Contributions to the Mathematical Technology Transfer with Finite Volume Methods

Abstract

At the early 1980s, the research group in Mathematical Engineering, mat+i, started working on finite volume methods for the simulation of environmental issues concerning Galician rias (Spain). The focus was on the study of hyperbolic balance laws due to the presence of source terms related to the bathymetry. A correct treatment of these terms, an upwind discretization, was presented in [2, 7, 22]. The transfer of this knowledge has motivated the registration of the software Iber (http://www.iberaula.es). Latterly, under different research problems, we have been working on the development of a numerical algorithm for the resolution of Euler and Navier–Stokes equations. A hybrid projection finite volume/finite element method is employed making use of unstructured staggered grids (see [3, 9]). To attain second order of accuracy ADER methodology is employed [10]. On the other hand, with numerical simulation of gas transportation networks in view, a first-order well balanced finite volume scheme for the solution of a model, for the flow of a multicomponent gas in a pipe on non-flat topography, is introduced. The mathematical model consists of Euler equations, with source terms, coupled with the mass conservation equations of species. We propose a segregated scheme in which Euler and species equations are solved separately [6].