Benchmarks

The test suite contains a number of verification benchmarks (such as convergence tests against analytical or manufactured solutions). Moreover, DuMux has been employed in multiple collaborative benchmark projects. Below, we provide link to descriptions of these benchmarks and instructions to reproduce the results.

Note

This doc page is currently incomplete. Help expanding the documentation of implemented benchmarks: see issue tracker for more information.

Porous medium flow benchmarks

Image	Benchmark description	Topics	Comment
	↗️ Richards Infiltration (M2.1)	1D, soil infiltration, Richards, Two-point flux approximation (Tpfa)	Travelling-wave benchmark for three soil types (sand, loam, clay); analytical solution from Vanderborght et al. (2005) [101] and Schnepf et al. (2020) [88]
	↗️ Richards Evaporation (M2.2)	1D, soil evaporation, Richards, Two-point flux approximation (Tpfa)	Desorptivity-based evaporation benchmark for three soil types; analytical solution from Vanderborght et al. (2005) [101] and Schnepf et al. (2020) [88]
	↗️ Laplace Annulus Rotational Symmetry (TODO link/readme)	rotational symmetry, 1p	A simple annulus domain with known analytical solution for the Laplace equation with Dirichlet boundary conditions
	↗️ Buckley-Leverett	2p, Two-point flux approximation (Tpfa)	Two-phase fluid displacement
	↗️ McWhorter-Sunada	2p, Two-point flux approximation (Tpfa)	Counter-current imbibition compared with Fučík's semi-analytical reference
	↗️ Onset of Convection (Horton-Rogers-Lapwood)	density-driven flow, Boussinesq approximation, 1pnc, PQ1 CVFE (Box) scheme	Growth rate of a convection cell in a porous layer with dense fluid on top, compared with linear stability theory [48] [57]
	↗️ SPE11	CO2 Storage, 2pnc, CO2	A DuMux module for running the benchmark scenarios of the 11th Society of Petroleum Engineers' Comparative Solution Project (SPE11) from 2024 (organized by J.M. Nordbotten, M. Fernø, A.R. Kovscek, K.-A. Lie, B. Flemisch).
	↗️ SPE10	Upscaling, 2p	A DuMux module for running the benchmark scenarios of the 10th Society of Petroleum Engineers' Comparative Solution Project (SPE10) from 2001 (organized by M. Christie and M. Blunt).

Free flow benchmarks

Image	Benchmark description	Topics	Comment
	↗️ Shear-Driven Cavity Flow	2D, free flow, Navier-Stokes, Staggered Grid Finite Volume Method	Velocity profiles at Re = 1 and Re = 1000 compared against reference data from Ghia et al. (1982) and Jurjević (1999)
	↗️ Taylor-Couette Flow	2D, free flow, Navier-Stokes, Diamond discretization scheme, Two-point flux approximation (Tpfa)	Circular Couette flow between two rotating cylinders at Re = 100; second-order convergence of velocity and pressure towards the analytical solution [98]

Solid mechanics benchmarks

Image	Benchmark description	Topics	Comment
	↗️ Clamped Circular Membrane	plate mechanics, Membrane plate, PQ1 CVFE (Box) scheme	Clamped circular membrane under uniform load; convergence against analytical solution
	↗️ Clamped Circular Plate (Kirchhoff-Love)	plate mechanics, Kirchhoff-Love plate, PQ1 CVFE (Box) scheme, PQ1-B CVFE scheme, Multidomain framework	Clamped circular plate under uniform load; convergence against analytical solution
	↗️ Clamped Circular Plate (Mindlin-Reissner)	plate mechanics, Mindlin-Reissner plate, PQ1 CVFE (Box) scheme, PQ1-B CVFE scheme, Multidomain framework	Clamped circular plate under uniform load with shear correction; convergence against analytical solution
	↗️ Cook's Membrane, Linear Elasticity	solid mechanics, linear elasticity, locking, Solid mechanics linear elasticity, PQ1 CVFE (Box) scheme, PQ1-bubble and PQ2	Tapered panel under shear load with a nearly incompressible material; tip displacement under mesh refinement compared with [22]
	↗️ Hyperelastic Dynamic (CSM1-3)	solid mechanics, hyperelasticity, PQ1 CVFE (Box) scheme	oscillating/flapping thin solid rectangle ; comparison against reference data from [100]
	↗️ Cook's Membrane, Hyperelastic (SPP 1748)	solid mechanics, hyperelasticity, locking, mixed formulation, Hyperelasticity with volumetric-isochoric split, MINI and Taylor–Hood elements	Tapered cantilever under shear load, 2D plane strain and 3D, Poisson's ratio from 0.35 to 0.4999; tip displacement compared with [89]
	↗️ Incompressible Block (SPP 1748)	solid mechanics, hyperelasticity, locking, mixed formulation, Hyperelasticity with volumetric-isochoric split, MINI, Taylor–Hood and Q2–Q1 elements	Nearly incompressible block under a partial surface load; displacement of the load centre compared with [89]

Poromechanics benchmarks

Image	Benchmark description	Topics	Comment
	↗️ Mandel's Problem	poromechanics, consolidation, 1p, Solid mechanics with fluid pressure, Two-point flux approximation (Tpfa), PQ1 CVFE (Box) scheme, Multidomain framework	Consolidation of a poroelastic slab between rigid plates (Mandel-Cryer effect), also with compressible solid grains; comparison with the analytical solution [2]

Time integration benchmarks

Image	Benchmark description	Topics	Comment
	↗️ Time-Stepping Methods	time integration, MultiStageMethod, MultiStageTimeStepper	Observed temporal convergence order and linear stability regions of 8 explicit, implicit and DIRK schemes, verified against analytical references

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