CFV Module Unit Tests

Table of Contents

• Building and Running
• Target Summary
• Limiter Functions (test_Limiters.cpp)
  • PolynomialSquaredNorm
  • PolynomialDotProduct
  • FMINMOD_Biway (classical minmod)
  • FVanLeer_Biway (Van Leer limiter)
  • FWBAP_L2_Biway (weighted-bounded averaging, L2 norm)
  • FWBAP_L2_Cut_Biway
  • Multiway Limiters
  • Biway Polynomial-Norm Limiters
  • Cross-Consistency and Edge Cases
• Variational Reconstruction 2D (test_Reconstruction.cpp)
  • Meshes
  • Reconstruction Methods
  • Polynomial Exactness (Wall Mesh)
  • Convergence Series (Periodic Meshes)
  • Iteration Convergence
  • Limiter Procedure Tests
• Variational Reconstruction 3D (test_Reconstruction3D.cpp)
  • Constant Exactness
  • Golden-Value Regression
  • Structural Tests
• FiniteVolume Python Tests (test_fv_correctness.py)
  • Test Classes
• VR and ModelEvaluator Python Tests (test_vr_correctness.py)
  • Test Classes

Tests for the Compact Finite Volume module (src/CFV/). C++ tests use doctest; Python tests use pytest.

Building and Running

# Build all CFV C++ test executables
cmake --build build -t cfv_unit_tests -j8
 
# Run every CFV CTest (serial + MPI np=1,2,4)
ctest --test-dir build -R cfv_ --output-on-failure
 
# Python tests (requires pybind11 .so to be installed first)
cmake --build build -t dnds_pybind11 geom_pybind11 cfv_pybind11 -j32
cmake --install build --component py
PYTHONPATH=python pytest test/CFV/ -v

Target Summary

CMake target	CTest names	Source file	Type
cfv_test_limiters	cfv_limiters	test_Limiters.cpp	Serial
cfv_test_reconstruction	cfv_reconstruction_np{1,2,4}	test_Reconstruction.cpp	MPI
cfv_test_reconstruction3d	cfv_reconstruction3d_np{1,2,4}	test_Reconstruction3D.cpp	MPI
—	—	test_fv_correctness.py	pytest
—	—	test_vr_correctness.py	pytest

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Limiter Functions (test_Limiters.cpp)

See also

test_Limiters.cpp

Serial tests for every standalone limiter function in CFV/Limiters.hpp. 36 test cases, 306 assertions. No mesh or MPI required — pure Eigen array computations.

PolynomialSquaredNorm

Weighted squared norms used internally by polynomial-aware limiters.

Test case	Description
PolynomialSquaredNorm<2> with 2 rows (P1)	Uniform weight (w=1); result[j] = sum(theta(i,j)^2).
PolynomialSquaredNorm<2> with 3 rows (P2)	Mixed weights (1, 0.5, 1); checks exact values.
PolynomialSquaredNorm<2> with 4 rows (P3)	Weights (1, 1/3, 1/3, 1); single-column check.
PolynomialSquaredNorm<3> with 3 rows (P1)	3D uniform weight; verifies column-wise sums.
PolynomialSquaredNorm<3> with 6 rows (P2)	3D mixed weights (1,1,1, 0.5,0.5,0.5).
PolynomialSquaredNorm<3> with 10 rows (P3)	3D full weight vector (1,1/3,1/6).

PolynomialDotProduct

Test case	Description
PolynomialDotProduct<2> self-product equals PolynomialSquaredNorm	dot(theta, theta) == norm(theta) for nRows in {2,3,4}.
PolynomialDotProduct<2> linearity	dot(alpha*a, b) == alpha * dot(a, b).

FMINMOD_Biway (classical minmod)

Test case	Description
same-sign inputs	Returns min-magnitude: minmod(1,2)=1, minmod(3,6)=3, etc.
opposite-sign inputs produce zero	Opposite signs always give zero output.
zero input	Any zero input produces zero output.

FVanLeer_Biway (Van Leer limiter)

Test case	Description
same-sign inputs	VanLeer(2,4) = 8/3; VanLeer(-3,-6) = -4.
opposite-sign produces zero	Opposite signs give zero.
equal inputs return same value	VanLeer(a,a) = a.

FWBAP_L2_Biway (weighted-bounded averaging, L2 norm)

Test case	Description
identical inputs pass through	WBAP(u,u) = u for any u.
no NaN for random inputs	Robustness: random arrays produce finite results.
output bounded by inputs for same-sign	All-positive inputs yield non-negative output.

FWBAP_L2_Cut_Biway

Test case	Description
opposite-sign cut to zero	Opposite-sign pairs are hard-zeroed.
no NaN	Random inputs produce finite results.

