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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
    • Viscous fingering of a Darcy fluid in a porous rectangle with Neumann boundary conditions
    • Viscous fingering of a Darcy fluid in a porous rectangle with periodic boundary conditions
    • Viscous fingering of a Darcy fluid 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
  • .md

Gallery

Contents

  • Further Applications
  • Convection
  • Flow
  • Transport
  • Introductory

Gallery#

Further Applications#

Viscous fingering of a Darcy fluid in a porous rectangle with Neumann boundary conditions Viscous fingering of a Darcy fluid in a porous rectangle with periodic boundary conditions Viscous fingering of a Darcy fluid in a porous annulus
ABC convection of a Darcy fluid in a porous rectangle

Convection#

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
Rayleigh-Bénard convection of an isoviscous Stokes fluid Rayleigh-Bénard convection of a non-isoviscous Stokes fluid 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 Rayleigh-Bénard convection of a Darcy-Brinkman fluid in a partially porous rectangle

Flow#

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 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 Flow of Navier-Stokes fluid past a circular obstacle
Flow of a Navier-Stokes fluid with vertical forcing Flow of a Darcy-Brinkman fluid past a permeable obstacle

Transport#

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 steady advection-diffusion-reaction with a skew velocity DG advection-diffusion of a tophat on an interval
DG advection-diffusion in a rectangle SUPG steady advection-diffusion in an interval SUPG steady advection-diffusion of the Hemker problem
SUPG steady advection-diffusion with a skew velocity SUPG advection-diffusion of a Gaussian in an interval SUPG advection-diffusion-reaction of a rotating pulse in a rectangle
Splitting method for the advection-reaction equation Predictor-corrector method for the advection-diffusion equation

Introductory#

Poisson equation in a rectangle Poisson equation on an annulus Vector Poisson equation in a rectangle
Diffusion of a Gaussian in an interval Diffusion of a Gaussian in a rectangle Advection of a Gaussian in an interval
Advection-diffusion of a Gaussian in an interval Advection-diffusion of a Gaussian in a rectangle Helmholtz eigenvalue problem in a rectangle
Helmholtz boundary value problem in a rectangle Mathieu eigenvalue problem in an interval Wave equation in an interval
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 Steady diffusion-reaction with mesh refinement
Poisson equation with method of manufactured solutions

next

Table of partial differential equations

Contents
  • Further Applications
  • Convection
  • Flow
  • Transport
  • Introductory

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