Numerical Analysis of Space–Time Finite Element Formulations for Miscible Displacements

A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates.     

Let’s not forget about non-land-falling cyclones: tendencies and impacts in Puerto Rico

The paper introduces a three-dimensional numerical technique to assess typhoon hazards in China coastal regions based on a series of full-set numerical meteorology simulations. The boundary and initial conditions of the simulations are provided by adding pseudorandom fluctuations, which represent the localized, short-term meteorological variations, to synoptic fields, which show the large-scale, long-term meteorological patterns. A series of bogus typhoons are inserted into the initial field to provide the “seeds” from which the artificial typhoons could grow. The initial positions and intensities of the bogus typhoons are drawn from the random variables whose statistics agree with those derived from historical typhoon track data. In the present study, 1503 full-set meteorology simulations of artificial typhoons are conducted. The extreme wind speeds versus return periods calculated from the simulation results are compared to not only the specifications in the load code, but also the results from the previous studies. It is found that the extreme wind speeds in the Pearl-River Delta are, contradicting to the common expectation, higher than at the mainland side of the Taiwan Strait, which imply that the typhoons hitting Guangdong are, on average, more intense than those influencing Fujian. Given the possibility to improve the three-dimensional meteorology model in the future, the simulation technique proposed in the present study provides a novel direction to assess the meteorological hazards, including threads posted by typhoons.

     

Symmetric horseshoe periodic orbits in the general planar three-body problem

We present some families of horseshoe periodic orbits in the general planar three-body problem for the case of two equal masses. The considered system is a symmetric version of the one formed by Saturn, Janus and Epimetheus. We use a mass ratio equal to 35×10⁻⁵, corresponding to 10⁵ times the Saturn-Janus mass parameter of the restricted case; for this mass ratio the satellites have a significantly bigger influence on the planet than in the classical Saturn, Janus and Epimetheus system. To obtain periodic orbits, we search those horseshoe orbits passing through two reversible configurations. A particular kind of periodic orbits where the minor bodies follow the same path is discussed.     

Doubly-symmetric horseshoe orbits in the general planar three-body problem

We present some results about the continuation of doubly-symmetric horseshoe orbits in the general planar three-body problem. This is done by means of solving a boundary value problem with one free parameter which is the quotient of the masses of two bodies μ ₃=m ₃/m ₁, keeping constant μ ₂=m ₂/m ₁ (m ₁ represents the mass of a big planet whereas m ₂ and m ₃ of minor bodies). For the numerical continuation of the horseshoe orbits we have considered m ₂/m ₁=3.5×10^?4, and the variation of μ ₃ from 3.5×10^?4 to 9.7×10^?5 or vice versa, depending on the orbit selected as “seed”. We discuss some issues related to the periodicity and symmetry of the orbits. We study the stability of some of them taking the limit μ ₃→0. The numerical continuation was done using the software AUTO.     

Numerical Analysis of Space–Time Finite Element Formulations for Miscible Displacements

A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates.