Euler equations (fluid dynamics)In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.
Web-based simulationWeb-based simulation (WBS) is the invocation of computer simulation services over the World Wide Web, specifically through a web browser. Increasingly, the web is being looked upon as an environment for providing modeling and simulation applications, and as such, is an emerging area of investigation within the simulation community. Web-based simulation is used in several contexts: In e-learning, various principles can quickly be illustrated to students by means of interactive computer animations, for example during lecture demonstrations and computer exercises.
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.
Headward erosionHeadward erosion is erosion at the origin of a stream channel, which causes the origin to move back away from the direction of the stream flow, lengthening the stream channel. It can also refer to the widening of a canyon by erosion along its very top edge, when sheets of water first enter the canyon from a more roughly planar surface above it, such as at Canyonlands National Park in Utah. When sheets of water on a roughly planar surface first enter a depression in it, this erodes the top edge of the depression.
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.
Floating-point arithmeticIn computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision: However, unlike 12.345, 12.3456 is not a floating-point number in base ten with five digits of precision—it needs six digits of precision; the nearest floating-point number with only five digits is 12.
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.
Sheet erosionSheet erosion or sheet wash is the even erosion of substrate along a wide area. It occurs in a wide range of settings such as coastal plains, hillslopes, floodplains, beaches, savanna plains and semi-arid plains. Water moving fairly uniformly with a similar thickness over a surface is called sheet flow, and is the cause of sheet erosion. Sheet erosion implies that any flow of water that causes the erosion is not canalized. If a hillslope surface contains many irregularities, sheet erosion may give way to erosion along small channels called rills, which can then converge forming gullies.
Soil erosionSoil erosion is the denudation or wearing away of the upper layer of soil. It is a form of soil degradation. This natural process is caused by the dynamic activity of erosive agents, that is, water, ice (glaciers), snow, air (wind), plants, and animals (including humans). In accordance with these agents, erosion is sometimes divided into water erosion, glacial erosion, snow erosion, wind (aeolean) erosion, zoogenic erosion and anthropogenic erosion such as tillage erosion.
Cycle of erosionThe geographic cycle, or cycle of erosion, is an idealized model that explains the development of relief in landscapes. The model starts with the erosion that follows uplift of land above a base level and ends, if conditions allow, in the formation of a peneplain. Landscapes that show evidence of more than one cycle of erosion are termed "polycyclical". The cycle of erosion and some of its associated concepts have, despite their popularity, been a subject of much criticism.
