Computational fluid dynamics

Computational fluid dynamics
Lawrence Livermore National Laboratory · Public domain · source
Name	Computational fluid dynamics
Field	Aerospace engineering, Mechanical engineering, Chemical engineering
Introduced	1960s
Pioneers	John von Neumann, Lewis Fry Richardson, Ludwig Prandtl

Computational fluid dynamics

Computational fluid dynamics is the numerical study of fluid flow using algorithms implemented on computers to solve the equations of fluid motion. Practitioners combine models from Isaac Newton-era continuum mechanics with numerical methods developed by figures associated with Alan Turing, John von Neumann, Norbert Wiener, and institutions like Massachusetts Institute of Technology, Stanford University, NASA. The field supports design and analysis in sectors linked to Wright brothers-era aviation, Apollo program-scale spaceflight, Shell plc, ExxonMobil, and national laboratories such as Oak Ridge National Laboratory.

Overview

CFD emerged from efforts by researchers including Lewis Fry Richardson, Ludwig Prandtl, and John von Neumann to discretize partial differential equations on early computers like those at Los Alamos National Laboratory and University of Cambridge Computer Laboratory. The discipline sits at the intersection of practices associated with Aerospace engineering, Mechanical engineering, Navier–Stokes equations-focused research groups, and industrial programs at organizations such as Rolls-Royce, Boeing, Airbus, General Electric, and Siemens. Historical milestones include contributions from centers like NASA Ames Research Center, research consortia tied to DARPA, and initiatives connected to the European Space Agency.

Governing Equations and Physical Models

Governing equations derive from conservation laws linked to names like Leonhard Euler and Claude-Louis Navier; principal formulations include the compressible and incompressible forms of the Navier–Stokes equations studied in contexts such as Prandtl boundary layer theory and problems explored by Osborne Reynolds. Equations incorporate source terms from heat transfer traditions following Joseph Fourier and mass transfer traditions related to Thomas Graham (chemist). Multiphase and reacting flows use models developed alongside programs at Sandia National Laboratories and research associated with Max Planck Society. Constitutive relations often reference material databases maintained by institutions such as National Institute of Standards and Technology.

Numerical Methods and Algorithms

Discretization approaches reflect methods advanced by mathematicians from circles around Isaac Newton-era calculus to later contributors like John von Neumann and Richard Courant. Finite volume techniques propagate lineage from work at Imperial College London and École Polytechnique; finite element methods trace through Richard Courant and implementations used at ETH Zurich and Darmstadt University of Technology. Spectral methods connect to studies by J. H. Wilkinson and numerical linear algebra developed at Los Alamos National Laboratory. Time integration algorithms relate to solvers from Argonne National Laboratory and stability analyses influenced by Andrey Kolmogorov. Linear and nonlinear solvers incorporate libraries from projects at Lawrence Berkeley National Laboratory and collaborations with Microsoft Research and IBM Research.

Boundary Conditions and Turbulence Modeling

Boundary treatments build on experimental programs conducted at facilities such as National Physical Laboratory (United Kingdom) and wind tunnels at Wright-Patterson Air Force Base; inlet, outlet, and wall conditions reflect standards used by NASA Glenn Research Center and manufacturers like General Electric. Turbulence modeling evolved via seminal contributions by Andrey Kolmogorov, Ludwig Prandtl, Theodore von Kármán, and later developers of models used across Imperial College London and University of Cambridge—including Reynolds-averaged approaches, large eddy simulation concepts championed at Stanford University, and direct numerical simulation campaigns run on supercomputers at Argonne National Laboratory and Oak Ridge National Laboratory.

Software and Implementation

CFD software ecosystems include proprietary suites from ANSYS, Siemens PLM Software, and Dassault Systèmes as well as open-source projects originating with contributors connected to École Polytechnique Fédérale de Lausanne, Princeton University, and OpenFOAM Foundation. High-performance implementations exploit architectures developed by NVIDIA, Intel, and national infrastructure provisioned by National Science Foundation-funded centers. Verification and coding practices reference standards promoted by IEEE and software engineering groups at Carnegie Mellon University.

Applications and Industries

Applications span aviation work driven by Wright brothers-derived firms such as Boeing and Airbus, aerospace programs epitomized by Apollo program-era missions and current SpaceX developments, power generation industries involving General Electric and Siemens, and chemical processing plants managed by Dow Chemical Company and BASF. Other domains include automotive engineering led by Toyota and Volkswagen, biomedical flows studied at Johns Hopkins University and Mayo Clinic, environmental modeling tied to agencies like Environmental Protection Agency, and sports engineering collaborations with teams in competitions such as Formula One.

Validation, Verification, and Performance Considerations

Verification and validation workflows draw on practices from metrology institutions like National Institute of Standards and Technology and atmospheric campaigns coordinated with National Oceanic and Atmospheric Administration. Performance tuning leverages benchmarks run on systems at Lawrence Livermore National Laboratory, Argonne National Laboratory, and cloud providers such as Amazon Web Services that partner with research groups at University of Illinois Urbana-Champaign and University of Michigan. Governance of computational accuracy is informed by test cases originating in classical experiments by Osborne Reynolds, standardized suites distributed by research consortia including ERCOFTAC and committees assembled under the aegis of International Council on Systems Engineering.

Category:Computational physics