The outer scale of solar-wind turbulence from GALILEO coronal-sounding data

Radio sounding experiments on of the solar plasma were carried out by the GALILEO spacecraft using S-band (2295 MHz) signals in 1995–1996 a period of minimum solar activity. Equatorial regions at heliocentric distances of 7–80 solar radii were studied. The frequency of the received signal was detected by three ground stations. By carrying out continuous observations of unprecedented duration and processing the data using spectral and correlation methods, we have obtained reliable information on large-scale inhomogeneities of the solar-wind density for the first time. The outer turbulence scale increases with heliocentric distance, the dependence being close to linear. We estimate the outer turbulence scale and analyze its dependence on distance from the Sun and local plasma parameters for a model in which the outer scale is formed due to competition between the linear amplification of Alfven waves in the irregular, moving solar-wind plasma and the nonlinear transfer of turbulent energy to higher frequencies. A comparison of predictions for various specific cases of this model with the observational data suggests that the main nonlinear processes responsible for the formation of the inertial range of the spectrum on the investigated scales are three-wave decay processes involving Alfven and magnetoacoustic waves.     

Variational inequalities for modeling flow in heterogeneous porous media with entry pressure

One of the driving forces in porous media flow is the capillary pressure. In standard models, it is given depending on the saturation. However, recent experiments have shown disagreement between measurements and numerical solutions using such simple models. Hence, we consider in this paper two extensions to standard capillary pressure relationships. Firstly, to correct the nonphysical behavior, we use a recently established saturation-dependent retardation term. Secondly, in the case of heterogeneous porous media, we apply a model with a capillary threshold pressure that controls the penetration process. Mathematically, we rewrite this model as inequality constraint at the interfaces, which allows discontinuities in the saturation and pressure. For the standard model, often finite-volume schemes resulting in a nonlinear system for the saturation are applied. To handle the enhanced model at the interfaces correctly, we apply a mortar discretization method on nonmatching meshes. Introducing the flux as a new variable allows us to solve the inequality constraint efficiently. This method can be applied to both the standard and the enhanced capillary model. As nonlinear solver, we use an active set strategy combined with a Newton method. Several numerical examples demonstrate the efficiency and flexibility of the new algorithm in 2D and 3D and show the influence of the retardation term. This work was supported in part by IRTG NUPUS.     

Dynamic capillary effects in heterogeneous porous media

In standard multi-phase flow models on porous media, a capillary pressure saturation relationship developed under static conditions is assumed. Recent experiments have shown that this static relationship cannot explain dynamic effects as seen for example in outflow experiments. In this paper, we use a static capillary pressure model and a dynamic capillary pressure model based on the concept of Hassanizadeh and Gray and examine the behavior with respect to material interfaces. We introduce a new numerical scheme for the one-dimensional case using a Lagrange multiplier approach and develop a suitable interface condition. The behavior at the interface is discussed and verified by various numerical simulations.     

Coronal velocity measurements with Ulysses: multi-link correlation studies during two superior conjunctions

A well-known method for studying the solar wind very close to the Sun (heliocentric distances: 4 to 40 solar radii) is by radio sounding between a spacecraft at superior conjunction and the Earth. The Ulysses Solar Corona Experiment was performed at the spacecraft's two solar conjunctions in summer 1991 and winter 1995, during which dual-frequency ranging and Doppler observations were conducted globally on a nearly continuous basis at the NASA Deep Space Network and other ground stations. The dual-frequency Doppler measurements were used to determine coronal plasma velocities by a cross-correlation analysis during those occasions when tracking data were recorded simultaneously at two well-separated ground stations. A filtering technique was developed to suppress noise and enhance the 2-station correlations, a procedure particularly effective at small solar offsets. From the electron content measurements during the two solar conjunctions it was found that regions of higher electron density tend to occur when the two-station correlations yield slower outward flow velocities.     

A two-scale operator-splitting method for two-phase flow in porous media

In this paper, we develop a two-scale operator-splitting method for the classical two-phase flow model, which handles advective and diffusive processes on different grids. The aim is to reduce computational complexity without loss of accuracy by using the numerical flexibility of operator-splitting techniques. To enhance the stability and the robustness with regards to sharp fronts, an additional slope limiter is introduced as a local post-processing step. For simplicity of notation, we provide the method in one dimension first and then generalize it to higher dimensions. Numerical examples illustrate the effect of the slope-limiting step and show the performance and flexibility of the proposed two-scale method.     

Streamline method for resolving sharp fronts for complex two-phase flow in porous media

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided.