Euler Module Unit Tests

Table of Contents

• Building and Running
• Target Summary
• Gas Thermodynamics and Eigenvectors (test_GasThermo.cpp)
  • IdealGasThermal
  • Conservative / Primitive Round-Trip
  • Stagnation Quantities
  • Eigenvectors
  • Inviscid Flux
  • Conservative Increments
  • Roe Average
  • Gradient Transformation
  • Compression Ratio and Viscous Flux
• Riemann Solvers (test_RiemannSolvers.cpp)
  • Consistency (F(U,U) = exact flux)
  • Variant Consistency
  • Symmetry (F(UL,UR,n) = -F(UR,UL,-n))
  • Sod Shock Tube
  • Golden Values
  • Additional Checks
• RANS Turbulence Models (test_RANS.cpp)
  • Turbulent Viscosity (GetMut)
  • Mut Sensitivity
  • Source Terms (GetSource, mode=0: full)
  • Source Terms (mode=1: implicit Jacobian diagonal)
  • Viscous Flux (GetVisFlux)
• EulerEvaluator Pipeline (test_EulerEvaluator.cpp)
  • Test Cases
  • Pipeline Steps

Tests for the compressible Navier-Stokes solver module (src/Euler/). All C++ tests use doctest.

Building and Running

# Build all Euler C++ test executables
cmake --build build -t euler_unit_tests -j8
 
# Run every Euler CTest (serial + MPI np=1,2,4)
ctest --test-dir build -R euler_ --output-on-failure
 
# Run a single test
ctest --test-dir build -R euler_gas_thermo --output-on-failure

Target Summary

CMake target	CTest names	Source file	Type
euler_test_gas_thermo	euler_gas_thermo	test_GasThermo.cpp	Serial
euler_test_riemann_solvers	euler_riemann_solvers	test_RiemannSolvers.cpp	Serial
euler_test_rans	euler_rans	test_RANS.cpp	Serial
euler_test_evaluator_pipeline	euler_evaluator_pipeline_np{1,2,4}	test_EulerEvaluator.cpp	MPI (600 s)

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Gas Thermodynamics and Eigenvectors (test_GasThermo.cpp)

See also

test_GasThermo.cpp

Serial tests for ideal-gas thermodynamics and Euler eigenvector routines in Gas.hpp. 22 test cases, 93 assertions. No MPI or mesh; all functions are pure.

IdealGasThermal

Test case	Description
standard quiescent air	rho=1, p=1/gamma: checks a=1, H=gamma/(gamma-1), internal energy.
Mach 2 flow	Supersonic state: verifies p, a, H, total energy.

Conservative / Primitive Round-Trip

Test case	Description
Cons2Prim and Prim2Cons round-trip: 3D	5-component state round-trips to 1e-14.
Cons2Prim and Prim2Cons round-trip: 2D	4-component state round-trips to 1e-14.
Prim2Cons: known state verification	Manually computed state matches exactly.

Stagnation Quantities

Test case	Description
PrimitiveGetP0T0: quiescent gas	At rest: p0 = p, T0 = T.
PrimitiveGetP0T0: p0 > p for moving gas	Stagnation pressure exceeds static pressure.

Eigenvectors

Verifies L * R = I (orthogonality) for the Euler flux Jacobian eigenvectors.

Test case	Description
EulerGas eigenvectors: L*R = I for 3D	Quiescent state, x-normal.
EulerGas eigenvectors: L*R = I for non-trivial velocity	Moving flow, oblique normal.
IdealGas convenience wrappers produce L*R=I	Same check via IdealGas_EulerGasRight/LeftEigenVector.

Inviscid Flux

Test case	Description
GasInviscidFlux: x-direction, quiescent gas	F = [0, p, 0, 0, 0] at rest.
GasInviscidFlux: x-direction, moving gas	Full flux against hand-computed values.
GasInviscidFlux_XY: n=(1,0,0) equals GasInviscidFlux	Rotated-normal variant matches direct formula.

Conservative Increments

Test case	Description
IdealGasUIncrement: zero increment gives zero	delta_U = 0 produces delta_{u,p} = 0.
IdealGasUIncrement: finite-difference verification	Increment matches prim(U+dU) - prim(U) to O(dU^2).

Roe Average

Test case	Description
GetRoeAverage: identical states give same state	Roe(U,U) = U.
GetRoeAverage: density is geometric mean	rho_Roe = sqrt(rhoL * rhoR).

Gradient Transformation

Test case	Description
GradientCons2Prim: zero gradient produces zero	Pure sanity check.
GradientCons2Prim: finite-difference verification	Transformed gradient matches numerical differentiation.

Compression Ratio and Viscous Flux

Test case	Description
CompressionRatio: zero increment gives alpha=0	No compression needed for zero perturbation.
CompressionRatio: alpha in [0,1]	Output is bounded for random perturbations.
ViscousFlux: zero gradient produces zero flux	Sanity check for viscous flux routine.

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Riemann Solvers (test_RiemannSolvers.cpp)

See also

test_RiemannSolvers.cpp

Serial tests for Roe, HLLC, and HLLEP Riemann solvers in Gas.hpp. 11 test cases, 147 assertions.

Consistency (F(U,U) = exact flux)

Test case	Description
Roe consistency: identical states give exact flux	F_Roe(U,U,n) == F_exact(U,n).
HLLC consistency	Same check for HLLC.
HLLEP consistency	Same check for HLLEP.
Roe consistency: diagonal normal	Oblique normal n = (1,1,1)/sqrt(3).

