Nonlinear multigrid for fully-implicit and high-order accurate simluation of multiphase flow in porous media

High-order accurate and fully implicit finite difference schemes are widely used for multiphase flow problems. In this paper we analyze the use of point Gauss-Seidel relaxation in a nonlinear multigrid method for the resulting nonlinear systems of equations. Point Gauss-Seidel is unstable for calculating the steady-state of high-order accurate discretizations of the 2D convection equation. Here we present a local Fourier mode smoothing analysis for the transient case. It appears that point Gauss-Seidel is a good smoother provided that the time step is taken small enough. Numerical computations show good multigrid convergence rates for typical test problems

A simple cell-centered multigrid method for 33D interface problems

AbstractA multigrid algorithm is presented for cell-centered discretizations of interface problems. Instead of constructing the coarse grid operators by means of the Galerkin approximation, the coarse grid operators are obtained by discretization on the coarse grids. The advantage of this approach is that we obtain M-matrices on all grids, and that the sparsity pattern of the fine grid matrix is retained on all grids. Moreover, the coarse grid operators are very easy to construct. Numerical results of several test problems are presented

Nonlinear multigrid for fully-implicit and high-order accurate simulation of multiphase flow in porous media

High-order accurate and fully implicit finite difference schemes are widely used for multiphase flow problems. In this paper we analyze the use of point Gauss-Seidel relaxation in a nonlinear multigrid method for the resulting nonlinear systems of equations. Point Gauss-Seidel is unstable for calculating the steady-state of high-order accurate discretizations of the 2D convection equation. Here we present a local Fourier mode smoothing analysis for the transient case. It appears that point Gauss-Seidel is a good smoother provided that the time step is taken small enough. Numerical computations show good multigrid convergence rates for typical test problems

Multigrid methods for high-order accurate fully implicit simulation of flowin porous media

High-order accurate finite difference schemes are widely used to avoid the detrimental effects of numerical diffusion in first-order upwind schemes. If an implicit time integration scheme is employed, we have to solve large systems of nonlinear equations in every time step. The price paid for the high-order accuracy is a larger discretization stencil. In this paper we consider the use of multigrid methods for the iterative solutions of these systems of equations. We consider both a direct multigrid approach and a defect correction approach, in which only first-order accurate discretized problems have to be solved. In both approaches we do not need to store the Jacobean matrix. Therefore the memory requirements are moderate, and very fine grid simulations are feasible on a standard workstation

Analysis of DNAPL infiltration in a medium with a low-permeable lens

In this paper we study the infiltration of DNAPL in a porous medium containing a single low-permeable lens. Our aim is to determine whether DNAPL infiltrates into the lens, or not. A key role is played by the capillary pressure: DNAPL cannot infiltrate into the lens unless the capillary pressure exceeds the entry pressure of the lens. In the model this is reflected by an interface condition for the capillary pressure. Both a homogeneous medium and a medium with a lens are analyzed. For the homogeneous configuration we derive an estimate of the stationary DNAPL plume width as a function of depth, and an asymptotic solution for small saturations. For the configuration with a lens we assume that the lens is much larger than the width of the unperturbed DNAPL plume in the homogeneous medium. We show that DNAPL infiltrates into the lens if a critical inflow rate is exceeded. This inflow rate is determined explicitly. A numerical algorithm is presented in which the extended capillary pressure condition is incorporated. Good agreement is found between the numerical and analytical results

Long-term study of extreme giant pulses from PSR B0950+08 with AARTFAAC

We report on the detection of extreme giant pulses (GPs) from one of the oldest-known pulsars, the highly variable PSR B0950+08, with the Amsterdam-ASTRON Radio Transient Facility And Analysis Centre (AARTFAAC), a parallel transient detection instrument operating as a subsystem of the LOw Frequency ARray (LOFAR). During processing of our Northern Hemisphere survey for low-frequency radio transients, a sample of 275 pulses with fluences ranging from 42 to 177 kJy ms were detected in one-second snapshot images. The brightest pulses are an order of magnitude brighter than those previously reported at 42 and 74 MHz, on par with the levels observed in a previous long-term study at 103 MHz. Both their rate and fluence distribution differ between and within the various studies done to date. The GP rate is highly variable, from 0 to 30 per hour, with only two three-hour observations accounting for nearly half of the pulses detected in the 96 h surveyed. It does not vary significantly within a few-hour observation, but can vary strongly one from day to the next. The spectra appear strongly and variably structured, with emission sometimes confined to a single 195.3 kHz subband, and the pulse spectra changing on a timescale of order 10 min.Comment: 10 pages, 9 figures, 1 table. Submitted to MNRA