Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
Particle image velocimetry (PIV) is an optical method of flow visualization used in education and research. It is used to obtain instantaneous velocity measurements and related properties in fluids. The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics. The fluid with entrained particles is illuminated so that particles are visible. The motion of the seeding particles is used to calculate speed and direction of the flow being studied.
Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. Also, the level-set method makes it very easy to follow shapes that change topology, for example, when a shape splits in two, develops holes, or the reverse of these operations. All these make the level-set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water.
Velocimetry is the measurement of the velocity of fluids. This is a task often taken for granted, and involves far more complex processes than one might expect. It is often used to solve fluid dynamics problems, study fluid networks, in industrial and process control applications, as well as in the creation of new kinds of fluid flow sensors. Methods of velocimetry include particle image velocimetry and particle tracking velocimetry, Molecular tagging velocimetry, laser-based interferometry, ultrasonic Doppler methods, Doppler sensors, and new signal processing methodologies.
Particle tracking velocimetry (PTV) is a velocimetry method i.e. a technique to measure velocities and trajectories of moving objects. In fluid mechanics research these objects are neutrally buoyant particles that are suspended in fluid flow. As the name suggests, individual particles are tracked, so this technique is a Lagrangian approach, in contrast to particle image velocimetry (PIV), which is an Eulerian method that measures the velocity of the fluid as it passes the observation point, that is fixed in space. There are two experimental PTV methods:
Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them.
In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river.
Stokesian dynamics is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle. The method treats the suspended particles in a discrete sense while the continuum approximation remains valid for the surrounding fluid, i.e., the suspended particles are generally assumed to be significantly larger than the molecules of the solvent. The particles then interact through hydrodynamic forces transmitted via the continuum fluid, and when the particle Reynolds number is small, these forces are determined through the linear Stokes equations. In addition, the method can also resolve non-hydrodynamic forces, such as Brownian forces, arising from the fluctuating motion of the fluid, and interparticle or external forces. Stokesian Dynamics can thus be applied to a variety of problems, including sedimentation, diffusion and rheology, and it aims to provide the same level of understanding for multiphase particulate systems as molecular dynamics does for statistical properties of matter. For rigid particles of radius suspended in an incompressible Newtonian fluid of viscosity and density , the motion of the fluid is governed by the Navier–Stokes equations, while the motion of the particles is described by the coupled equation of motion:
The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions. In the MPM, a continuum body is described by a number of small Lagrangian elements referred to as 'material points'. These material points are surrounded by a background mesh/grid that is used to calculate terms such as the deformation gradient. Unlike other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead categorized as a meshless/meshfree or continuum-based particle method, examples of which are smoothed particle hydrodynamics and peridynamics. Despite the presence of a background mesh, the MPM does not encounter the drawbacks of mesh-based methods which makes it a promising and powerful tool in computational mechanics.
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations. In the immersed boundary method the fluid is represented on an Eulerian coordinate and the structure is represented on a Lagrangian coordinate. For Newtonian fluids governed by the incompressible Navier–Stokes equations, the fluid equations are
Gretar Tryggvason is Department Head of Mechanical Engineering and Charles A. Miller Jr. Distinguished Professor at Johns Hopkins University. He is known for developing the front tracking method to simulate multiphase flows and free surface flows. Tryggvason was the editor-in-chief of Journal of Computational Physics from 2002–2015.
Turbulent diffusion is the transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions. It occurs when turbulent fluid systems reach critical conditions in response to shear flow, which results from a combination of steep concentration gradients, density gradients, and high velocities. It occurs much more rapidly than molecular diffusion and is therefore extremely important for problems concerning mixing and transport in systems dealing with combustion, contaminants, dissolved oxygen, and solutions in industry. In these fields, turbulent diffusion acts as an excellent process for quickly reducing the concentrations of a species in a fluid or environment, in cases where this is needed for rapid mixing during processing, or rapid pollutant or contaminant reduction for safety.
The Semi-Lagrangian scheme (SLS) is a numerical method that is widely used in numerical weather prediction models for the integration of the equations governing atmospheric motion. A Lagrangian description of a system focuses on following individual air parcels along their trajectories as opposed to the Eulerian description, which considers the rate of change of system variables fixed at a particular point in space. A semi-Lagrangian scheme uses Eulerian framework but the discrete equations come from the Lagrangian perspective.
The moving particle semi-implicit (MPS) method is a computational method for the simulation of incompressible free surface flows. It is a macroscopic, deterministic particle method developed by Koshizuka and Oka (1996).
In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium such as density, velocity, pressure, and temperature.
Particle-laden flows refers to a class of two-phase fluid flow, in which one of the phases is continuously connected and the other phase is made up of small, immiscible, and typically dilute particles. Fine aerosol particles in air is an example of a particle-laden flow; the aerosols are the dispersed phase, and the air is the carrier phase.
The multiphase particle-in-cell method (MP-PIC) is a numerical method for modeling particle-fluid and particle-particle interactions in a computational fluid dynamics (CFD) calculation. The MP-PIC method achieves greater stability than its particle-in-cell predecessor by simultaneously treating the solid particles as computational particles and as a continuum. In the MP-PIC approach, the particle properties are mapped from the Lagrangian coordinates to an Eulerian grid through the use of interpolation functions. After evaluation of the continuum derivative terms, the particle properties are mapped back to the individual particles. This method has proven to be stable in dense particle flows, computationally efficient, and physically accurate. This has allowed the MP-PIC method to be used as particle-flow solver for the simulation of industrial-scale chemical processes involving particle-fluid flows.
Magnetic resonance velocimetry (MRV) is an experimental method to obtain velocity fields in fluid mechanics. MRV is based on the phenomenon of nuclear magnetic resonance and adapts a medical magnetic resonance imaging system for the analysis of technical flows. The velocities are usually obtained by phase contrast magnetic resonance imaging techniques. This means velocities are calculated from phase differences in the image data that has been produced using special gradient techniques. MRV can be applied using common medical MRI scanners. The term magnetic resonance velocimetry became current due to the increasing use of MR technology for the measurement of technical flows in engineering.
Joseph Katz is an Israel-born American fluid dynamicist, known for his work on experimental fluid mechanics, cavitation phenomena and multiphase flow, turbulence, turbomachinery flows and oceanography flows, flow-induced vibrations and noise, and development of optical flow diagnostics techniques, including Particle Image Velocimetry (PIV) and Holographic Particle Image Velocimetry (HPIV). As of 2005, he is the William F. Ward Sr. Distinguished Professor at the Department of Mechanical Engineering of the Whiting School of Engineering at the Johns Hopkins University.
Lagrangian ocean analysis is a way of analysing ocean dynamics by computing the trajectories of virtual fluid particles, following the Lagrangian perspective of fluid flow, from a specified velocity field. Often, the Eulerian velocity field used as an input for Lagrangian ocean analysis has been computed using an ocean general circulation model (OGCM). Lagrangian techniques can be employed on a range of scales, from modelling the dispersal of biological matter within the Great Barrier Reef to global scales. Lagrangian ocean analysis has numerous applications, from modelling the diffusion of tracers, through the dispersal of aircraft debris and plastics, to determining the biological connectivity of ocean regions.