Variant Consistency

Test case	Description
Roe variants M1-M8 consistency	eigScheme 1,3,4,5,6,7,8 pass consistency; 2 and 9 are unimplemented.

Symmetry (F(UL,UR,n) = -F(UR,UL,-n))

Test case	Description
Roe symmetry	Verified for 3 state pairs.
HLLC symmetry	Same check with 3 pairs.

Sod Shock Tube

Test case	Description
Sod shock tube: flux is finite and bounded	UL=(1,0,0,0,2.5), UR=(0.125,0,0,0,0.25): flux has finite components.

Golden Values

Test case	Description
Golden flux values for mixed-state test vector	Roe, HLLC, HLLEP flux components against captured golden values (tolerance 1e-8).

Additional Checks

Test case	Description
All solvers: quiescent gas produces same flux	Roe, HLLC, HLLEP agree on a zero-velocity state.
Roe eigenvalue output: lam0 < lam123 < lam4 for subsonic	Wave speed ordering: u-a < u < u+a.

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RANS Turbulence Models (test_RANS.cpp)

See also

test_RANS.cpp

Serial tests for k-omega Wilcox 2006, k-omega SST, and Realizable k-epsilon model functions in RANS_ke.hpp. 26 test cases, 48 assertions.

The SA model is excluded because GetSource_SA references EulerEvaluator::settings (evaluator context) and cannot be tested standalone. SA coverage is provided through the EulerEvaluator pipeline test on the NACA0012 case.

Turbulent Viscosity (GetMut)

Test case	Description
GetMut_KOWilcox: non-negative	mut >= 0.
GetMut_KOWilcox: bounded by 1e5 * muLam	CFL3D limiting.
GetMut_KOWilcox: golden value	Regression against captured value.
GetMut_SST: non-negative	mut >= 0.
GetMut_SST: bounded by 1e5 * muLam	CFL3D limiting.
GetMut_SST: golden value	Regression against captured value.
GetMut_RealizableKe: non-negative	mut >= 0.
GetMut_RealizableKe: bounded by 1e5 * muLam	CFL3D limiting.
GetMut_RealizableKe: golden value	Regression against captured value.

Mut Sensitivity

Test case	Description
GetMut_KOWilcox: mut increases with k	Higher k produces higher mut.
GetMut_SST: mut increases with k	Same check for SST.
GetMut_KOWilcox: very small k/omega produces finite mut	Robustness near zero.
GetMut_SST: very small k/omega produces finite mut	Robustness near zero.
GetMut_RealizableKe: very small k/eps produces finite mut	Robustness near zero.

Source Terms (GetSource, mode=0: full)

Test case	Description
GetSource_KOWilcox: zero gradient finite and has destruction	Zero velocity gradient: production=0, destruction from omega.
GetSource_SST: zero gradient finite	Same check for SST.
GetSource_RealizableKe: zero gradient finite	Same check for Realizable k-epsilon.
GetSource_KOWilcox: shear gradient golden	Non-zero dU/dx: golden source vector regression.
GetSource_SST: shear gradient golden	Same check for SST.
GetSource_RealizableKe: shear gradient golden	Same check for Realizable k-epsilon.

Source Terms (mode=1: implicit Jacobian diagonal)

Test case	Description
GetSource_KOWilcox mode=1: implicit diagonal non-negative	Diagonal terms are >= 0 (stabilizing).
GetSource_SST mode=1: implicit diagonal non-negative	Same check for SST.

Viscous Flux (GetVisFlux)

Test case	Description
GetVisFlux_KOWilcox: zero gradient -> zero flux	No gradient, no transport.
GetVisFlux_SST: zero gradient -> zero flux	Same for SST.
GetVisFlux_RealizableKe: zero gradient -> zero flux	Same for Realizable k-epsilon.
GetVisFlux_KOWilcox: k-gradient produces k-flux	Non-zero dk/dx generates flux in the k-equation.

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EulerEvaluator Pipeline (test_EulerEvaluator.cpp)

See also

test_EulerEvaluator.cpp

MPI integration test (np=1,2,4, 600 s timeout) exercising the full evaluator pipeline: config → mesh → initialize DOF → EvaluateDt → EvaluateRHS → Jacobi solve (Forward + Backward).

For each case the test measures:

• RHS L1 norm (golden regression)
• Jacobi increment L1 norm (golden regression)

Jacobi update (not LU-SGS) is used for MPI-deterministic increment norms.

Test Cases

Test case	Config	Physics	Mesh	Notes
IV (NS, P1, 2D)	euler_config_IV.json	Inviscid, isentropic vortex	IV10_10 (100 quads, periodic)	2D Euler
NACA0012 (NS_SA, P1)	eulerSA_config.json	Viscous + SA turbulence	NACA0012_H2 (external, wall)	Tests SA model in-situ
Box (NS_3D, P1)	euler3D_config_Box.json	Inviscid, 3D periodic	Uniform32_3D_Periodic (32768 hexes)	3D Euler

Pipeline Steps

For each case:

1. Write default config with ConfigureFromJson(path, false), then merge-patch with the case JSON and test overrides (Jacobi update, P1, absolute mesh paths).
2. ReadMeshAndInitialize — reads mesh, builds VR.
3. eval.InitializeUDOF(u) — sets initial condition.
4. EvaluateDt — computes local time steps.
5. EvaluateRHS — computes the spatial residual.
6. LUSGSMatrixInit + Forward + Backward — one Jacobi-style iteration (despite the LU-SGS name, the code path uses Jacobi when configured).
7. Check RHS and increment norms against golden values (tolerance 1e-6).