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- W1206200310 abstract "This chapter elaborates finite volume method (FVM) and conservative discretization with an introduction to finite element method (FEM). The FVM is the name given to the technique by which the integral formulation of the conservation laws is discretized directly in the physical space. Once a grid has been generated, the FVM consists in associating a local finite volume, also called control volume, to each mesh point and applying the integral conservation law to this local volume. This is a first major distinction from the finite difference approach, where the discretized space is considered as a set of points, while in the FVM the discretized space is formed by a set of small cells, one cell being associated to one mesh point. Flow equations are the expression of a conservation law. The essential property has to be satisfied by the numerical discretization of the flux contributions in order for a scheme to be conservative. Numerical experiments and comparisons consistently show that nonconservative formulations are generally less accurate than conservative ones, particularly in the presence of strong gradients. The FEM definition of interpolation functions is also analyzed." @default.
- W1206200310 created "2016-06-24" @default.
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- W1206200310 date "2007-01-01" @default.
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- W1206200310 title "Finite Volume Method and Conservative Discretization with an Introduction to Finite Element Method" @default.
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- W1206200310 doi "https://doi.org/10.1016/b978-075066594-0/50046-1" @default.
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