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In this work has been proposed a numerical scheme with the aim of simulate the coalescence process between water drops immersed in a continuous phase (n-heptane). This numerical scheme is based in the Finite Volume method and two different…
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
Volume estimation in large indoor spaces is an important challenge in robotic inspection of industrial warehouses. We propose an approach for volume estimation for autonomous systems using visual features for indoor localization and surface…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for $SU(N)$ gauge…
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have…
We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error…
Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather…
We present an efficient numerical scheme based on Monte Carlo integration to approximate statistical solutions of the incompressible Euler equations. The scheme is based on finite volume methods, which provide a more flexible framework than…
A finite-volume method for the one-dimensional shallow-water equations including topographic source terms is presented. Exploiting an original idea by Leroux, the system of partial-differential equations is completed by a trivial equation…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
Numerical model forecasts of near-surface temperatures are prone to error. This is because terrain can exert a strong influence on temperature that is not captured in numerical weather models due to spatial resolution limitations. To…
After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…
In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty…
The climate is a forced and dissipative nonlinear system featuring non-trivial dynamics of a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…