We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool is the construction of an area-decreasing map to the Jacobi torus, streamlining and generalizing the construction of the first author in collaboration with D. Burago. It turns out that one can successfully combine thi...

Numerical grid adaptation method for finite volume methods is presented. Unlike traditional adaptation methods, the method presented moves vertices of control volumes instead of their centers. To perform such movement, geometric information is used generated for the control volume method. The presented method can be used for twoand three-dimensional grids of arbitrary structure. Possibilities a...

Article history: Received 17 May 2013 Received in revised form 3 April 2014 Accepted 7 April 2014 Available online 15 April 2014

We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic n + 1-orbifold.

Water impact phenomenon of general bow section is a critical event for planning hulls. In this paper, the water entry of several arbitrary bow sections is investigated. For this purpose, arbitrary bow shapes which are introduced by Lewis form approximation are considered. In order to obtain pressure distribution and free surface profile, volume of fluid (VOF) method coupled with finite volume m...

This paper deals with the upwind finite volume method applied to the linear advection equation on a bounded domain and with natural boundary conditions. We introduce what we call the geometric corrector which is a sequence associated with every finite volume mesh in Rnd and every non vanishing vector a of Rnd. First we show that if the continuous solution is regular enough and if the norm of th...

We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h1/4 in L∞([0, T ], Lloc(R d)) .