Search results

The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection.

The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations.

The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements.

The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible.

The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media.

The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.

The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.

The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.

Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.

The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.

The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.

The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

Two new mixed finite element schemes for discretizing current continuity equations are presented. Together with the good features of the already‐known mixed scheme (current preservation and good approximation of sharp shapes), they provide M‐matrices, even when a zero order term is present in the equations.

The purpose of this paper is to present a new formulation for taking into account the convective term due to an imposed velocity field in the induction equation in a code based on Whitney elements called DOLMEN. Different Whitney forms are used to approximate the dependent variables. The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. DOLMEN is developed to investigate the dynamo action in non-axisymmetric domains like the impeller driven flow of the von Kármán Sodium (VKS) experiment. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field.

Different Whitney forms are used to approximate the dependent variables. The vector potential is discretized using first-order edge elements of the first family. The velocity is approximated by using the first-order Raviart-Thomas elements. The time stepping is done by using the Crank-Nicolson scheme.

The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field.

The findings offer a basis to a scenario for the VKS dynamo.

We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin plate theory and a mixed‐interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16‐node quadrilateral elements and our 7 and 12‐node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.

A mixed variational formulation of the free boundary problem involved in the analysis of reverse‐biased semiconductor devices is put forward. This can be profitably used in the investigation of the field distribution near the junction and at the surface of devices. A peculiar feature of the new formulation is that the electric field is assumed as a variable in the solution, together with the potential, thus enabling the electric field to be determined directly and accurately. The numerical algorithm associated with the method turns out to be quite simple and can be easily and readily implemented even on a desktop computer.

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

We present an abstract mathematical and numerical analysis for Drift‐Diffusion equation of heterojunction semiconductor devices with Fermi‐Dirac statistic. For the approximation, a mixed finite element method is considered. This can be profitably used in the investigation of the current through the device structure. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities jn and jp for electrons and holes, are taken as unknowns, together with the potential φ and quas‐Fermi levels φn and φp. This enably D, jn and jp to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteriori error estimates are also presented. A nonlinear implicit scheme with local time steps is used. This algorithm appears to be efficient and gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.

The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements.

Discusses a systematic strategy for the realization of arbitrary order hierarchic H(curl)‐conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as lowest order Nédélec, higher‐order edge‐based, face‐based (only in 3D) and element‐based ones.

Our new shape functions provide not only the global complete sequence property but also local complete sequence properties for each edge‐, face‐, and element‐block. This local property allows an arbitrary variable choice of the polynomial degree for each edge, face, and element. A second advantage of this construction is that simple block‐diagonal preconditioning gets efficient. Our high order shape functions contain gradient shape functions explicitly. In the case of a magnetostatic boundary value problem, the gradient basis functions can be skipped, which reduces the problem size, and improves the condition number.

Successfully applies the new high order elements for a 3D magnetostatic boundary value problem, and a Maxwell eigenvalue problem showing severe edge and corner singularities.

This contribution discusses a continuum model of large discrete networks in planar domains. For this model, the Kirchhoff law, boundary conditions and capacity constraints lead in a system optimisation approach to a infinite dimensional constrained optimisation problem and to “mixed” variational inequalities. Mixed finite element methods can be formulated for these variational inequalities such that computable discretizations of the continuum problem are obtained.