120,702 research outputs found
Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity
© 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach
Bivariate hierarchical Hermite spline quasi--interpolation
Spline quasi-interpolation (QI) is a general and powerful approach for the
construction of low cost and accurate approximations of a given function. In
order to provide an efficient adaptive approximation scheme in the bivariate
setting, we consider quasi-interpolation in hierarchical spline spaces. In
particular, we study and experiment the features of the hierarchical extension
of the tensor-product formulation of the Hermite BS quasi-interpolation scheme.
The convergence properties of this hierarchical operator, suitably defined in
terms of truncated hierarchical B-spline bases, are analyzed. A selection of
numerical examples is presented to compare the performances of the hierarchical
and tensor-product versions of the scheme
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