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Lethe documentation
Lethe documentation
  • Installation
    • Regular Installation on Linux
    • Windows with WSL
    • Installation on Apple ARM (M1 or M2)
    • Docker
    • Running Lethe on Digital Research Alliance of Canada Clusters
  • Applications Overview
  • Folder Structure of Lethe
  • Launching Your First Simulation
  • Parameters Guide
    • General, CFD and Multiphysics
      • Arbitrary Lagrangian-Eulerian
      • Analytical Solution
      • Boundary Conditions - CFD
      • Boundary Conditions - Multiphysics
      • Box Refinement
      • Cahn-Hilliard
      • Constrain Stasis
      • Dimensionality
      • Dynamic Flow Control
      • Finite Element Interpolation (FEM)
      • Force and Torque Calculation
      • Initial Conditions
      • Laser Heat Source
      • Linear Solver
      • Manifolds
      • Mesh
      • Mesh Adaptation
      • Multiphysics
      • Nitsche Immersed Boundary
      • Non-linear Solver
      • Physical Properties
      • Post-processing
      • Restart
      • Simulation Control
      • Source Term
      • Stabilization
      • Timer
      • Tracer Drift Velocity
      • Velocity Source
      • Volume of Fluid (Multiphase Flow)
    • Discrete Element Method (DEM)
      • Boundary Conditions
      • Floating Wall
      • Insertion Info
      • Lagrangian Physical Properties
      • Mesh
      • Model Parameters
      • Post-processing
      • Simulation Control
      • Solid Objects
      • Test
      • Timer
    • Unresolved CFD-DEM
      • CFD-DEM
      • Void Fraction
    • Sharp-Immersed-Boundary
    • Radioactive Particle Tracking (RPT)
      • Detector Parameters
      • FEM Reconstruction
      • Parameter Tuning
      • RPT Parameters
  • Examples
    • Incompressible Flow
      • Lid-Driven Cavity Flow
      • Flow around a Cylinder
      • Taylor-Couette Flow
      • Flow past a Backward-Facing Step
      • Transient Flow around an Ahmed Body
      • Transient Flow around a Cylinder
      • Flow around NACA0012 at Low Reynolds Number
      • Taylor-Couette Flow Using Nitsche Immersed Boundary
      • Flow around a Sphere
      • Taylor-Green Vortex
      • Turbulent Taylor-Couette Flow
      • Flow over Periodic Hills
      • Ribbon Mixer Using a Single Rotating Reference Frame
      • Mixer with Pitched-Blade Turbine Impeller Using Nitsche Immersed Boundary
    • Multiphysics
      • VOF
        • Dam-Break
        • Rayleigh-Taylor Instability
        • Static Bubble
        • Rising Bubble
        • Sloshing in a Rectangular Tank
        • Capillary Wave
        • Rayleigh-Plateau Instability
        • 3D Dam-Break with an Obstacle
        • Water Injection in a Closed Cell
        • Air Bubble Compression
      • Heat Transfer
        • Rayleigh-Bénard Convection
        • Stefan Problem: Melting of a Solid
        • Warming up a Viscous Fluid
        • Melting Cavity
        • Laser Heating
        • Laser Melt Pool
        • Concentric Heat Exchanger
      • Tracer
        • Tracer through CAD Junction in Simplex
      • CHNS
        • Jurin’s Law
        • Bubble detachment in shear flow
    • Discrete Element Method (DEM)
      • Bouncing Particle
      • Oblique Wall Impact
      • Packing in Circle
      • Packing in Ball
      • Small Scale Rotating Drum
      • Small Scale Rotating Drum Postprocessing
      • Rotating Drum
      • Rotation of Box
      • Silo
      • Rectangular Hopper
      • Granular Dam-Break
      • Plate Discharge
      • Bunny Drill
      • Granular Mixer
      • Granuheap
    • Unresolved CFD-DEM
      • Cylindrical Packed Bed
      • Gas-Solid Fluidized Bed
      • Gas-Solid Spouted Bed
      • Liquid-Solid Fluidized Bed
      • Boycott Effect
      • Gas-Solid Spouted Cylinder Bed
      • Dense Pneumatic Conveying
    • Sharp Immersed Boundary Solver
      • Resolved CFD-DEM
        • Sedimentation of One Particle
        • Sedimentation of 64 Particles
      • Incompressible Flow
        • Flow around a Cylinder Using the Sharp Interface Method
        • Non-Newtonian Flow past a Sphere
        • 3D Mixer with Pitched-Blade Turbine Impeller Using Composite Sharp-Immersed Boundary
        • 3D Mixer with Pitched-Blade Turbine Impeller Using OpenCascade Sharp-Immersed Boundary
        • 3D Static Mixer Using RBF Sharp Immersed Boundary
        • Inclined 3D Mixer with Pitched-Blade Turbine Impeller Using Composite Sharp-Immersed Boundary
        • Flow around a Finite Cylindrical Particle Using the Sharp Interface Method
      • Geometry Definition
        • Simple Plane Model From Composite
    • Radioactive Particle Tracking (RPT)
      • Photon Count Calculation in a Cylindrical Vessel
      • Tuning Count Calculation Model Parameters with NOMAD
      • Particle FEM Reconstruction
  • Theory
    • Multiphysics
      • Fluid Dynamics
        • The Incompressible Navier-Stokes Equations
        • Origin of the Finite Element Formulation
        • On the Need for Stabilization
        • Linear Solvers
        • Rheology and Non-Newtonian Fluids
      • Heat Transfer
        • Heat Transfer Equations
        • Finite Element Formulation
        • Stabilization Techniques
      • Passive Tracer
        • Passive Tracer Equations
      • Electromagnetism
        • Time Harmonic Maxwell’s Equations
        • Finite Element Method for Time-Harmonic Maxwell’s Equations
        • Magnetohydrodynamics Equations
    • Multiphase
      • One-Fluid Models
        • The Volume of Fluid (VOF) Method
        • Cahn-Hilliard Method
      • CFD-DEM
        • Discrete Element Method (DEM)
        • Resolved CFD-DEM
        • Unresolved CFD-DEM
  • Tools
    • Updating Test Results
    • Introduction on How to Use GMSH
    • Introduction on How to Use Pointwise
    • How to Automatically Create and Launch Lethe Simulations
    • Remote Data Visualization on ParaView
    • Post-processing Lethe with PyVista
  • Publications
  • Referencing Lethe
  • Contributing
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Fluid Dynamics#

  • The Incompressible Navier-Stokes Equations
  • Origin of the Finite Element Formulation
  • On the Need for Stabilization
  • Linear Solvers
  • Rheology and Non-Newtonian Fluids
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The Incompressible Navier-Stokes Equations
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Multiphysics
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