README.md

Examples

To get started with DuMu^x, we recommend the following documented examples. Each example folder contains a ready-to-use DuMu^x simulation example. Click on the respective example to get to a detailed documentation of the example code (best viewed in a browser). For each example in this overview, the model equations and discretization method are described in words and the DuMu^x name of the model is given in parenthesis: e.g. (OneP) / (CCTpfaModel).

📂 Example 1: One-phase flow and tracer transport

In this example, we simulate tracer transport through a confined aquifer with a randomly distributed permeability field. We first solve the pressure field, compute the steady state flow field, and then solve the tracer transport equation. You learn how to generate a randomly distributed permeability field sequentially solve two types of problems after each other: solve a one-phase flow in porous media problem compute the flow field from a pressure solution to pass to a tracer problem solve an unsteady tracer transport problem with a given flow field Model equations: Single-phase flow Darcy equation and advection-diffusion equation in porous media (OneP and Tracer) Discretization method: Cell-centered finite volumes with two-point flux approximation (CCTpfaModel)

📂 Example 2: Two-phase flow with infiltration and adaptive grid

In this example we model a soil contamination problem where a DNAPL (dense non-aqueous phase liquid) infiltrates a water-saturated porous medium (two-phase flow). The initial distribution of DNAPL is read in from a txt-file. The grid is adaptively refined where DNAPL enters the domain, around the plume, and around an injection well. You learn how to solve a two-phase flow in porous media problem with two immiscible phases set boundary conditions and a simple injection well implement a problem with heterogeneous material parameters use adaptive grid refinement around the saturation front Model equations: Immiscible two-phase flow Darcy equations in porous media (TwoP) Discretization method: Cell-centered finite volumes with two-point flux approximation (CCTpfaModel)

📂 Example 3: Shallow water model

The shallow water flow model is applied to simulate steady subcritical flow in a channel including a bottom friction model. You learn how to solve a shallow water flow problem including bottom friction compute and output (VTK) an analytical reference solution Model equations: 2D shallow water equations (ShallowWater) Discretization method: Cell-centered finite volumes with Riemann solver (CCTpfaModel)

📂 Example 4: Freeflow channel

In this example, we simulate a free flow between two plates in two dimensions. You learn how to solve a free flow problem set outflow boundary conditions in the free-flow context Model equations: 2D Stokes equations (NavierStokes) Discretization method: Finite volumes with staggered grid arrangement (StaggeredFreeFlowModel)

📂 Example 5: One-phase flow with rotation-symmetric solution

In this example, a rotation-symmetric solution for the single-phase flow equation is discussed. You learn how to solve a rotation-symmetric problem perform a convergence test against an analytical solution do post-processing in ParaView Model equations: (rotation-symmetric) single-phase flow Darcy equation (OneP) Discretization method: Vertex-centered finite volumes / control-volume finite elements (Lagrange, P1) (BoxModel)

📂 Example 6: Biomineralization

In this example, we simulate microbially-induced calcite precipitation You learn how to solve a reactive transport model including biofilm growth mineral precipitation and dissolution changing porosity and permeability use complex fluid and solid systems set a complex time loop with checkpoints, reading the check points from a file set complex injection boundary conditions, reading the injection types from a file Model equations: Miscible two-phase multi-component flow Darcy equations with precipitation and reaction (TwoPNCMin) Discretization method: Vertex-centered finite volumes / control-volume finite elements (Lagrange, P1) (BoxModel)

📂 Example 7: Lid-driven cavity

In this example, we simulate laminar incompressible flow in a cavity with the Navier-Stokes equations. You learn how to solve a single-phase Navier-Stokes flow problem compare the results of Stokes flow (Re = 1) and Navier-Stokes flow (Re = 1000) compare the numerical results with the reference data using the plotting library matplotlib Model equations: Navier-Stokes equations (NavierStokes) Discretization method: Finite volumes with staggered grid arrangement (StaggeredFreeFlowModel)

📂 Example 8: Permeability estimation using a pore-network model

In this example, we use a single-phase flow pore-network model to estimate the upscaled Darcy permeability of a randomly generated grid. You learn how to solve a single-phase-flow pore-network problem use the total mass flow rate to estimate K_{xx}, K_{yy}, K_{zz} Model equations: Single-phase flow pore-network model (PNMOneP) Discretization method: Pore-network (PoreNetworkModel)

📂 Example 9: Embedded network 1D-3D model (tissue perfusion)

In this example, we compute the spread of a tracer in the blood stream and the embedding tissue (porous medium). We couple a 1D advection-diffusion equation on the network with a 3D diffusion equation in the embedding porous medium. You learn how to setup a multi-domain with domains of different dimension read data from a grid file specify input parameters in multi-domain simulations Model equations: 1D and 3D advection-diffusion equations (Tracer) Discretization method: Cell-centered finite volumes with two-point flux approximation (CCTpfaModel)