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Publications (12)
This work continues our study of a dynamic model for the process of contact between a linear elastic rod and a reactive obstacle, using the new damped normal compliance (DNC) contact condition, M. Shillor and I. Pahuja (2024) and G. Sosa Jones and M. Shillor (2024). The condition explicitly takes into account the energy dissipation during the proce...
This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first-order time extrapolation, which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well posed, and obtain a priori error estimates. Our numerical results val...
We present a compatible space–time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to identify the sharp interface between the two fluids. The incompressible two-fluid equations are discretized by an...
This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well-posed, and obtain a priori error estimates. Our numerical results vali...
We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness and to obtain a priori error estimates, our space-time HDG fo...
Two second-order finite difference methods in a staggered mesh to solve the static diffusion equation are proposed in this article. These methods were compared with a standard finite difference method and with two numerical schemes naturally established in staggered grids: mimetic method and conservative method. Also, mimetic discretization is pres...
The aim of this work is to solve the two-dimensional convection diffusion equation on non-rectangular grids formed only by quadrilaterals honoring the internal structures of a reservoir (preferential flow channels, faults, areas of high permeability contrast, changes in sediment type, etc.), taking into account different physical configurations of...
Traditionally, the finite difference method has been applied to solve numerically the PDE governing fluid flow on a rectangular mesh in porous media for its easy implementation and computational efficiency.
The aim of this work is to solve the two-dimensional convection diffusion equation on a non-rectangular grids formed only by quadrilaterals hon...
Traditionally, the finite difference method has been applied to solve numerically the PDE governing fluid flow on a rectangular mesh in porous media for its easy implementation and computational efficiency.
The aim of this work is to solve the two-dimensional convection diffusion equation on a non-rectangular grids formed only by quadrilaterals hon...
La simulación numérica de yacimientos petrolíferos es una herramienta indispensable y ampliamente aceptada en la industria petrolera, debido a que mediante modelos matemáticos y numéricos es posible simular el flujo de los fluidos presentes en el yacimiento, permitiendo así diseñar estrategias de explotación eficientes. En una serie de trabajos pre...
