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LUCiFEx Demo

  • Gallery

User Guide

  • Introduction
  • Time-dependence
  • Finite differences
  • Initial conditions
  • Time-dependent boundary conditions
  • Periodic boundary conditions

Introductory

  • Notation
  • 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
  • Helmholtz equation
    • Helmholtz eigenvalue problem in a rectangle
    • Helmholtz boundary value problem in a rectangle
  • Mathieu equation
    • Mathieu eigenvalue problem in an interval

Fluids

  • Notation
  • 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
  • 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

Transport

  • DG formulation of 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 vortex in a rectangle
  • DG formulation of the steady advection-diffusion-reaction equation
    • DG steady advection-diffusion in an interval
    • DG steady advection-diffusion in a rectangle
  • DG formulation of 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 of a rotating pulse in a rectangle

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 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
  • 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
  • .md

Gallery

Contents

  • Convection
  • Fluids
  • Transport
  • Introductory

Gallery#

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 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 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-Taylor instability of a Darcy-Brinkman fluid in a partially porous rectangle Rayleigh-Bénard convection of a Darcy-Brinkman fluid in a partially porous rectangle

Fluids#

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 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

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 vortex in a rectangle DG steady advection-diffusion in an interval DG steady advection-diffusion in a rectangle
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 of a rotating pulse in a rectangle

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 Helmholtz eigenvalue problem in a rectangle Helmholtz boundary value problem in a rectangle
Mathieu eigenvalue problem in an interval

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Introduction

Contents
  • Convection
  • Fluids
  • Transport
  • Introductory

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