Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
SailboatA sailboat or sailing boat is a boat propelled partly or entirely by sails and is smaller than a sailing ship. Distinctions in what constitutes a sailing boat and ship vary by region and maritime culture. List of sailing boat types Although sailboat terminology has varied across history, many terms have specific meanings in the context of modern yachting. A great number of sailboat-types may be distinguished by size, hull configuration, keel type, purpose, number and configuration of masts, and sail plan.
YachtA yacht jɒt is a sailing or power vessel used for pleasure, cruising, or racing. There is no standard definition, though the term generally applies to vessels with a cabin intended for overnight use. To be termed a , as opposed to a , such a pleasure vessel is likely to be at least in length and may have been judged to have good aesthetic qualities. The Commercial Yacht Code classifies yachts and over as . Such yachts typically require a hired crew and have higher construction standards.
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Large eddy simulationLarge eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer. The simulation of turbulent flows by numerically solving the Navier–Stokes equations requires resolving a very wide range of time and length scales, all of which affect the flow field.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Sailing yachtA sailing yacht (US ship prefixes SY or S/Y), is a leisure craft that uses sails as its primary means of propulsion. A yacht may be a sail or power vessel used for pleasure, cruising, or racing. There is no standard definition, so the term applies here to sailing vessels that have a cabin with amenities that accommodate overnight use. To be termed a "yacht", as opposed to a "boat", such a vessel is likely to be at least in length and have been judged to have good aesthetic qualities.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Fluid dynamicsIn physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Computational fluid dynamicsComputational 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 (liquids and gases) 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.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Boat racingBoat racing is a sport in which boats, or other types of watercraft, race on water. Boat racing powered by oars is recorded as having occurred in ancient Egypt, and it is likely that people have engaged in races involving boats and other water-borne craft for as long as such watercraft have existed. A regatta is a series of boat races. The term comes from the Venetian language, with regata meaning "contest, contention for mastery"(from regatare ("compete, haggle, sell at retail"), possibly from ''recatare') and typically describes racing events of rowed or sailed water craft, although some powerboat race series are also called regattas.
Atmospheric modelIn atmospheric science, an atmospheric model is a mathematical model constructed around the full set of primitive, dynamical equations which govern atmospheric motions. It can supplement these equations with parameterizations for turbulent diffusion, radiation, moist processes (clouds and precipitation), heat exchange, soil, vegetation, surface water, the kinematic effects of terrain, and convection. Most atmospheric models are numerical, i.e. they discretize equations of motion.
Boat buildingBoat building is the design and construction of boats and their systems. This includes at a minimum a hull, with propulsion, mechanical, navigation, safety and other systems as a craft requires. Wood is the traditional boat building material used for hull and spar construction. It is buoyant, widely available and easily worked. It is a popular material for small boats (of e.g. length; such as dinghies and sailboats). Its abrasion resistance varies according to the hardness and density of the wood and it can deteriorate if fresh water or marine organisms are allowed to penetrate the wood.
SailA sail is a tensile structure, which is made from fabric or other membrane materials, that uses wind power to propel sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and even sail-powered land vehicles. Sails may be made from a combination of woven materials—including canvas or polyester cloth, laminated membranes or bonded filaments, usually in a three- or four-sided shape. A sail provides propulsive force via a combination of lift and drag, depending on its angle of attack, its angle with respect to the apparent wind.
Fluid mechanicsFluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
Forces on sailsForces on sails result from movement of air that interacts with sails and gives them motive power for sailing craft, including sailing ships, sailboats, windsurfers, ice boats, and sail-powered land vehicles. Similar principles in a rotating frame of reference apply to windmill sails and wind turbine blades, which are also wind-driven. They are differentiated from forces on wings, and propeller blades, the actions of which are not adjusted to the wind.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
