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version 3.11-dev
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version 3.11-dev
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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.
| 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) [114] and Schnepf et al. (2020) [98] |
| | ↗️ 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) [114] and Schnepf et al. (2020) [98] |
 | ↗️ 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 [55] [64] |
| ↗️ Udell's Heat Pipe | 1D, non-isothermal, phase change, 2p1c, PQ1 CVFE (Box) scheme, Two-point flux approximation (Tpfa) | Steady counter-current liquid-vapor flow driven by a heat flux; first-order convergence with full upwinding and second-order convergence with central mobility weighting towards semi-analytical solution of Udell (1985) [113] |
 | ↗️ 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). |
| ↗️ Radial Injection into a Confined Aquifer | CO2 storage, vertical equilibrium, 2pve, Two-point flux approximation (Tpfa) | Interface of a CO2 plume injected into a confined aquifer; comparison with the similarity solution of Nordbotten and Celia (2006) [78] |
| 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 [109] |
| Image | Benchmark description | Topics | Comment |
|---|---|---|---|
| ↗️ Wet Dam Break | Riemann problem, Shallow water flow, Two-point flux approximation (Tpfa) | Bore and rarefaction wave after the removal of a gate; the relative \(L^1\) errors converge with approximately first order towards the exact solution [107], with the same rates as a textbook first-order Godunov scheme |
| ↗️ Oscillation in a Paraboloid Bowl (Thacker) | wetting and drying, Shallow water flow, Two-point flux approximation (Tpfa) | Oscillation of the free surface in a bowl without friction with a moving shoreline; the first-order scheme damps the oscillation, and the relative \(L^1\) error of the water depth converges with approximately first order on fine grids towards the exact solution [111] |
| ↗️ Lake at Rest | well-balancing, wetting and drying, Shallow water flow, Two-point flux approximation (Tpfa) | Water at rest over a hump [67] and a sill with discontinuous flanks; preserved to round-off on a submerged bed |
| ↗️ Shallow Water Poiseuille Flow | viscous flux, bed friction, Shallow water flow, Two-point flux approximation (Tpfa) | Steady channel flow with an eddy viscosity and no-slip side walls, and laminar film flow with viscous bed friction; approximately first-order convergence along the channel, caused by the bed being constant in each cell, and approximately second-order convergence across the channel towards the exact velocity |
| ↗️ Flow in a Rough Channel | bed friction, Shallow water flow, Two-point flux approximation (Tpfa) | Normal flow with the friction law of Gauckler, Manning and Strickler; approximately first-order convergence towards the normal depth, caused by the bed being constant in each cell |
| 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 [26] | |
| ↗️ Hyperelastic Dynamic (CSM1-3) | solid mechanics, hyperelasticity, PQ1 CVFE (Box) scheme | oscillating/flapping thin solid rectangle ; comparison against reference data from [112] |
| ↗️ 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 [99] |
| ↗️ 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 [99] |
 | ↗️ Cardiac Elastodynamics | solid mechanics, hyperelasticity, elastodynamics, Hyperelastic solid mechanics, PQ2 finite elements | A DuMux module for the heartbeat of an idealized left ventricle and biventricle (anisotropic, nearly incompressible, viscous, actively contracting material); probe displacements compared with the participants of [11] (code) |
| 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] |
| ↗️ Cryer Sphere Consolidation | poromechanics, consolidation, large deformation, 1p, Solid mechanics with fluid pressure, Large-deformation poroelasticity, Multi-point flux approximation (Mpfa), PQ2 CVFE scheme, PQ1 CVFE (Box) scheme, Multidomain framework | Mandel–Cryer effect: the centre pore pressure of a drained poroelastic sphere overshoots the surface load; linear and large-deformation poroelasticity, comparison with Cryer's solution [33] |
| 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 |
3.11-dev
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