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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
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DG formulation of the steady advection-diffusion-reaction equation
DG formulation of the steady advection-diffusion-reaction equation
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