146,992 research outputs found
Three-points interfacial quadrature for geometrical source terms on nonuniform grids
International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which -error estimates, , are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)
Reservoir formation in shallow granular flows through a contraction
We consider flow of dry granular matter down an inclined chute with a localized contraction. Measurements and analysis show that changes in particle volume fraction are important, especially across granular bores. For fixed upstream conditions and depending on the nozzle width of the contraction, we observe either small oblique jumps, a reservoir with a steady jump, or a reservoir with an upstream traveling bore. Shallow layer theory extended to include porosity changes qualitatively predicts these regimes. Implications for volcanic debris \ud
ows are discussed
Near-best quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains
In this paper, we present new quasi-interpolating spline schemes defined on
3D bounded domains, based on trivariate quartic box splines on type-6
tetrahedral partitions and with approximation order four. Such methods can be
used for the reconstruction of gridded volume data. More precisely, we propose
near-best quasi-interpolants, i.e. with coefficient functionals obtained by
imposing the exactness of the quasi-interpolants on the space of polynomials of
total degree three and minimizing an upper bound for their infinity norm. In
case of bounded domains the main problem consists in the construction of the
coefficient functionals associated with boundary generators (i.e. generators
with supports not completely inside the domain), so that the functionals
involve data points inside or on the boundary of the domain.
We give norm and error estimates and we present some numerical tests,
illustrating the approximation properties of the proposed quasi-interpolants,
and comparisons with other known spline methods. Some applications with real
world volume data are also provided.Comment: In the new version of the paper, we have done some minor revisions
with respect to the previous version, CALCOLO, Published online: 10 October
201
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