Multiway Limiters

Test case	Description
FWBAP_L2_Multiway: all identical pass through	4 identical inputs produce the same output.
FWBAP_L2_Multiway: no NaN	5 random stencils produce finite results.
FWBAP_L2_Multiway_Polynomial2D: all identical pass through	Polynomial-norm variant preserves identical inputs.
FWBAP_L2_Multiway_Polynomial2D: no NaN (nRows=2,3,4)	Robust across P1/P2/P3 row counts.
FMEMM_Multiway_Polynomial2D: center unchanged when smallest	MEMM leaves the minimum-norm candidate untouched.
FMEMM_Multiway_Polynomial2D: no NaN	Random inputs produce finite results.
FWBAP_L2_Multiway_PolynomialOrth: all identical pass through	Orthogonal variant preserves identical inputs.
FWBAP_L2_Multiway_PolynomialOrth: no NaN	Robustness check.

Biway Polynomial-Norm Limiters

Test case	Description
FWBAP_L2_Biway_PolynomialNorm<2,1>: identical inputs pass through	Fixed-1-var variant preserves identical inputs.
FWBAP_L2_Biway_PolynomialNorm<2,Dynamic>: no NaN	Dynamic-var variant is NaN-free.
FWBAP_L2_Biway_PolynomialNorm<3,Dynamic>: no NaN for 3D dims	Tests nRows in {3,6,10}.
FMEMM_Biway_PolynomialNorm<2,Dynamic>: u2 smaller returns u2	MEMM reduces toward the smaller-norm input.
FMEMM_Biway_PolynomialNorm<2,Dynamic>: no NaN	Robustness check.
FWBAP_L2_Biway_PolynomialOrth: identical inputs pass through	Orthogonal biway preserves identical inputs.
FWBAP_L2_Biway_PolynomialOrth: no NaN	Robustness check.

Cross-Consistency and Edge Cases

Test case	Description
Limiter ordering: FMINMOD <= FWBAP for same-sign	Minmod is the most restrictive; 100-element check.
All limiters handle near-zero inputs without NaN	Inputs at 1e-300: 6 subcases (MINMOD, VanLeer, WBAP, Cut, PolyNorm, PolyOrth).

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Variational Reconstruction 2D (test_Reconstruction.cpp)

See also

test_Reconstruction.cpp

MPI tests (np=1,2,4) exercising the full VR pipeline for scalar fields on 2D meshes. Uses Jacobi iteration (SOR disabled) for MPI-deterministic golden values.

Meshes

Mesh	Cells	Domain	Boundary
Uniform_3x3_wall.cgns	9 quads	[-1, 2]^2	Wall (Dirichlet)
IV10_10.cgns	100 quads	[0, 10]^2	Periodic
IV10U_10.cgns	322 tris	[0, 10]^2	Periodic

Periodic meshes are bisected 0/1/2 times via O2-elevation + bisection (yielding 100/400/1600 quads and 322/~1288/~5152 tris).

Reconstruction Methods

Label	Description
GG	Explicit 2nd-order Gauss-Green gradient
P1-HQM	Iterative VFV, maxOrder=1, HQM_OPT + HQM_SD weights
P2-HQM	Iterative VFV, maxOrder=2, HQM weights
P3-HQM	Iterative VFV, maxOrder=3, HQM weights
P1-Def	Iterative VFV, maxOrder=1, Factorial + GWNone weights
P2-Def	Iterative VFV, maxOrder=2, default weights
P3-Def	Iterative VFV, maxOrder=3, default weights

Polynomial Exactness (Wall Mesh)

The following tests verify exact recovery of polynomial fields on the 9-cell wall mesh with Dirichlet boundary conditions:

Polynomial	Methods verified exact (error < 1e-12)
Constant (f = 1)	GG, P1-HQM, P2-HQM, P3-HQM, P1-Def
Linear (f = x + 2y)	GG, P1-HQM, P2-HQM, P3-HQM, P1-Def
Quadratic (f = x^2 + y^2)	P2-HQM, P3-HQM, P2-Def
Cubic (f = x^3 + xy^2)	P3-HQM, P3-Def

Convergence Series (Periodic Meshes)

L1/volume errors at bisection levels 0, 1, 2 are compared against golden values captured from commit c774b89 (tolerance 1e-6).

11 parameter combinations:

• IV10 quad + sin*cos: GG, P1-HQM, P2-HQM, P3-HQM, P1-Def, P3-Def
• IV10U tri + sin*cos: GG, P1-HQM, P2-HQM, P3-HQM
• IV10 quad + cos+cos: P3-HQM

Iteration Convergence

VFV P2 HQM converges on IV10 base mesh — verifies the Jacobi iteration reaches an increment below 1e-14 within 200 iterations.

