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LUCiFEx Demo
Gallery
Table
Notation
Introductory
Poisson equation
Poisson equation in a rectangle
Poisson equation on an annulus
Vector Poisson equation in a rectangle
Diffusion equation
Diffusion of a Gaussian in an interval
Diffusion of a Gaussian in a rectangle
Advection equation
Advection of a Gaussian in an interval
Advection-diffusion equation
Advection-diffusion of a Gaussian in an interval
Advection-diffusion of a Gaussian in a rectangle
Helmholtz equation
Helmholtz eigenvalue problem in a rectangle
Helmholtz boundary value problem in a rectangle
Mathieu equation
Mathieu eigenvalue problem in an interval
Wave equation
Wave equation in an interval
Other boundary conditions
Diffusion-reaction equation with time-dependent Dirichlet boundary conditions
Diffusion equation with time-dependent Neumann boundary conditions
Poisson equation with periodic boundary conditions
Diffusion equation with Robin boundary conditions
Poisson equation with Nitsche boundary conditions
Spatial and temporal resolution
Steady diffusion-reaction with mesh refinement
Poisson equation with method of manufactured solutions
Transport
DG methods for the advection equation
DG advection of a step in an interval
DG advection of a cosine in an interval
DG advection of a rotating cone in a rectangle
DG advection with a vortical velocity
DG methods for the steady advection-diffusion-reaction equation
DG steady advection-diffusion-reaction with a skew velocity
DG methods for the advection-diffusion-reaction equation
DG advection-diffusion of a tophat on an interval
DG advection-diffusion in a rectangle
SUPG stabilization of the steady advection-diffusion-reaction equation
SUPG steady advection-diffusion in an interval
SUPG steady advection-diffusion of the Hemker problem
SUPG steady advection-diffusion with a skew velocity
SUPG stabilization of the advection-diffusion-reaction equation
SUPG advection-diffusion of a Gaussian in an interval
SUPG advection-diffusion-reaction of a rotating pulse in a rectangle
Splitting methods for the transport equation
Splitting method for the advection-reaction equation
Predictor-corrector methods for the transport equation
Predictor-corrector method for the advection-diffusion equation
Flow
Darcy equations
Flow of a Darcy fluid through a lens of low permeability
Flow of a Darcy fluid across an anticline of heterogeneous permeability
Flow of a Darcy fluid in an annulus
Flow of a Darcy fluid injected and extracted in a porous rectangle
Stokes equations
Flow of a Stokes fluid in a pressure-driven channel
Flow of a Stokes fluid in a lid-driven cavity
Flow of a Stokes fluid with vertical forcing
Flow of a Stokes fluid in a corrugated channel
Navier-Stokes equations
Flow of Navier-Stokes fluid past a circular obstacle
Flow of a Navier-Stokes fluid with vertical forcing
Darcy-Brinkman equations
Flow of a Darcy-Brinkman fluid past a permeable obstacle
Convection
Darcy convection equations
Rayleigh-Bénard convection of a Darcy fluid in a porous rectangle
Rayleigh-Bénard convection of a Darcy fluid in a porous annulus
Rayleigh-Bénard convection of a Darcy fluid in a porous semicircle
Evolving convection of a Darcy fluid in an isotropic porous rectangle
Evolving convection of a Darcy fluid in a cross-bedded porous rectangle
Evolving convection of a Darcy fluid in a layered porous rectangle
Evolving convection of a Darcy fluid in an inclined porous rectangle
Elder convection of a Darcy fluid in a porous rectangle
Data-driven convection of a Darcy fluid in a porous rectangle
Stokes convection equations
Rayleigh-Bénard convection of an isoviscous Stokes fluid
Rayleigh-Bénard convection of a non-isoviscous Stokes fluid
Navier-Stokes convection equations
Thermosolutal convection of a Navier-Stokes fluid in a rectangle
Rayleigh-Taylor instability of a Navier-Stokes fluid in a rectangle
Marangoni convection of a Navier-Stokes fluid in a rectangle
Darcy-Brinkman convection equations
Rayleigh-Bénard convection of a Darcy-Brinkman fluid in a partially porous rectangle
Further Applications
Darcy fingering equations
Darcy fingering in a porous rectangle with Neumann boundary conditions
Darcy fingering in a porous rectangle with periodic boundary conditions
Darcy fingering in a porous annulus
Darcy ABC convection-reaction equations
ABC convection of a Darcy fluid in a porous rectangle
Benchmarks
Rayleigh-Bénard convection benchmark
Taylor-Green vortex benchmark
.ipynb
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Flow of a Darcy-Brinkman fluid past a permeable obstacle
Flow of a Darcy-Brinkman fluid past a permeable obstacle
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