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NUEN-430 Lecture 4

Unknowns are point values of the solution finite

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Unformatted text preview: o derivatives. Unknowns are point values of the solution. Finite volume schemes are a subclass of finite difference schemes that are applied to balance or conservation equations. Most finite difference approximations used in nuclear engineering are of this type. The basic idea behind these schemes is to ensure that the discrete approximation makes a statement of conservation on each mesh cell in analogy with the fact that the analytic equation makes a statement of conservation over each differential volume. Finite element methods are based upon the use of finite-dimensional function spaces to approximate the solution to the differential equations. This sounds sophisticated, but an element of a function space is just a function, ̃( ) , that is defined in terms of a set of Basis functions, { ( ⃗ )} and an associated set of coefficients, { } . Thus, ̃( ) ∑ ( ⃗) A finite-element basis set is always related to a mesh structure, and the expansion coefficients often take the form of discrete val...
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