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.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
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.
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.
Stokes' paradoxIn the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes equations around an infinitely long cylinder. This is opposed to the 3-dimensional case, where Stokes' method provides a solution to the problem of flow around a sphere. The velocity vector of the fluid may be written in terms of the stream function as The stream function in a Stokes flow problem, satisfies the biharmonic equation.
Ice-sheet modelIn climate modelling, Ice-sheet models use numerical methods to simulate the evolution, dynamics and thermodynamics of ice sheets, such as the Greenland ice sheet, the Antarctic ice sheet or the large ice sheets on the northern hemisphere during the last glacial period. They are used for a variety of purposes, from studies of the glaciation of Earth over glacial–interglacial cycles in the past to projections of ice-sheet decay under future global warming conditions. Beginning in the mid-18th Century, investigation into ice sheet behavior began.
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.
Antarctic ice sheetThe Antarctic ice sheet is one of the two polar ice caps of Earth. It covers about 98% of the Antarctic continent and is the largest single mass of ice on Earth, with an average thickness of over 2 kilometers. Separate to the Antarctic sea ice it covers an area of almost and contains of ice. A cubic kilometer of ice weighs approximately 0.92 metric gigatonnes, meaning that the ice sheet weighs about 24,380,000 gigatonnes. It holds approximately 61% of all fresh water on Earth, equivalent to about 58 meters of sea level rise if all the ice were above sea level.
Ice calvingIce calving, also known as glacier calving or iceberg calving, is the breaking of ice chunks from the edge of a glacier. It is a form of ice ablation or ice disruption. It is the sudden release and breaking away of a mass of ice from a glacier, iceberg, ice front, ice shelf, or crevasse. The ice that breaks away can be classified as an iceberg, but may also be a growler, bergy bit, or a crevasse wall breakaway. Calving of glaciers is often accompanied by a loud cracking or booming sound before blocks of ice up to high break loose and crash into the water.
Ice ageAn ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages and greenhouse periods, during which there are no glaciers on the planet. Earth is currently in the ice age called Quaternary glaciation. Individual pulses of cold climate within an ice age are termed glacial periods (or, alternatively, glacials, glaciations, glacial stages, stadials, stades, or colloquially, ice ages), and intermittent warm periods within an ice age are called interglacials or interstadials.
