Numerical solution of the Navier-Stokes equations

1968/01/01 by Alexandre Joel Chorin, Alexandre J. Chorin · 72 citations
Engineering · Mathematics · #Lattice Boltzmann Simulation Studies #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions

paper · doi:10.1090/s0025-5718-1968-0242392-2

Abstract

A finite-difference method for solving the time-dependent NavierStokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an application to a three-dimensional convection problem is presented.

Cited by

• New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
• A priori and a posteriori analysis of finite volume discretizations of Darcy?s equations
• Patient-Specific Modelling of Blood Coagulation
• The structure of the solution to the generalized Stokes equations and a new method for solving them
• Second Order Reduced Model via Incremental Projection for Navier Stokes
• Training-Free Bayesian Filtering with Generative Emulators
• Extending a serial 3D two-phase CFD code to parallel execution over MPI by using the PETSc library for domain decomposition
• Hydrodynamics of Lock-exchange Turbidity Currents down a Slope Based on Direct Numerical Simulation
• A time-splitting finite-element approximation for the Ericksen-Leslie equations
• A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks
• A family of energy stable, skew-symmetric finite difference schemes on\n collocated grids
• On the Reynolds-number scaling of Poisson solver complexity
• Optimal mixing in two-dimensional stratified plane Poiseuille flow at finite Peclet and Richardson numbers
• Transient growth calculations obtained directly from the Orr-Sommerfeld matrices
• Optimal first-order error estimates of a fully segregation scheme for the Navier-Stokes equations
• A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations
• Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics
• A pressure-projection formulation in a least-squares meshfree method for the incompressible Navier-Stokes equations using a staggered-variable arrangement
• Vortices, turbulence, and center of pressure in flow over pitching swept wings
• An efficient fully decoupled finite element method with second-order accuracy for the micropolar Rayleigh-Benard convection system
• Solution of Incompressible Flow Equations with Physics and Equality Constrained Artificial Neural Networks
• pyro: A teaching code for computational astrophysical hydrodynamics
• Modelling of Flow Past Long Cylindrical Structures
• Gravity current propagating against constant and pulsating counter flows
• Quaternion wavefunction formulation of incompressible inviscid fluid dynamics
• Diversity in emergent cell locomotion from the coupling cytosolic and cortical Marangoni flows with reaction-diffusion dynamics
• Evaluating simulation techniques for lubricant distribution in gearboxes
• Unconditionally stable Gauge-Uzawa finite element schemes for the chemo-repulsion-Navier-Stokes system
• Dynamics of retracting surfactant-laden ligaments at intermediate Ohnesorge number
• Deep Multi-Fidelity Active Learning of High-dimensional Outputs
• Linear and Nonlinear Stability Analysis in Microfluidic Systems
• A viscosity-splitting scheme for the nonlinear fluid-fluid interaction problem
• An adaptive implicit deferred correction method for incompressible flow
• Modern discontinuous Galerkin methods for the simulation of transitional\n and turbulent flows in biomedical engineering: A comprehensive LES study of\n the FDA benchmark nozzle model
• DPM: A deep learning PDE augmentation method (with application to\n large-eddy simulation)
• A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
• A phase inversion benchmark for multiscale multiphase flows
• Convergence analysis of a fractional time-stepping technique for incompressible fluids with microstructure
• Convergence Analysis of a Class of Massively Parallel Direction Splitting Algorithms for the Navier-Stokes Equations
• Leray weak solutions of the Incompressible Navier Stokes system on exterior domains via the artificial compressibility method
• Gauss Principle in Incompressible Flow: Unified Variational Perspective on Pressure and Projection
• Smart Sensor Placement: A Correlation-Aware Attribution Framework (CAAF) for Real-world Data Modeling
• On the artificial compressibility method for the Navier Stokes Fourier system
• Numerical Methods for Viscoelastic Fluid Flows
• Physics-informed Neural-operator Predictive Control for Drag Reduction in Turbulent Flows
• oRANS: Online optimisation of RANS machine learning models with embedded DNS data generation
• A Besov-based integration-by-parts method for the incompressible Navier-Stokes equations
• Interface tracking using patches
• Introducing new morphometric parameters to improve urban canopy air flow modeling: A CFD to machine-learning study in real urban environments
• Scalable Variational Gaussian Process Regression Networks
• Beyond smoothness: the art of surface texturing battling against friction
• A Variable Stepsize, Variable Order Family of Low Complexity
• On the accurate evaluation of unsteady Stokes layer potentials in moving two-dimensional geometries
• Training-Free Data Assimilation with GenCast
• A nonhydrostatic version of FVCOM: 1. Validation experiments
• An adaptive Hermite spectral method for the Boltzmann equation
• kh2d-solver: A Python Library for Idealized Two-Dimensional Incompressible Kelvin-Helmholtz Instability
• A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows
• A hybrid Eulerian-Lagrangian flow solver
• Convergence of a Second-Order Projection Method to Leray-Hopf Solutions of the Incompressible Navier-Stokes Equations
• On the Accuracy of Finite-Volume Schemes for Fluctuating Hydrodynamics
• Down-scale marine hydrodynamic analysis at the Norwegian coast -- the NORA-SARAH open framework
• Adjoint-Based Optimal Control of Time-Dependent Free Boundary Problems
• A new embedded variable stepsize, variable order family of low computational complexity
• A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces
• Reference Map Technique for Incompressible Fluid-Structure Interaction
• A convergence proof for a finite element discretization of Chorin's projection method of the incompressible Navier-Stokes equations
• Flow Matching for Efficient and Scalable Data Assimilation
• Deep Coregionalization for the Emulation of Spatial-Temporal Fields
• An optimal complexity spectral method for Navier--Stokes simulations in the ball
• Error estimates of linear decoupled structure-preserving incremental viscosity splitting methods for the Cahn--Hilliard--Navier--Stokes system
• Quantum Solvers: Predictive Aeroacoustic & Aerodynamic modeling

Related

• A finite difference method for inhomogeneous incompressible Navier-Stokes equations
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• Analytical solution of the incompressible Navier-Stokes equations
• Investigation of 2-dimensional fluid flow using finite difference flow method of Navier-Stokes equation
• Analytical solution for 3-dimensional, incompressible Navier-Stokes equations