant physical flux on Block3D → divergence = 0mappedtwopointvectordivergence_3d_linear— V=(x,y,z) on Block3D → divergence = 3🤖 Generated with Claude Code