Limiter Procedure Tests

After iterative reconstruction converges, tests apply DoCalculateSmoothIndicator followed by DoLimiterWBAP_C or DoLimiterWBAP_3, then measure the post-limiter L1 error against golden values.

5 parameter combinations:

Mesh	Method	Limiter	Note
IV10 quad	P2-HQM	CWBAP	ifAll=true, 3 bisection levels
IV10 quad	P3-HQM	CWBAP	ifAll=true, 3 bisection levels
IV10U tri	P2-HQM	CWBAP	ifAll=true, 3 bisection levels
IV10 quad	P2-HQM	3WBAP	ifAll=true, 3 bisection levels
IV10 quad	P3-HQM	3WBAP	ifAll=true, 3 bisection levels

The eigenvalue transform (FM/FMI) is set to identity since the test field is scalar (nVars=1).

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Variational Reconstruction 3D (test_Reconstruction3D.cpp)

See also

test_Reconstruction3D.cpp

MPI tests (np=1,2,4) exercising the 3D VR template instantiation. Uses Uniform32_3D_Periodic.cgns (32768 hex cells on the unit cube). 7 test cases.

Constant Exactness

All methods reproduce f=1 with error < 1e-12:

• Gauss-Green
• VFV P1-HQM
• VFV P2-HQM

Golden-Value Regression

6 method/function combinations:

Method	Function	Golden error
GG	sin*cos*cos	1.510e-03
P1-HQM	sin*cos*cos	3.248e-03
P2-HQM	sin*cos*cos	7.482e-05
GG	cos+cos+cos	1.493e-03
P1-HQM	cos+cos+cos	2.426e-03
P2-HQM	cos+cos+cos	3.701e-05

Structural Tests

Test case	Description
VFV P1 HQM converges on sinCos3D	Iteration reaches inc < 1e-14 within 200 iters.
VFV P2 HQM error < P1 on sinCos3D	Higher order gives lower error.
cell volumes sum to 1.0 (unit cube)	Sum of all cell volumes equals domain volume.

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FiniteVolume Python Tests (test_fv_correctness.py)

See also

test_fv_correctness.py

Pytest tests (16 tests) for the CFV.FiniteVolume Python bindings. Uses the Uniform_3x3_wall mesh (9 quads, [-1,2]^2) and IV10_10 periodic mesh (100 quads, [0,10]^2).

Test Classes

TestCellVolumes — Cell volumes are positive and match known values (1.0 per quad for 3x3 wall; sum = 100 for IV10 periodic).

TestGlobalVolume — Global volume sums correctly: 9.0 for wall mesh, 100.0 for periodic mesh.

TestFaceAreas — Face areas are positive; internal face areas equal 1.0 for a uniform grid.

TestCellBarycenters — Barycenters lie within the domain; for the 3x3 wall mesh, barycenters are at half-integer coordinates.

TestDOFArrays — BuildUDof (dynamic and fixed-5), BuildUGrad allocate arrays with correct sizes; DOF write-then-read round-trips.

TestArrayBytes — DataSizeBytes() returns a positive value for both DOF and adjacency arrays.

TestSmoothScale — GetSmoothScale returns a sensible ratio (between 0.1 and 10 for uniform grids).

TestJacobiDet — Cell and face Jacobian determinants are positive.

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VR and ModelEvaluator Python Tests (test_vr_correctness.py)

See also

test_vr_correctness.py

Pytest tests (16 tests) for CFV.VariationalReconstruction and CFV.ModelEvaluator through Python bindings. Uses the Uniform_3x3 periodic mesh (9 quads, [0,3]^2).

Test Classes

TestVRConstruction — Global volume matches 9.0; barycenters lie in [0,3]^2; cell volumes and face areas are positive.

TestVRDOFBuilding — BuildURec, BuildUDof, BuildUGrad produce arrays with correct shapes.

TestConstantExactness — A constant field (u=1 everywhere) produces zero uRec coefficients after reconstruction.

TestLinearFieldReconstruction — Linear field f(x)=x produces uRec coefficients with a dominant first component (approximating df/dx).

TestModelEvaluatorRHS — EvaluateRHS produces finite results; a non-uniform field gives nonzero RHS; a constant field gives near-zero RHS.

TestReconstructionConvergence — Iterative VR converges (increment decreases monotonically).

TestMatrixAccess — matrixAAInvB and vectorAInvB accessors return arrays with correct shapes.

TestBoundaryCallback — getFBoundary returns a callable.