arXiv subjects

Abimael F. D. Loula

Publications and source records attributed to Abimael F. D. Loula.

6 recordsLinked to original sources

arXiv2025

On Finite Element Methods for Heterogeneous Elliptic Problems

Dealing with variational formulations of second order elliptic problems with discontinuous coefficients, we recall a single field minimization problem of an extended functional presented by Bevilacqua et al (1974), which we associate with the basic idea supporting discontinuous Galerkin finite element methods. We review residual based stabilized mixed methods applied to Darcy flow in homogeneous porous media and extend them to heterogeneous media with an interface of discontinuity. For smooth interfaces, the proposed formulations preserve the continuity of the flux and exactly imposes the constraint between the tangent components of Darcy velocity on the interface. Convergence studies for a heterogeneous and anisotropic porous medium confirm the same rates of convergence predicted for homogeneous problem with smooth solutions.

math.NA↗

arXiv2025

Unconditionally Stable Mixed Finite Element Methods for Darcy Flow

Unconditionally stable finite element methods for Darcy flow are derived by adding least-squares residual forms of the governing equations to the classical mixed formulations. The proposed methods are free of mesh dependent stabilization parameters and allow the use of the classical continuous Lagrangian finite element spaces of any order for the velocity and the potential. Stability, convergence and error estimates are derived and numerical experiments are presented to demonstrate the flexibility of the proposed finite element formulations and to confirm the predicted rates of convergence.

math.NA↗

arXiv2025

Stabilized velocity post-processings for Darcy flow in heterogeneous porous media

Stable and accurate finite element methods are presented for Darcy flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor. Accurate velocity fields are computed through global or local post-processing formulations that use previous approximations of the hydraulic potential. Stability is provided by combining Galerkin and Least Squares (GLS) residuals of the governing equations with an additional stabilization on the interface that incorporates the discontinuity on the tangential component of the velocity field in a strong sense. Numerical analysis is outlined and numerical results are presented to illustrate the good performance of the proposed methods. Convergence studies for a heterogeneous and anisotropic porous medium confirm the same orders of convergence predicted for homogeneous problem with smooth solutions, for both global and local post-processings.

math.NA↗

arXiv2004

Collisionless wave dissipation in a D-shaped tokamak with Soloviev type equilibrium

Parallel permittivity elements are derived for radio frequency waves in an axisymmetric D-shaped tokamak with Soloviev type equilibrium under arbitrary aspect ratio, arbitrary elongation and moderate triangularity. The drift-kinetic equation is solved separately for untrapped (passing or circulating) and three groups of trapped particles as a boundary-value problem, accounting for the transit-time and bounce resonances, respectively. It is shown that the new two groups of trapped particles can appear only in tokamaks with large elongation and large central beta. Our dielectric characteristics can be applied for both the large and low aspect ratio tokamaks with circular, elliptic and D-shaped magnetic surfaces to study the wave propagation and wave dissipation by electron Landau damping during the plasma heating and current drive generation. The dissipated wave power is expressed by the summation of terms including the imaginary parts of both the diagonal and non-diagonal elements of the parallel permittivity.

physics.plasm-ph↗

arXiv2004

Electron Landau damping in a laboratory dipole magnetic field plasma

Transverse and longitudinal dielectric permittivity elements are derived for radio frequency waves in a laboratory dipole magnetic field plasma (LDMFP) accounting for the finite ring current radius. The main feature of LDMFP is the fact that, in contrast to planetary magnetospheric plasmas, the untrapped (circulating) particles can exist/circulate (together with the trapped particles) along the equilibrium magnetic field lines. To estimate the wave power absorbed in LDMFP the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. The wave absorption is expressed by the summation of contributions of all harmonics of the perturbed electric field and both the diagonal and non-diagonal dielectric permittivity elements. In this paper, we analyze numerically the separate contributions of the trapped and untrapped electrons to the imaginary part of the longitudinal permittivity elements in LDMFP with an equilibrium (Maxwellian) distribution functions of plasma particles in velocity space. This information is necessary to estimate the collisionless wave dissipation by electron Landau damping. The computations are carried out in a wide range of the wave frequencies.

physics.plasm-ph↗

arXiv2004

Influence of bounce resonance effects on the cyclotron wave instabilities in dipole magnetospheric plasmas with anisotropic temperature

In this paper, we derive the dispersion equations for field-aligned cyclotron waves in an axisymmetric dipole magnetospheric plasmas with both the bi-Maxwellian and bi-Lorentzian distribution functions. To evaluate the contribution of trapped particles to the transverse current density components the Vlasov equation is solved using a standard method of switching to new variables associated with conservation integrals; new time-like variable is introduced (instead of the geomagnetic latitude angle) to describe the bounce-motion of trapped particles along the geomagnetic field; the perturbed electric field and current density components are Fourier-decomposed over the length of the geomagnetic field lines. As a result, the transverse permittivity elements are expressed by summation of bounce-resonant terms including the double integration in velocity space, the resonant denominators, and the corresponding phase coefficients. Due to geomagnetic field nonuniformity, the wave-particle resonance conditions in magnetospheric plasmas are entirely different from ones in the straight magnetic field; the all spectrum of the electric field is present in the given current density harmonic; the left- and right-hand polarized waves are coupled. To have some analogy with the linear theory of cyclotron waves in the straight magnetic field, we assume that the n-th harmonic of the electric field gives the main contribution to the n-th harmonic of the current density, and the connection of the left- and right-hand polarized waves is small. In this case, the dispersion equations for cyclotron waves have the simplest form and are suitable to analyze the instabilities of both the electron- and ion-cyclotron waves accounting for the bounce resonance effects.

physics.plasm-ph↗