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Conservation Form
Conservation form or ''Eulerian form'' refers to an arrangement of an equation or system of equations, usually representing a hyperbolic system, that emphasizes that a property represented is conserved, i.e. a type of continuity equation. The term is usually used in the context of continuum mechanics. General form Equations in conservation form take the form \frac + \boldsymbol \nabla \cdot \mathbf f(\xi) = 0 for any conserved quantity \xi, with a suitable function \mathbf f. An equation of this form can be transformed into an integral equation \frac d \int_V \xi ~ dV = -\oint_ \mathbf f(\xi) \cdot \boldsymbol \nu ~ dS using the divergence theorem. The integral equation states that the change rate of the integral of the quantity \xi over an arbitrary control volume V is given by the flux \mathbf f(\xi) through the boundary of the control volume, with \boldsymbol \nu being the outer surface normal through the boundary. \xi is neither produced nor consumed inside of V and is hence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
